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+\index{#1}% +\index{defun!#1}% +\index{#1!defun}} +\newcommand{\defmacro}[1]{% e.g. \defmacro{functionname} +\subsection{defmacro {#1}}% +\label{#1}% +\index{#1}% +\index{defmacro!#1}% +\index{#1!defmacro}} +\newcommand{\defvar}[1]{% e.g. \defvar{varname} +\subsection{defvar \${#1}}% +\label{#1}% +\index{#1}% +\index{defvar!#1}% +\index{#1!defvar}} +\newcommand{\defstruct}[1]{% e.g. \defstruct{varname} +\subsection{defstruct \${#1}}% +\label{#1}% +\index{#1}% +\index{defstruct!#1}% +\index{#1!defstruct}} +\newcommand{\defdollar}[1]{% e.g. \defdollar{functionname} +\subsection{defvar \${#1}}% +\label{#1}% +\index{\${#1}}% +\index{defvar!\${#1}}% +\index{\${#1}!defvar}} +\newcommand{\defconstant}[1]{% e.g. \defconst{varname} +\subsection{defconstant \${#1}}% +\label{#1}% +\index{#1}% +\index{defconstant!#1}% +\index{#1!defconstant}} +\newcommand{\defdollarconstant}[1]{% e.g. \defdollarconstant{functionname} +\subsection{defconstant \${#1}}% +\label{#1}% +\index{\${#1}}% +\index{defconstant!\${#1}}% +\index{\${#1}!defconstant}} +\newcommand{\pagehead}[2]{% e.g. \pagehead{name}{abb} +\dest{#1}% +\dest{#2}% +\subsection{#1 (#2)}% +\label{#1}% +\label{#2}% +\index{{#1}}% +\index{{#2}}} +\newcommand{\pagetitle}[3]{% e.g. \pagetitle{page}{file.ht}{title} +\subsection{#3}% +\label{#1}% +\index{pages!#1!#2}% +\index{#1!#2!pages}% +\index{#2!pages!#1}} +\newcommand{\calls}[2]{% e.g. \calls{thisfunc}{thatfunc} +[#2 p\pageref{#2}]\\% +\index{#2!{calledby #1}}% +\index{#1!{calls #2}}}% +\newcommand{\seebook}[3]{% e.g. \seebook{thisfunc}{thatfunc}{5} +[#1 #2 (vol#3)]\\% +\index{#2[#3]!{called by #1}}% +\index{#1!{calls #2[#3]}}}% +\newcommand{\throws}[2]{% e.g. \throws{thisfunc}{tagvar} +[#2 p\pageref{#2}]\\% +\index{throws!#1}% +\index{#1!throws}} +\newcommand{\catches}[2]{% e.g. \catches{thisfunc}{tagvar} +[#2 p\pageref{#2}]\\% +\index{catches!#1}% +\index{#1!catches}} +\newcommand{\uses}[2]{% e.g. \uses{thisfunc}{specialvar} +[#2 p\pageref{#2}]\\% +\index{#2!{usedby #1}}% +\index{#1!{uses #2}}}% +\newcommand{\callsdollar}[2]{% e.g. \callsdollar{thisfunc}{thatfunc} +[\$#2 p\pageref{#2}]\\% +\index{\$#2!{calledby \$#1}}% +\index{#1!{calls \$#2}}} +\newcommand{\usesdollar}[2]{% e.g. \usesdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{usedby #1}}% +\index{#1!{uses \${#2}}}} +\newcommand{\defsdollar}[2]{% e.g. \defsdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{local def #1}}% +\index{#1!{local def \${#2}}}} +\newcommand{\refsdollar}[2]{% e.g. \refsdollar{thisfunc}{specialvar} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{local ref #1}}% +\index{#1!{local ref \${#2}}}} +\newcommand{\usesstruct}[2]{% e.g. \usesstruct{thisfunc}{structname} +[\$#2 p\pageref{#2}]\\% +\index{\${#2}!{usedby #1}}% +\index{#1!{uses \${#2}}}} +\newcommand{\tpdhere}[1]{% e.g. \tpdhere{Some note} +{\bf TPDHERE: #1}% +\index{TPDHERE!{#1}}} +\newcommand{\pagepic}[3]{% e.g. \pagepic{pathandfile}{abb}{scale} +\includegraphics[scale=#3]{#1}\\% +\index{images!#2}} +\newcommand{\refto}[1]{% e.g. \refto{name} +(p\pageref{#1}) #1} +\newcommand{\pageto}[2]{% e.g. \pageto{linkstring}{pagename} +\ \\${\bf\Rightarrow{}}${``#1''} (#2) \ref{#2} on page~\pageref{#2}} +\newcommand{\pagefrom}[2]{% e.g. \pagefrom{linkstring}{pagename} +\ \\${\bf\Leftarrow{}}${``#1''} (#2) \ref{#2} on page~\pageref{#2}} +\newcommand{\fnref}[1]{% e.g. \fnref{functionname} +``#1'' (\ref{#1} p~\pageref{#1})} +\newcommand{\varref}[1]{% e.g. \varref{variablename} +``#1'' (\ref{#1} p~\pageref{#1})} +\newcommand{\cross}[2]{% e.g. \pagefrom{cat}{funcname} +\index{#1!#2}% +\index{#2!#1}% +#2} +\newcommand{\lanb}{{\tt [}} +\newcommand{\ranb}{{\tt ]}} +\newcommand{\vertline}{$|$} +% axiom.sty -- LaTeX support for Axiom +% DON'T edit this file! Use src/doc/axiom.sty.pamphlet instead. +\usepackage{verbatim} + +\chardef\atcode=\catcode`\@ +\catcode`\@=11 +\renewcommand{\verbatim@font}{\ttfamily\small} +\catcode`\@=\atcode + +\newenvironment{chunk}[1]{% we need the chunkname as an argument +{\ }\newline\noindent% make sure we are in column 1 +%{\small $\backslash{}$begin\{chunk\}\{{\bf #1}\}}% alternate begin mark +\hbox{\hskip 2.0cm}{\bf --- #1 ---}% mark the beginning +\verbatim}% say exactly what we see +{\endverbatim% process \end{chunk} +\par{}% we add a newline +\noindent{}% start in column 1 +\hbox{\hskip 2.0cm}{\bf ----------}% mark the end +%$\backslash{}$end\{chunk\}% alternate end mark (commented) +\par% and a newline +\normalsize\noindent}% and return to the document + +\providecommand{\getchunk}[1]{% +\noindent% +{\small $\backslash{}$begin\{chunk\}\{{\bf #1}\}}}% mark the reference + +{\obeyspaces\AtBeginDocument{\global\let =\ }} % from texbook, p 381 +\def\nwopt@nomargintag{\let\nwmargintag=\@gobble} +\def\nwopt@margintag{% + \def\nwmargintag##1{\leavevmode\llap{##1\kern\nwmarginglue\kern\codemargin}}} +\def\nwopt@margintag{% + \def\nwmargintag##1{\leavevmode\kern-\codemargin\nwthemargintag{##1}\kern\codemargin}} +\def\nwthemargintag#1{\llap{#1\kern\nwmarginglue}} +\nwopt@margintag +\newdimen\nwmarginglue +\nwmarginglue=0.3in +\def\nwtagstyle{\footnotesize\Rm} +% make \hsize in code sufficient for 88 columns +\setbox0=\hbox{\tt m} +\newdimen\codehsize +\codehsize=91\wd0 % 88 columns wasn't enough; I don't know why +\newdimen\codemargin +\codemargin=0pt +\newdimen\nwdefspace +\nwdefspace=\codehsize +% need to use \textwidth in {\LaTeX} to handle styles with +% non-standard margins (David Bruce). Don't know why we sometimes +% wanted \hsize. 27 August 1997. +%% \advance\nwdefspace by -\hsize\relax +\ifx\textwidth\undefined + \advance\nwdefspace by -\hsize\relax +\else + \advance\nwdefspace by -\textwidth\relax +\fi +\chardef\other=12 +\def\setupcode{% + \chardef\\=`\\ + \chardef\{=`\{ + \chardef\}=`\} + \catcode`\$=\other + \catcode`\&=\other + \catcode`\#=\other + \catcode`\%=\other + \catcode`\~=\other + \catcode`\_=\other + \catcode`\^=\other + \catcode`\"=\other % fixes problem with german.sty + \obeyspaces\Tt +} +\let\nwlbrace=\{ +\let\nwrbrace=\} +\def\nwendquote{\relax\ifhmode\spacefactor=1000 \fi} +{\catcode`\^^M=\active % make CR an active character + \gdef\newlines{\catcode`\^^M=\active % make CR an active character + \def^^M{\par\startline}}% + \gdef\eatline#1^^M{\relax}% +} + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +%%% DON'T \gdef^^M{\par\startline}}% in case ^^M appears in a \write +\def\startline{\noindent\hskip\parindent\ignorespaces} +\def\nwnewline{\ifvmode\else\hfil\break\leavevmode\hbox{}\fi} +\def\setupmodname{% + \catcode`\$=3 + \catcode`\&=4 + \catcode`\#=6 + \catcode`\%=14 + \catcode`\~=13 + \catcode`\_=8 + \catcode`\^=7 + \catcode`\ =10 + \catcode`\^^M=5 + \let\{\nwlbrace + \let\}\nwrbrace + % bad news --- don't know what catcode to give " + \Rm} +\def\LA{\begingroup\maybehbox\bgroup\setupmodname\It$\langle$} +\def\RA{\/$\rangle$\egroup\endgroup} +\def\code{\leavevmode\begingroup\setupcode\newlines} +\def\edoc{\endgroup} +\let\maybehbox\relax +\newbox\equivbox +\setbox\equivbox=\hbox{$\equiv$} +\newbox\plusequivbox +\setbox\plusequivbox=\hbox{$\mathord{+}\mathord{\equiv}$} +% \moddef can't have an argument because there might be \code...\edoc +\def\moddef{\leavevmode\kern-\codemargin\LA} +\def\endmoddef{\RA\ifmmode\equiv\else\unhcopy\equivbox\fi + \nobreak\hfill\nobreak} +\def\plusendmoddef{\RA\ifmmode\mathord{+}\mathord{\equiv}\else\unhcopy\plusequivbox\fi + \nobreak\hfill\nobreak} +\def\chunklist{% +\errhelp{I changed \chunklist to \nowebchunks. +I'll try to avoid such incompatible changes in the future.}% +\errmessage{Use \string\nowebchunks\space instead of \string\chunklist}} +\def\nowebchunks{\message{}} +\def\nowebindex{\message{}} +% here is support for the new-style (capitalized) font-changing commands +% thanks to Dave Love +\ifx\documentstyle\undefined + \let\Rm=\rm \let\It=\it \let\Tt=\tt % plain +\else\ifx\selectfont\undefined + \let\Rm=\rm \let\It=\it \let\Tt=\tt % LaTeX OFSS +\else % LaTeX NFSS + \def\Rm{\reset@font\rm} + \def\It{\reset@font\it} + \def\Tt{\reset@font\tt} + \def\Bf{\reset@font\bf} +\fi\fi +\ifx\reset@font\undefined \let\reset@font=\relax \fi +\def\noweboptions#1{% + \def\@nwoptionlist{#1}% + \@for\@nwoption:=\@nwoptionlist\do{% + \@ifundefined{nwopt@\@nwoption}{% + \@latexerr{There is no such noweb option as '\@nwoption'}\@eha}{% + \csname nwopt@\@nwoption\endcsname}}} +\codemargin=10pt +\advance\codehsize by \codemargin % make room for indentation of code +\advance\nwdefspace by \codemargin % and fix adjustment for def/use +\def\setcodemargin#1{% + \advance\codehsize by -\codemargin % make room for indentation of code + \advance\nwdefspace by -\codemargin % and fix adjustment for def/use + \codemargin=#1 + \advance\codehsize by \codemargin % make room for indentation of code + \advance\nwdefspace by \codemargin % and fix adjustment for + % def/use +} +\def\nwopt@shift{% + \dimen@=-0.8in + \if@twoside % Values for two-sided printing: + \advance\evensidemargin by \dimen@ + \else % Values for one-sided printing: + \advance\evensidemargin by \dimen@ + \advance\oddsidemargin by \dimen@ + \fi +% \advance \marginparwidth -\dimen@ +} +\let\nwopt@noshift\@empty +\def\nwbegincode#1{% + \begingroup + \topsep \nwcodetopsep + \@beginparpenalty \@highpenalty + \@endparpenalty -\@highpenalty + \@begincode } +\def\nwendcode{\endtrivlist \endgroup \filbreak} % keeps code on 1 page + +\newenvironment{webcode}{% + \@begincode +}{% + \endtrivlist} +\def\@begincode{% + \trivlist \item[]% + \leftskip\@totalleftmargin \advance\leftskip\codemargin + \rightskip\hsize \advance\rightskip -\codehsize + \parskip\z@ \parindent\z@ \parfillskip\@flushglue + \linewidth\codehsize + \@@par + \def\par{\leavevmode\null \@@par \penalty\nwcodepenalty}% + \obeylines + \@noligs \ifx\verbatim@nolig@list\undefined\else + \let\do=\nw@makeother \verbatim@nolig@list \do@noligs\` + \fi + \setupcode \frenchspacing \@vobeyspaces + \nowebsize \setupcode + \let\maybehbox\mbox } + \newskip\nwcodetopsep \nwcodetopsep = 3pt plus 1.2pt minus 1pt + \let\nowebsize=\normalsize + \def\nwopt@tinycode{\let\nowebsize=\tiny} + \def\nwopt@footnotesizecode{\let\nowebsize=\footnotesize} + \def\nwopt@scriptsizecode{\let\nowebsize=\scriptsize} + \def\nwopt@smallcode{\let\nowebsize=\small} + \def\nwopt@normalsizecode{\let\nowebsize=\normalsize} + \def\nwopt@largecode{\let\nowebsize=\large} + \def\nwopt@Largecode{\let\nowebsize=\Large} + \def\nwopt@LARGEcode{\let\nowebsize=\LARGE} + \def\nwopt@hugecode{\let\nowebsize=\huge} + \def\nwopt@Hugecode{\let\nowebsize=\Huge} +\newcount\nwcodepenalty \nwcodepenalty=\@highpenalty +\def\nw@makeother#1{\catcode`#1=12 } +\def\nwbegindocs#1{\ifvmode\noindent\fi} +\let\nwenddocs=\relax +\let\nwdocspar=\filbreak +\raggedbottom +\def\code{\leavevmode\begingroup\setupcode\@vobeyspaces\obeylines} +\let\edoc=\endgroup +\newdimen\@original@textwidth +\def\ps@noweb{% + \@original@textwidth=\textwidth + \let\@mkboth\@gobbletwo + \def\@oddfoot{}\def\@evenfoot{}% No feet. + \if@twoside % If two-sided printing. + \def\@evenhead{\hbox to \@original@textwidth{% + \Rm \thepage\qquad{\Tt\leftmark}\hfil\today}}% Left heading. + \def\@oddhead{\hbox to \@original@textwidth{% + \Rm \today\hfil{\Tt\leftmark}\qquad\thepage}}% Right heading. + \else % If one-sided printing. + \def\@oddhead{\hbox to \@original@textwidth{% + \Rm \today\hfil{\Tt\leftmark}\qquad\thepage}}% Right heading. + \let\@evenhead\@oddhead + \fi + \let\chaptermark\@gobble + \let\sectionmark\@gobble + \let\subsectionmark\@gobble + \let\subsubsectionmark\@gobble + \let\paragraphmark\@gobble + \let\subparagraphmark\@gobble + \def\nwfilename{\begingroup\let\do\@makeother\dospecials + \catcode`\{=1 \catcode`\}=2 \nw@filename} + \def\nw@filename##1{\endgroup\markboth{##1}{##1}\let\nw@filename=\nw@laterfilename}% +} +\def\nw@laterfilename#1{\endgroup\clearpage \markboth{#1}{#1}} +\let\nwfilename=\@gobble +\def\nwcodecomment#1{\@@par\penalty\nwcodepenalty + \if@firstnwcodecomment + \vskip\nwcodecommentsep\penalty\nwcodepenalty\@firstnwcodecommentfalse + \fi% + \hspace{-\codemargin}{% + \rightskip=0pt plus1in + \interlinepenalty\nwcodepenalty + \let\\\relax\footnotesize\Rm #1\@@par\penalty\nwcodepenalty}} +\def\@nwalsodefined#1{\nwcodecomment{\@nwlangdepdef\ \nwpageprep\ \@pagesl{#1}.}} +\def\@nwused#1{\nwcodecomment{\@nwlangdepcud\ \nwpageprep\ \@pagesl{#1}.}} +\def\@nwnotused#1{\nwcodecomment{\@nwlangdeprtc.}} +\def\nwoutput#1{\nwcodecomment{\@nwlangdepcwf\ {\Tt \@stripstar#1*\stripped}.}} +\def\@stripstar#1*#2\stripped{#1} +\providecommand{\nwprevdefptr}[1]{% + \mbox{$\mathord{\triangleleft}\,\mathord{\mbox{\subpageref{#1}}}$}} +\providecommand{\nwnextdefptr}[1]{% + \mbox{$\mathord{\mbox{\subpageref{#1}}}\,\mathord{\triangleright}$}} + +\providecommand{\@nwprevnextdefs}[2]{% + {\nwtagstyle + \ifx\relax#1\else ~~\nwprevdefptr{#1}\fi + \ifx\relax#2\else ~~\nwnextdefptr{#2}\fi}} +\providecommand{\@nwusesondefline}[1]{{\nwtagstyle~~(\@pagenumsl{#1})}} +\providecommand{\@nwstartdeflinemarkup}{\nobreak\hskip 1.5em plus 1fill\nobreak} +\providecommand{\@nwenddeflinemarkup}{\nobreak\hskip \nwdefspace minus\nwdefspace\nobreak} +\def\nwopt@longxref{% + \let\nwalsodefined\@nwalsodefined + \let\nwused\@nwused + \let\nwnotused\@nwnotused + \let\nwprevnextdefs\@gobbletwo + \let\nwusesondefline\@gobble + \let\nwstartdeflinemarkup\relax + \let\nwenddeflinemarkup\relax +} +\def\nwopt@shortxref{% + \let\nwalsodefined\@gobble + \let\nwused\@gobble + \let\nwnotused\@gobble + \let\nwprevnextdefs\@nwprevnextdefs + \let\nwusesondefline\@nwusesondefline + \let\nwstartdeflinemarkup\@nwstartdeflinemarkup + \let\nwenddeflinemarkup\@nwenddeflinemarkup +} +\def\nwopt@noxref{% + \let\nwalsodefined\@gobble + \let\nwused\@gobble + \let\nwnotused\@gobble + \let\nwprevnextdefs\@gobbletwo + \let\nwusesondefline\@gobble + \let\nwstartdeflinemarkup\relax + \let\nwenddeflinemarkup\relax +} +\nwopt@shortxref % to hell with backward compatibility! +\newskip\nwcodecommentsep \nwcodecommentsep=3pt plus 1pt minus 1pt +\newif\if@firstnwcodecomment\@firstnwcodecommenttrue +\newcount\@nwlopage\newcount\@nwhipage % range lo..hi-1 +\newcount\@nwlosub % subpage of lo +\newcount\@nwhisub % subpage of hi +\def\@nwfirstpage#1#2#3{% subpage page xref-tag + \@nwlopage=#2 \@nwlosub=#1 + \def\@nwloxreftag{#3}% + \advance\@nwpagecount by \@ne + \@nwhipage=\@nwlopage\advance\@nwhipage by \@ne } +\def\@nwnextpage#1#2#3{% subpage page xref-tag + \ifnum\@nwhipage=#2 + \advance\@nwhipage by \@ne + \advance\@nwpagecount by \@ne + \@nwhisub=#1 + \def\@nwhixreftag{#3}\else + \ifnum#2<\@nwlopage \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\@nwfirstpage{#1}{#2}{#3}\else + \ifnum#2>\@nwhipage \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\@nwfirstpage{#1}{#2}{#3}\else + \@nwlosub=0 \@nwhisub=0 + \fi\fi\fi + } +\newcount\@nwpagetemp +\newcount\@nwpagecount +\def\@nwfirstpagel#1{% label + \@ifundefined{r@#1}{\@warning{Reference `#1' on page \thepage \space undefined}% + \nwix@cons\nw@pages{\\{\bf ??}}}{% + \edef\@tempa{\noexpand\@nwfirstpage\subpagepair{#1}{#1}}\@tempa}} +\def\@nwnextpagel#1{% label + \@ifundefined{r@#1}{\@warning{Reference `#1' on page \thepage \space undefined}% + \nwix@cons\nw@pages{\\{\bf ??}}}{% + \edef\@tempa{\noexpand\@nwnextpage\subpagepair{#1}{#1}}\@tempa}} +\def\@pagesl#1{% list of labels + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\@nwfirstpagel{##1}\let\\=\@nwnextpagel}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\def\\##1{\@nwhyperpagenum##1}% + \ifnum\@nwpagecount=1 \nwpageword \else \nwpagesword\fi~\commafy{\nw@pages}} +\def\@nwhyperpagenum#1#2{\nwhyperreference{#2}{#1}} + +\def\@pagenumsl#1{% list of labels -- doesn't include word `pages', commas, or `and' + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\@nwfirstpagel{##1}\let\\=\@nwnextpagel}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa% + \def\\##1{\@nwhyperpagenum##1\let\\=\@nwpagenumslrest}\nw@pages} +\def\@nwpagenumslrest#1{~\@nwhyperpagenum#1} +\def\subpages#1{% list of {{subpage}{page}} + \gdef\nw@pages{}\@nwpagecount=0 + \def\\##1{\edef\@tempa{\noexpand\@nwfirstpage##1{}}\@tempa + \def\\####1{\edef\@tempa{\noexpand\@nwnextpage####1}\@tempa}}#1% + \advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa\def\\##1{\@firstoftwo##1}% + \ifnum\@nwpagecount=1 \nwpageword \else \nwpagesword\fi~\commafy{\nw@pages}} +\def\@nwaddrange{\advance\@nwhipage by \m@ne + \ifnum\@nwhipage=\@nwlopage + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}}% + \else + \count@=\@nwhipage \advance\count@ by \m@ne + \ifnum\count@=\@nwlopage % consecutive pages + \edef\@tempa{\noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwlosub}{\number\@nwlopage}}% + {\@nwloxreftag}}% + \noexpand\noexpand\noexpand\\% + {{\nwthepagenum{\number\@nwhisub}{\number\@nwhipage}} + {\@nwhixreftag}}}% + \else \ifnum\@nwlopage<110 \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 \multiply\count@ by 100 + \ifnum\count@=\@nwlopage \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}\else + \count@=\@nwlopage \divide\count@ by 100 + \@nwpagetemp=\@nwhipage \divide\@nwpagetemp by 100 + \ifnum\count@=\@nwpagetemp % lo--least 2 digits of hi + \multiply\@nwpagetemp by 100 + \advance \@nwhipage by -\@nwpagetemp + \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \else \edef\@tempa{\noexpand\noexpand\noexpand\\{{\number\@nwlopage--\number\@nwhipage}{}}}% + \fi + \fi + \fi% + \fi + \fi% + \edef\@tempa{\noexpand\nwix@cons\noexpand\nw@pages{\@tempa}}\@tempa} +\def\nwpageword{\@nwlangdepchk} % chunk, was page +\def\nwpagesword{\@nwlangdepchks} % chunk, was page +\def\nwpageprep{\@nwlangdepin} % in, was on +\providecommand\nw@genericref[2]{% what to do, name of ref + \expandafter\nw@g@nericref\csname r@#2\endcsname#1{#2}} +\providecommand\nw@g@nericref[3]{% control sequence, what to do, name + \ifx#1\relax + \ref{#3}% trigger the standard `undefined ref' mechanisms + \else + \expandafter#2#1.\\% + \fi} +\def\nw@selectone#1#2#3\\{#1} +\def\nw@selecttwo#1#2#3\\{#2} +\def\nw@selectonetwo#1#2#3\\{{#1}{#2}} +\providecommand{\subpageref}[1]{% + \nwhyperreference{#1}{\nw@genericref\@subpageref{#1}}} +\def\@subpageref#1#2#3\\{% + \@ifundefined{2on#2}{#2}{\nwthepagenum{#1}{#2}}} +\providecommand{\subpagepair}[1]{% % produces {subpage}{page} + \@ifundefined{r@#1}% + {{0}{0}}% + {\nw@genericref\@subpagepair{#1}}} +\def\@subpagepair#1#2#3\\{% + \@ifundefined{2on#2}{{0}{#2}}{{#1}{#2}}} +\providecommand{\sublabel}[1]{% + \@bsphack + \nwblindhyperanchor{#1}% + \if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newsublabel{#1}{{}{\thepage}}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand{\nosublabel}[1]{% + \@bsphack\if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newlabel{#1}{{0}{\thepage}}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand\newsublabel{% + \nw@settrailers + \global\let\newsublabel\@newsublabel + \@newsublabel} +\providecommand{\@newsublabel}[2]{% + \edef\this@page{\@cdr#2\@nil}% + \ifx\this@page\last@page\else + \sub@page=\z@ + \fi + \edef\last@page{\this@page} + \advance\sub@page by \@ne + \ifnum\sub@page=\tw@ + \global\@namedef{2on\this@page}{}% + \fi + \pendingsublabel{#1}% + \edef\@tempa##1{\noexpand\newlabel{##1}% + {{\number\sub@page}{\this@page}\nw@labeltrailers}}% + \pending@sublabels + \def\pending@sublabels{}} +\providecommand\nw@settrailers{% -- won't work on first run + \@ifpackageloaded{nameref}% + {\gdef\nw@labeltrailers{{}{}{}}}% + {\gdef\nw@labeltrailers{}}} +\renewcommand\nw@settrailers{% + \@ifundefined{@secondoffive}% + {\gdef\nw@labeltrailers{}}% + {\gdef\nw@labeltrailers{{}{}{}}}} +\providecommand{\nextchunklabel}[1]{% + \nwblindhyperanchor{#1}% % looks slightly bogus --- nr + \@bsphack\if@filesw {\let\thepage\relax + \edef\@tempa{\write\@auxout{\string\pendingsublabel{#1}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\providecommand\pendingsublabel[1]{% + \def\@tempa{\noexpand\@tempa}% + \edef\pending@sublabels{\noexpand\@tempa{#1}\pending@sublabels}} +\def\pending@sublabels{} +\def\last@page{\relax} +\newcount\sub@page +\def\@alphasubpagenum#1#2{#2\ifnum#1=0 \else\@alph{#1}\fi} +\def\@nosubpagenum#1#2{#2} +\def\@numsubpagenum#1#2{#2\ifnum#1=0 \else.\@arabic{#1}\fi} +\def\nwopt@nosubpage{\let\nwthepagenum=\@nosubpagenum\nwopt@nomargintag} +\def\nwopt@numsubpage{\let\nwthepagenum=\@numsubpagenum} +\def\nwopt@alphasubpage{\let\nwthepagenum=\@alphasubpagenum} +\nwopt@alphasubpage +\newcount\@nwalph@n +\let\@nwalph@d\@tempcnta +\let\@nwalph@bound\@tempcntb +\def\@nwlongalph#1{{% + \@nwalph@n=#1\advance\@nwalph@n by-1 + \@nwalph@bound=26 + \loop\ifnum\@nwalph@n<\@nwalph@bound\else + \advance\@nwalph@n by -\@nwalph@bound + \multiply\@nwalph@bound by 26 + \repeat + \loop\ifnum\@nwalph@bound>1 + \divide\@nwalph@bound by 26 + \@nwalph@d=\@nwalph@n\divide\@nwalph@d by \@nwalph@bound + % d := d * bound ; n -:= d; d := d / bound --- saves a temporary + \multiply\@nwalph@d by \@nwalph@bound + \advance\@nwalph@n by -\@nwalph@d + \divide\@nwalph@d by \@nwalph@bound + \advance\@nwalph@d by 1 \@alph{\@nwalph@d}% + \repeat +}} +\newcount\nw@chunkcount +\nw@chunkcount=\@ne +\providecommand{\weblabel}[1]{% + \@bsphack + \nwblindhyperanchor{#1}% + \if@filesw {\let\thepage\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string + \newsublabel{#1}{{}{\number\nw@chunkcount}}}}% + \expandafter}\@tempa + \global\advance\nw@chunkcount by \@ne + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\def\nwopt@webnumbering{% + \let\sublabel=\weblabel + \def\nwpageword{chunk}\def\nwpagesword{chunks}% + \def\nwpageprep{in}} +% \nwindexdefn{printable name}{identifying label}{label of chunk} +% \nwindexuse{printable name}{identifying label}{label of chunk} + +\def\nwindexdefn#1#2#3{\@auxix{\protect\nwixd}{#2}{#3}} +\def\nwindexuse#1#2#3{\@auxix{\protect\nwixu}{#2}{#3}} + +\def\@auxix#1#2#3{% {marker}{id label}{subpage label} + \@bsphack\if@filesw {\let\nwixd\relax\let\nwixu\relax + \def\protect{\noexpand\noexpand\noexpand}% + \edef\@tempa{\write\@auxout{\string\nwixadd{#1}{#2}{#3}}}% + \expandafter}\@tempa + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +% \nwixadd{marker}{idlabel}{subpage label} +\def\nwixadd#1#2#3{% + \@ifundefined{nwixl@#2}% + {\global\@namedef{nwixl@#2}{#1{#3}}}% + {\expandafter\nwix@cons\csname nwixl@#2\endcsname{#1{#3}}}} +\def\@nwsubscriptident#1#2{\mbox{$\mbox{#1}_{\mathrm{\subpageref{#2}}}$}} +\def\@nwnosubscriptident#1#2{#1} +\def\@nwhyperident#1#2{\leavevmode\nwhyperreference{#2}{#1}} +\def\nwopt@subscriptidents{% + \let\nwlinkedidentq\@nwsubscriptident + \let\nwlinkedidentc\@nwsubscriptident +} +\def\nwopt@nosubscriptidents{% + \let\nwlinkedidentq\@nwnosubscriptident + \let\nwlinkedidentc\@nwnosubscriptident +} +\def\nwopt@hyperidents{% + \let\nwlinkedidentq\@nwhyperident + \let\nwlinkedidentc\@nwhyperident +} +\def\nwopt@nohyperidents{% + \let\nwlinkedidentq\@nwnosubscriptident + \let\nwlinkedidentc\@nwnosubscriptident +} +\def\nwopt@subscriptquotedidents{% + \let\nwlinkedidentq\@nwsubscriptident +} +\def\nwopt@nosubscriptquotedidents{% + \let\nwlinkedidentq\@nwnosubscriptident +} +\def\nwopt@hyperquotedidents{% + \let\nwlinkedidentq\@nwhyperident +} +\def\nwopt@nohyperquotedidents{% + \let\nwlinkedidentq\@nwnosubscriptident +} +\nwopt@hyperidents +\newcount\@commacount +\def\commafy#1{% + {\nwix@listcount{#1}\@commacount=\nwix@counter + \let\@comma@each=\\% + \ifcase\@commacount\let\\=\@comma@each\or\let\\=\@comma@each\or + \def\\{\def\\{ \@nwlangdepand\ \@comma@each}\@comma@each}\else + \def\\{\def\\{, % + \advance\@commacount by \m@ne + \ifnum\@commacount=1 \@nwlangdepand~\fi\@comma@each}\@comma@each}\fi + #1}} +\def\nwix@cons#1#2{% {list}{\marker{element}} + {\toks0=\expandafter{#1}\def\@tempa{#2}\toks2=\expandafter{\@tempa}% + \xdef#1{\the\toks0 \the\toks2 }}} +\def\nwix@uses#1{% {label} + \def\nwixu{\\}\let\nwixd\@gobble\@nameuse{nwixl@#1}} +\def\nwix@defs#1{% {label} + \def\nwixd{\\}\let\nwixu\@gobble\@nameuse{nwixl@#1}} +\newcount\nwix@counter +\def\nwix@listcount#1{% {list with \\} + {\count@=0 + \def\\##1{\advance\count@ by \@ne }% + #1\global\nwix@counter=\count@ }} +\def\nwix@usecount#1{\nwix@listcount{\nwix@uses{#1}}} +\def\nwix@defcount#1{\nwix@listcount{\nwix@defs{#1}}} +\def\nwix@id@defs#1{% index pair + {{\Tt \@car#1\@nil}% + \def\\##1{~\subpageref{##1}}\nwix@defs{\@cdr#1\@nil}}} +\def\nwidentuses#1{% list of index pairs + \nwcodecomment{\@nwlangdepuss\ \let\\=\nwix@id@defs\commafy{#1}.}} +\def\nwix@totaluses#1{% list of index pairs + {\count@=0 + \def\\##1{\nwix@usecount{\@cdr##1\@nil}\advance\count@ by\nwix@counter}% + #1\global\nwix@counter\count@ }} +\def\nwix@id@uses#1#2{% {ident}{label} + \nwix@usecount{#2}\ifnum\nwix@counter>0 + {\advance\leftskip by \codemargin + \nwcodecomment{{\Tt #1}, \@nwlangdepusd\ \nwpageprep\ \@pagesl{\nwix@uses{#2}}.}}% + \else + \ifnw@hideunuseddefs\else + {\advance\leftskip by \codemargin \nwcodecomment{{\Tt #1}, \@nwlangdepnvu.}}% + \fi + \fi} +\def\nwidentdefs#1{% list of index pairs + \ifnw@hideunuseddefs\nwix@totaluses{#1}\else\nwix@listcount{#1}\fi + \ifnum\nwix@counter>0 + \nwcodecomment{\@nwlangdepdfs:}% + {\def\\##1{\nwix@id@uses ##1}#1}% + \fi} +\newif\ifnw@hideunuseddefs\nw@hideunuseddefsfalse +\def\nwopt@hideunuseddefs{\nw@hideunuseddefstrue} +\def\nwopt@noidentxref{% + \let\nwidentdefs\@gobble + \let\nwidentuses\@gobble} +\def\nw@underlinedefs{% {list with \nwixd, \nwixu} + \let\\=\relax\def\nw@comma{, } + \def\nwixd##1{\\\underline{\subpageref{##1}}\let\\\nw@comma}% + \def\nwixu##1{\\\subpageref{##1}\let\\\nw@comma}} + +\def\nw@indexline#1#2{% + {\indent {\Tt #1}: \nw@underlinedefs\@nameuse{nwixl@#2}\par}} + +\newenvironment{thenowebindex}{\parindent=-10pt \parskip=\z@ + \advance\leftskip by 10pt + \advance\rightskip by 0pt plus1in\par\@afterindenttrue + \def\\##1{\nw@indexline##1}}{} +\def\nowebindex{% + \@ifundefined{nwixs@i}% + {\@warning{The \string\nowebindex\space is empty}}% + {\begin{thenowebindex}\@nameuse{nwixs@i}\end{thenowebindex}}} +\def\nowebindex@external{% + {\let\nwixadds@c=\@gobble + \def\nwixadds@i##1{\nw@indexline##1}% + \def\nwixaddsx##1##2{\@nameuse{nwixadds@##1}{##2}}% + \begin{thenowebindex}\@input{\jobname.nwi}\end{thenowebindex}}} +\def\nwixlogsorted#1#2{% list data + \@bsphack\if@filesw + \toks0={#2}\immediate\write\@auxout{\string\nwixadds{#1}{\the\toks0}} + \if@nobreak \ifvmode\nobreak\fi\fi\fi\@esphack} +\def\nwixadds#1#2{% + \@ifundefined{nwixs@#1}% + {\global\@namedef{nwixs@#1}{\\{#2}}}% + {\expandafter\nwix@cons\csname nwixs@#1\endcsname{\\{#2}}}} +\let\nwixaddsx=\@gobbletwo +\def\nwopt@externalindex{% + \ifx\nwixadds\@gobbletwo % already called + \else + \let\nwixaddsx=\nwixadds \let\nwixadds=\@gobbletwo + \let\nowebindex=\nowebindex@external + \let\nowebchunks=\nowebchunks@external + \fi} +\def\nowebchunks{% + \@ifundefined{nwixs@c}% + {\@warning{The are no \string\nowebchunks}}% + {\begin{thenowebchunks}\@nameuse{nwixs@c}\end{thenowebchunks}}} +\def\nowebchunks@external{% + {\let\nwixadds@i=\@gobble + \def\nwixadds@c##1{\nw@onechunk##1}% + \def\nwixaddsx##1##2{\@nameuse{nwixadds@##1}{##2}}% + \begin{thenowebchunks}\@input{\jobname.nwi}\end{thenowebchunks}}} + \@namedef{r@nw@notdef}{{0}{(\@nwlangdepnvd)}} +\def\nw@chunkunderlinedefs{% {list of labels with \nwixd, \nwixu} + \let\\=\relax\def\nw@comma{, } + \def\nwixd##1{\\\underline{\subpageref{##1}}\let\\\nw@comma}% + \def\nwixu##1{\\\subpageref{##1}\let\\\nw@comma}} +\def\nw@onechunk#1#2#3{% {name}{label of first definition}{list with \nwixd, \nwixu} + \@ifundefined{r@#2}{}{% + \indent\LA #1~{\nwtagstyle\subpageref{#2}}\RA + \if@nwlongchunks{~\nw@chunkunderlinedefs#3}\fi\par}} +\newenvironment{thenowebchunks}{\vskip3pt + \parskip=\z@\parindent=-10pt \advance\leftskip by 10pt + \advance\rightskip by 0pt plus10pt \@afterindenttrue + \def\\##1{\nw@onechunk##1}}{} +\newif\if@nwlongchunks +\@nwlongchunksfalse +\let\nwopt@longchunks\@nwlongchunkstrue +\providecommand\@nw@hyper@ref{\hyperreference} % naras +\providecommand\@nw@hyper@anc{\blindhyperanchor} % naras +\providecommand\@nw@hyperref@ref[2]{\hyperlink{noweb.#1}{#2}} % nr +\providecommand\@nw@hyperref@anc[1]{\hypertarget{noweb.#1}{\relax}} % nr +%%\renewcommand\@nw@hyperref@ref[2]{{#2}} % nr +%%\renewcommand\@nw@hyperref@anc[1]{} % nr +\providecommand\nwhyperreference{% + \@ifundefined{hyperlink} + {\@ifundefined{hyperreference} + {\global\let\nwhyperreference\@gobble} + {\global\let\nwhyperreference\@nw@hyper@ref}} + {\global\let\nwhyperreference\@nw@hyperref@ref}% + \nwhyperreference +} + +\providecommand\nwblindhyperanchor{% + \@ifundefined{hyperlink} + {\@ifundefined{hyperreference} + {\global\let\nwblindhyperanchor\@gobble} + {\global\let\nwblindhyperanchor\@nw@hyper@anc}} + {\global\let\nwblindhyperanchor\@nw@hyperref@anc}% + \nwblindhyperanchor +} +\providecommand\nwanchorto{% + \begingroup\let\do\@makeother\dospecials + \catcode`\{=1 \catcode`\}=2 \nw@anchorto} +\providecommand\nw@anchorto[1]{\endgroup\def\nw@next{#1}\nw@anchortofin} +\providecommand\nw@anchortofin[1]{#1\footnote{See URL \texttt{\nw@next}.}} +\let\nwanchorname\@gobble +\newif\ifhtml +\htmlfalse +\let\nwixident=\relax +\def\nwbackslash{\char92} +\def\nwlbrace{\char123} +\def\nwrbrace{\char125} +\def\nwopt@english{% + \def\@nwlangdepdef{This definition is continued}% + \def\@nwlangdepcud{This code is used}% + \def\@nwlangdeprtc{Root chunk (not used in this document)}% + \def\@nwlangdepcwf{This code is written to file}% + \def\@nwlangdepchk{chunk}% + \def\@nwlangdepchks{chunks}% + \def\@nwlangdepin{in}% + \def\@nwlangdepand{and}% + \def\@nwlangdepuss{Uses}% + \def\@nwlangdepusd{used}% + \def\@nwlangdepnvu{never used}% + \def\@nwlangdepdfs{Defines}% + \def\@nwlangdepnvd{never defined}% +} +\let\nwopt@american\nwopt@english +\def\nwopt@portuges{% + \def\@nwlangdepdef{Defini\c{c}\~ao continuada em}% + % This definition is continued + \def\@nwlangdepcud{C\'odigo usado em}% + % This code is used + \def\@nwlangdeprtc{Fragmento de topo (sem uso no documento)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Este c\'odigo foi escrito no ficheiro}% + % This code is written to file + \def\@nwlangdepchk{fragmento}% + % chunk + \def\@nwlangdepchks{fragmentos}% + % chunks + \def\@nwlangdepin{no(s)}% + % in + \def\@nwlangdepand{e}% + % and + \def\@nwlangdepuss{Usa}% + % Uses + \def\@nwlangdepusd{usado}% + % used + \def\@nwlangdepnvu{nunca usado}% + % never used + \def\@nwlangdepdfs{Define}% + % Defines + \def\@nwlangdepnvd{nunca definido}% + % never defined +} +\def\nwopt@frenchb{% + \def\@nwlangdepdef{Cette d\'efinition suit}% + % This definition is continued + \def\@nwlangdepcud{Ce code est employ\'e}% + % This code is used + \def\@nwlangdeprtc{Morceau racine (pas employ\'e dans ce document)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Ce code est \'ecrit aux fichier}% + % This code is written to file + \def\@nwlangdepchk{le morceau}% + % chunk + \def\@nwlangdepchks{les morceaux}% + % chunks + \def\@nwlangdepin{dans}% + % in + \def\@nwlangdepand{et}% + % and + \def\@nwlangdepuss{Il emploie}% + % Uses + \def\@nwlangdepusd{employ\'{e}}% + % used + \def\@nwlangdepnvu{jamais employ\'{e}}% + % never used + \def\@nwlangdepdfs{Il d\'{e}fine}% + % Defines + % Cannot use the accent here: \def\@nwlangdepnvd{jamais d\'{e}fini}% + \def\@nwlangdepnvd{jamais defini}% + % never defined +} +\let\nwopt@french\nwopt@frenchb +\def\nwopt@german{% + \def\@nwlangdepdef{Diese Definition wird fortgesetzt}% + % This definition is continued + \def\@nwlangdepcud{Dieser Code wird benutzt}% + % This code is used + \def\@nwlangdeprtc{Hauptteil (nicht in diesem Dokument benutzt)}% + % Root chunk (not used in this document) + \def\@nwlangdepcwf{Dieser Code schreibt man zum File}% + % This code is written to file + \def\@nwlangdepchk{Teil}% + % chunk + \def\@nwlangdepchks{Teils}% + % chunks + \def\@nwlangdepin{im}% + % in + \def\@nwlangdepand{und}% + % and + \def\@nwlangdepuss{Benutztt}% + % Uses + \def\@nwlangdepusd{benutzt}% + % used + \def\@nwlangdepnvu{nicht benutzt}% + % never used + \def\@nwlangdepdfs{Definiert}% + % Defines + \def\@nwlangdepnvd{nicht definiert}% + % never defined +} +\let\nwopt@ngerman\nwopt@german +\ifx\languagename\undefined % default is English + \noweboptions{english} +\else + \@ifundefined{nwopt@\languagename} + {\noweboptions{english}} + {\expandafter\noweboptions\expandafter{\languagename}} +\fi +% Final names for the system and its components were in doubt so +% Language is used throughout the book to specify what the system is named. +\providecommand{\Language}{AXIOM} + +% HyperName was used to specify the name of the browser +\providecommand{\HyperName}{HyperDoc} + +% This is nothing more than inline math mode in Tex but has additional +% meaning within the browser. +\providecommand{\spad}[1]{${#1}$} + +% This is a way to say 8th, 100th, etc. +% We use providecommand so it doesn't clash with amsmath package +\providecommand{\eth}[1]{{#1}-th} + +% add the binom function for combfunc +\providecommand{\binom}[2]{\left(\begin{array}{c}#1\\#2\end{array}\right)} + +% spadcommands are the actual text that you type at the axiom prompt +\providecommand{\spadcommand}[1]% +{\begin{flushleft}{\tt #1}\end{flushleft}\vskip .1cm } + +% spadgraph are the actual text that you type at the axiom prompt for draw +\providecommand{\spadgraph}[1]% +{\begin{flushleft}{\tt #1}\end{flushleft}\vskip .1cm } + +%% spadsig gives the standard -> notation for signatures +\providecommand{\spadsig}[2]{{\sf #1 $\rightarrow$ #2}} + +% returnType is the type signature returned by the axiom interpreter +\providecommand{\returnType}[1]% +{\begin{flushright}{\tt #1}\end{flushright}\vskip .1cm} + +%%% Axiom commands are set off in a special boxed area. +%%% This is used to draw a line around that boxed area. +\providecommand\boxed[2]{% +\begin{center} +\begin{tabular}{|c|} +\hline +\begin{minipage}{#1} +\normalsize +{#2} +\end{minipage}\\ +\hline +\end{tabular} +\end{center}} + +% The book begins with some introductory material that is not really +% listed as a chapter. This creates a header similar to \chapter. +\providecommand{\pseudoChapter}[1]% +{\vskip .5in \noindent {\Huge{\bf #1}}\vskip .5in} + +% The book begins with some introductory material that is not really +% listed as a section. This creates a header similar to \section. +\providecommand{\pseudoSection}[1]% +{\vskip .25in \noindent {\large{\bf #1}}\vskip .25in} + +% spadofFrom records the operation in the index and the domain in the index +\providecommand{\spadopFrom}[2]{\index{library!operations!#1 @\begingroup \string\tt{} #1 \endgroup}\index{#2}``{\tt #1}''} + +% spadfunFrom records the function name and domain in the index +\providecommand{\spadfunFrom}[2]{{\bf #1}\index{#1 @\begingroup \string\bf{} #1 \endgroup}\index{#2}} + +% These are special markers within the text for Hypertex keywords +% They have no particular meaning in the book form. +\providecommand{\spadfun}[1]{{\it #1}} +\providecommand{\spadgloss}[1]{{\it #1}} +\providecommand{\spadkey}[1]{\index{#1 @\begingroup \string\tt{} #1 \endgroup}} + +% spadtype records the domain in the index +\providecommand{\spadtype}[1]{{\bf #1}\index{#1 @\begingroup \string\bf{} #1 \endgroup}} + +% This is used to create a caption on an included image +\providecommand{\simpleCaption}[1]{\def\thefigure{\@arabic\c@figure}\caption{#1}} + +% This is the name of the ``glossy'' pages in the physical book. +\providecommand{\Gallery}{\Language{} Images} + +% spadofFrom records the operation in the index and the domain in the index +\providecommand{\spadopFrom}[2]{\index{library!operations!#1 @\begingroup \string\tt{} #1 \endgroup}\index{#2}``{\tt #1}''} + +%% typeset e.g. and i.e. +\providecommand{\eg}{\emph{e.g.}} +\providecommand{\ie}{\emph{i.e.}} + +%% Typeset in-line code. +\providecommand{\Code}[1]{\texttt{#1}} + +%% Typeset a file name +\providecommand{\File}[1]{{\itshape{#1}}} + +%% Typeset a tool name, e.g. Axiom +\providecommand{\Tool}[1]{{\bfseries\sffamily{#1}}} +\providecommand\AXIOM{\vskip\parindent\indent{\bf AXIOM}\vskip\parindent\noindent\ignorespaces} +\providecommand\maxima{\vskip\parindent\noindent{\bf MAXIMA}\vskip\parindent\noindent\ignorespaces} +\providecommand\yacas{\vskip\parindent\noindent{\bf YACAS}\vskip\parindent\noindent\ignorespaces} diff --git a/src/axiom-website/CATS/index.html b/src/axiom-website/CATS/index.html index 60667b0..d2ad926 100644 --- a/src/axiom-website/CATS/index.html +++ b/src/axiom-website/CATS/index.html @@ -266,5 +266,140 @@ satisfies the original ordinary differential equation.

source pdf
+
+This portion of the CATS suite involves Albert Rich's Integration Suite. +They have been rewritten using Axiom syntax. +

+ algebraic000-099 + source + pdf
+ algebraic100-199 + source + pdf
+ algebraic200-299 + source + pdf
+ algebraic300-399 + source + pdf
+ algebraic400-461 + source + pdf
+
+ error000-078 + source + pdf
+
+ exponential + source + pdf
+
+ hyper000-099 + source + pdf
+ hyper100-199 + source + pdf
+ hyper100-199 + source + pdf
+ hyper200-299 + source + pdf
+ hyper300-399 + source + pdf
+ hyper400-499 + source + pdf
+ hyper500-599 + source + pdf
+ hyper600-699 + source + pdf
+ hyper700-799 + source + pdf
+ hyper800-899 + source + pdf
+ hyper900-999 + source + pdf
+ hyper1000-1098 + source + pdf
+
+ intfunc000-032 + source + pdf
+
+ invhyper000-099 + source + pdf
+ invhyper100-199 + source + pdf
+ invhyper200-296 + source + pdf
+
+ invtrig000-092 + source + pdf
+
+ log000-099 + source + pdf
+ log100-199 + source + pdf
+ log200-299 + source + pdf
+ log300-391 + source + pdf
+
+ rational + source + pdf
+
+ specfunc000-022 + source + pdf
+
+ trig000-099 + source + pdf
+ trig100-199 + source + pdf
+ trig200-299 + source + pdf
+ trig300-399 + source + pdf
+ trig400-499 + source + pdf
+ trig500-599 + source + pdf
+ trig600-699 + source + pdf
+ trig700-799 + source + pdf
+ trig800-899 + source + pdf
+ trig900-920 + source + pdf
+ - \ No newline at end of file + diff --git a/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet b/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet new file mode 100644 index 0000000..a93236a --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic000-099.input.pamphlet @@ -0,0 +1,4982 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic000-099.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic000-099.output +)spool richalgebraic000-099.output +)set message test on +)set message auto off +)clear all + +--S 1 of 518 +t0000:= (c*(a+b*x)^2)^(5/2) +--R +--R +--R (1) +--R +-----------------------+ +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 | 2 2 2 +--R (b c x + 4a b c x + 6a b c x + 4a b c x + a c )\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 518 +r0000:= 1/6*(a+b*x)*(c*(a+b*x)^2)^(5/2)/b +--R +--R +--R (2) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R / +--R 6b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 518 +a0000:= integrate(t0000,x) +--R +--R +--R (3) +--R 5 2 6 4 2 5 2 3 2 4 3 2 2 3 4 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a c x)\|c +--R ------------------------------------------------------------------------ +--R 6 +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 518 +m0000:= a0000-r0000 +--R +--R +--R (4) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +--R (- b c x - 5a b c x - 10a b c x - 10a b c x - 5a b c x - a c ) +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 2 6 5 2 5 2 4 2 4 3 3 2 3 4 2 2 2 5 2 +-+ +--R (b c x + 6a b c x + 15a b c x + 20a b c x + 15a b c x + 6a b c x)\|c +--R / +--R 6b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 518 +d0000:= D(m0000,x) +--R +--R +--R (5) +--R 5 2 5 4 2 4 2 3 2 3 3 2 2 2 4 2 5 2 +-+ +--R (b c x + 5a b c x + 10a b c x + 10a b c x + 5a b c x + a c )\|c +--R * +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R + +--R 6 3 6 5 3 5 2 4 3 4 3 3 3 3 4 2 3 2 5 3 +--R - b c x - 6a b c x - 15a b c x - 20a b c x - 15a b c x - 6a b c x +--R + +--R 6 3 +--R - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 5 + +--S 6 of 518 +t0001:= (c*(a+b*x)^2)^(3/2) +--R +--R +--R +-----------------------+ +--R 2 2 2 | 2 2 2 +--R (6) (b c x + 2a b c x + a c)\|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 518 +r0001:= 1/4*(a+b*x)*(c*(a+b*x)^2)^(3/2)/b +--R +--R +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|b c x + 2a b c x + a c +--R (7) --------------------------------------------------------------- +--R 4b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 518 +a0001:= integrate(t0001,x) +--R +--R +--R 3 4 2 3 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a c x)\|c +--R (8) --------------------------------------------- +--R 4 +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 518 +m0001:= a0001-r0001 +--R +--R +--R (9) +--R +-----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- b c x - 3a b c x - 3a b c x - a c)\|b c x + 2a b c x + a c +--R + +--R 4 4 3 3 2 2 2 3 +-+ +--R (b c x + 4a b c x + 6a b c x + 4a b c x)\|c +--R / +--R 4b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 518 +d0001:= D(m0001,x) +--R +--R +--R (10) +--R +-----------------------+ +--R 3 3 2 2 2 3 +-+ | 2 2 2 +--R (b c x + 3a b c x + 3a b c x + a c)\|c \|b c x + 2a b c x + a c +--R + +--R 4 2 4 3 2 3 2 2 2 2 3 2 4 2 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +-----------------------+ +--R | 2 2 2 +--R \|b c x + 2a b c x + a c +--R Type: Expression(Integer) +--E 10 + +--S 11 of 518 +t0002:= 1/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 2 2 2 +--R b x + 2a b x + a +--R (11) ---------------------- +--R +------------------+ +--R | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 11 + +--S 12 of 518 +r0002:= 1/4*(a+b*x)/b/(c/(a+b*x)^2)^(3/2) +--R +--R +--R 3 3 2 2 2 3 +--R b x + 3a b x + 3a b x + a +--R (12) ---------------------------- +--R +------------------+ +--R | c +--R 4b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 12 + +--S 13 of 518 +a0002:= integrate(t0002,x) +--R +--R +--R 3 4 2 3 2 2 3 +--R b x + 4a b x + 6a b x + 4a x +--R (13) ------------------------------- +--R +-+ +--R 4c\|c +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 518 +m0002:= a0002-r0002 +--R +--R +--R (14) +--R 3 3 2 2 2 3 +-+ +--R (- b x - 3a b x - 3a b x - a )\|c +--R + +--R +------------------+ +--R 4 4 3 3 2 2 2 3 | c +--R (b x + 4a b x + 6a b x + 4a b x) |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R | c +-+ +--R 4b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 14 + +--S 15 of 518 +d0002:= D(m0002,x) +--R +--R +--R (15) +--R +------------------+ +--R 3 3 2 2 2 3 | c +-+ 2 2 +--R (b x + 3a b x + 3a b x + a ) |------------------ \|c - b c x +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 2 +--R - 2a b c x - a c +--R / +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 15 + +--S 16 of 518 +t0003:= 1/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 4 4 3 3 2 2 2 3 4 +--R b x + 4a b x + 6a b x + 4a b x + a +--R (16) -------------------------------------- +--R +------------------+ +--R 2 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 16 + +--S 17 of 518 +r0003:= 1/6*(a+b*x)/b/(c/(a+b*x)^2)^(5/2) +--R +--R +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R b x + 5a b x + 10a b x + 10a b x + 5a b x + a +--R (17) -------------------------------------------------- +--R +------------------+ +--R 2 | c +--R 6b c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 17 + +--S 18 of 518 +a0003:= integrate(t0003,x) +--R +--R +--R 5 6 4 5 2 3 4 3 2 3 4 2 5 +--R b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a x +--R (18) ------------------------------------------------------ +--R 2 +-+ +--R 6c \|c +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 518 +m0003:= a0003-r0003 +--R +--R +--R (19) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +-+ +--R (- b x - 5a b x - 10a b x - 10a b x - 5a b x - a )\|c +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R (b x + 6a b x + 15a b x + 20a b x + 15a b x + 6a b x) +--R * +--R +------------------+ +--R | c +--R |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R / +--R +------------------+ +--R 2 | c +-+ +--R 6b c |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 19 + +--S 20 of 518 +d0003:= D(m0003,x) +--R +--R +--R (20) +--R 5 5 4 4 2 3 3 3 2 2 4 5 +--R (b x + 5a b x + 10a b x + 10a b x + 5a b x + a ) +--R * +--R +------------------+ +--R | c +-+ +--R |------------------ \|c +--R | 2 2 2 +--R \|b x + 2a b x + a +--R + +--R 4 4 3 3 2 2 2 3 4 +--R - b c x - 4a b c x - 6a b c x - 4a b c x - a c +--R / +--R +------------------+ +--R 3 | c +--R c |------------------ +--R | 2 2 2 +--R \|b x + 2a b x + a +--R Type: Expression(Integer) +--E 20 + +--S 21 of 518 +t0004:= 1/(2-3*x)^(1/2)/(2+3*x)^(1/2) +--R +--R +--R 1 +--R (21) -------------------- +--R +--------+ +------+ +--R \|- 3x + 2 \|3x + 2 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 518 +r0004:= 1/3*asin(3/2*x) +--R +--R +--R 3x +--R asin(--) +--R 2 +--R (22) -------- +--R 3 +--R Type: Expression(Integer) +--E 22 + +--S 23 of 518 +--a0004:= integrate(t0004,x) +-- bug 7207: causes infinite loop in integrator. +--E 23 + +--S 24 of 518 +t0005:= 1/(3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (23) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x + 5 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 518 +r0005:= asin(1/4+1/4*x) +--R +--R +--R x + 1 +--R (24) asin(-----) +--R 4 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 518 +--a0005:= integrate(t0005,x) +--E 26 + +--S 27 of 518 +--m0005:= a0005-r0005 +--E 28 + +--S 28 of 518 +--d0005:= D(m0005,x) +--E 28 + +--S 29 of 518 +t0006:= 1/(-3-x)^(1/2)/(5+x)^(1/2) +--R +--R +--R 1 +--R (25) ------------------ +--R +-------+ +-----+ +--R \|- x - 3 \|x + 5 +--R Type: Expression(Integer) +--E 29 + +--S 30 of 518 +r0006:= asin(4+x) +--R +--R +--R (26) asin(x + 4) +--R Type: Expression(Integer) +--E 30 + +--S 31 of 518 +--a0006:= integrate(t0006,x) +--E 31 + +--S 32 of 518 +--m0006:= a0006-r0006 +--E 32 + +--S 33 of 518 +--d0006:= D(m0006,x) +--E 33 + +--S 34 of 518 +t0007:= (1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (27) \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 518 +r0007:= 1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 +--R x\|- x + 1 + asin(x) +--R (28) ---------------------- +--R 2 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 518 +--a0007:= integrate(t0007,x) +--E 36 + +--S 37 of 518 +--m0007:= a0007-r0007 +--E 37 + +--S 38 of 518 +--d0007:= D(m0007,x) +--E 38 + +--S 39 of 518 +t0008:= 1/(1-x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (29) ------------------ +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 39 + +--S 40 of 518 +r0008:= asin(x) +--R +--R +--R (30) asin(x) +--R Type: Expression(Integer) +--E 40 + +--S 41 of 518 +--a0008:= integrate(t0008,x) +--E 41 + +--S 42 of 518 +--m0008:= a0008-r0008 +--E 42 + +--S 43 of 518 +--d0008:= D(m0008,x) +--E 43 + +--S 44 of 518 +t0009:= 1/(1-x)^(3/2)/(1+x)^(3/2) +--R +--R +--R 1 +--R (31) - -------------------------- +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 518 +r0009:= x/(1-x^2)^(1/2) +--R +--R +--R x +--R (32) ----------- +--R +--------+ +--R | 2 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 45 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +-------+ +-----+ + x\|- x + 1 \|x + 1 + (33) - ------------------- + 2 + x - 1 +--R Type: Union(Expression(Integer),...) +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 46 of 518 ok to fail. there appear to be 2 answers (see above) +a0009:= integrate(t0009,x) +--R +--R +--R +-------+ +-----+ +--R x\|- x + 1 \|x + 1 +--R (33) - ------------------- +--R 2 +--R x - 1 +--R Type: Union(Expression(Integer),...) +--E 46 + +\end{chunk} +Occasionally we get a different answer to this same integration: +\begin{verbatim} + + + +--------+ + | 2 +-------+ +-----+ 3 + - x\|- x + 1 \|- x + 1 \|x + 1 - x + x + (34) ----------------------------------------- + +--------+ + 2 | 2 + (x - 1)\|- x + 1 +\end{verbatim} +Both answers are correct as can be seen by taking the difference between +the original integrand and the derivative of the expression. +\begin{chunk}{*} +--S 47 of 518 ok to fail. there appear to be 2 answers (see above) +m0009:= a0009-r0009 +--R +--R +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ 2 | 2 3 +--R - 3x\|- x + 1 \|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 - 3x + 3x +--R (34) --------------------------------------------------------------------- +--R +--------+ +--R 2 | 2 +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 47 + +--S 48 of 518 +d0009:= D(m0009,x) +--R +--R +--R +--------+ +--R +-------+ +-----+ | 2 +--R \|- x + 1 \|x + 1 - \|- x + 1 +--R (35) ------------------------------------- +--R +--------+ +--R 2 | 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 48 + +--S 49 of 518 +t0010:= (3-x)^(1/2)*(-2+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (36) \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 518 +r0010:= -1/4*(5-2*x)*(-6+5*x-x^2)^(1/2)+1/8*asin(-5+2*x) +--R +--R +--R +-------------+ +--R | 2 +--R (4x - 10)\|- x + 5x - 6 + asin(2x - 5) +--R (37) ---------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 518 +--a0010:= integrate(t0010,x) +--E 51 + +--S 52 of 518 +--m0010:= a0010-r0010 +--E 52 + +--S 53 of 518 +--d0010:= D(m0010,x) +--E 53 + +--S 54 of 518 +t0011:= 1/(3-x)^(1/2)/(-2+x)^(1/2) +--R +--R +--R 1 +--R (38) ------------------ +--R +-------+ +-----+ +--R \|- x + 3 \|x - 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 518 +r0011:= asin(-5+2*x) +--R +--R +--R (39) asin(2x - 5) +--R Type: Expression(Integer) +--E 55 + +--S 56 of 518 +--a0011:= integrate(t0011,x) +--E 56 + +--S 57 of 518 +--m0011:= a0011-r0011 +--E 57 + +--S 58 of 518 +--d0011:= D(m0011,x) +--E 58 + +--S 59 of 518 +t0012:= x^(1/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R \|x +--R (40) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 59 + +--S 60 of 518 +r0012:= x^(1/2)/b/(a-b*x)-atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-+ +--R (- b x + a)atanh(--------) - \|a \|b \|x +--R +-+ +--R \|a +--R (41) ----------------------------------------- +--R 2 +-+ +-+ +--R (b x - a b)\|a \|b +--R Type: Expression(Integer) +--E 60 + +--S 61 of 518 +a0012:= integrate(t0012,x) +--R +--R +--R (42) +--R +-+ +---+ +--R - 2a b\|x + (b x + a)\|a b +---+ +-+ +--R (b x - a)log(----------------------------) - 2\|a b \|x +--R b x - a +--R [--------------------------------------------------------, +--R 2 +---+ +--R (2b x - 2a b)\|a b +--R +-----+ +-+ +--R \|- a b \|x +-----+ +-+ +--R (- b x + a)atan(------------) - \|- a b \|x +--R a +--R --------------------------------------------] +--R 2 +-----+ +--R (b x - a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 61 + +--S 62 of 518 +m0012a:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (43) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 62 + +--S 63 of 518 +d0012a:= D(m0012a,x) +--R +--R +--R (44) 0 +--R Type: Expression(Integer) +--E 63 + +--S 64 of 518 +m0012b:= a0012.1-r0012 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(----------------------------) + 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (45) ------------------------------------------------------------------ +--R +-+ +-+ +---+ +--R 2b\|a \|b \|a b +--R Type: Expression(Integer) +--E 64 + +--S 65 of 518 +d0012b:= D(m0012b,x) +--R +--R +--R (46) 0 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 518 +t0013:= x^(1/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R \|x +--R (47) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 66 + +--S 67 of 518 +r0013:= -1/2*x^(1/2)/b/(a-b*x)^2+1/4*x^(1/2)/a/b/(a-b*x)+_ + 1/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(3/2)/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (b x - 2a b x + a )atanh(--------) + (- b x - a)\|a \|b \|x +--R +-+ +--R \|a +--R (48) ------------------------------------------------------------- +--R 3 2 2 2 3 +-+ +-+ +--R (4a b x - 8a b x + 4a b)\|a \|b +--R Type: Expression(Integer) +--E 67 + +--S 68 of 518 +a0013:= integrate(t0013,x) +--R +--R +--R (49) +--R [ +--R +-+ +---+ +--R 2 2 2 2a b\|x + (b x + a)\|a b +--R (b x - 2a b x + a )log(--------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 2b x - 2a)\|a b \|x +--R / +--R 3 2 2 2 3 +---+ +--R (8a b x - 16a b x + 8a b)\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (b x - 2a b x + a )atan(------------) + (- b x - a)\|- a b \|x +--R a +--R ----------------------------------------------------------------] +--R 3 2 2 2 3 +-----+ +--R (4a b x - 8a b x + 4a b)\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 68 + +--S 69 of 518 +m0013a:= a0013.1-r0013 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R \|a \|b log(--------------------------) - 2\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (50) ---------------------------------------------------------------- +--R +-+ +-+ +---+ +--R 8a b\|a \|b \|a b +--R Type: Expression(Integer) +--E 69 + +--S 70 of 518 +d0013a:= D(m0013a,x) +--R +--R +--R (51) 0 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 518 +m0013b:= a0013.2-r0013 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R - \|- a b atanh(--------) + \|a \|b atan(------------) +--R +-+ a +--R \|a +--R (52) ------------------------------------------------------ +--R +-----+ +-+ +-+ +--R 4a b\|- a b \|a \|b +--R Type: Expression(Integer) +--E 71 + +--S 72 of 518 +d0013b:= D(m0013b,x) +--R +--R +--R (53) 0 +--R Type: Expression(Integer) +--E 72 + +--S 73 of 518 +t0014:= x^(3/2)/(-a+b*x)^2 +--R +--R +--R +-+ +--R x\|x +--R (54) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 73 + +--S 74 of 518 +r0014:= 3*x^(1/2)/b^2+x^(3/2)/b/(a-b*x)-_ + 3*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ \|b \|x +-+ +-+ +--R (- 3b x + 3a)\|a atanh(--------) + (2b x - 3a)\|b \|x +--R +-+ +--R \|a +--R (55) ------------------------------------------------------ +--R 3 2 +-+ +--R (b x - a b )\|b +--R Type: Expression(Integer) +--E 74 + +--S 75 of 518 +a0014:= integrate(t0014,x) +--R +--R +--R (56) +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R |a \|b +-+ +--R (3b x - 3a) |- log(----------------------) + (4b x - 6a)\|x +--R \|b b x - a +--R [------------------------------------------------------------, +--R 3 2 +--R 2b x - 2a b +--R +---+ +-+ +--R | a \|x +-+ +--R (- 3b x + 3a) |- - atan(------) + (2b x - 3a)\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------] +--R 3 2 +--R b x - a b +--R Type: Union(List(Expression(Integer)),...) +--E 75 + +--S 76 of 518 +m0014a:= a0014.1-r0014 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 3 |- \|b log(---------------------- + 6\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (57) ----------------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 76 + +--S 77 of 518 +d0014a:= D(m0014a,x) +--R +--R +--R (58) 0 +--R Type: Expression(Integer) +--E 77 + +--S 78 of 518 +m0014b:= a0014.2-r0014 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 3\|a atanh(--------) - 3 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (59) ---------------------------------------------- +--R 2 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 78 + +--S 79 of 518 +d0014b:= D(m0014b,x) +--R +--R +--R (60) 0 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 518 +t0015:= x^(3/2)/(-a+b*x)^3 +--R +--R +--R +-+ +--R x\|x +--R (61) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 80 + +--S 81 of 518 +r0015:= -1/2*x^(3/2)/b/(a-b*x)^2+_ + 3/4*x^(1/2)/b^2/(a-b*x)-_ + 3/4*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(1/2)/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 2 2 \|b \|x +-+ +-+ +-+ +--R (- 3b x + 6a b x - 3a )atanh(--------) + (- 5b x + 3a)\|a \|b \|x +--R +-+ +--R \|a +--R (62) ------------------------------------------------------------------- +--R 4 2 3 2 2 +-+ +-+ +--R (4b x - 8a b x + 4a b )\|a \|b +--R Type: Expression(Integer) +--E 81 + +--S 82 of 518 +a0015:= integrate(t0015,x) +--R +--R +--R (63) +--R [ +--R +-+ +---+ +--R 2 2 2 - 2a b\|x + (b x + a)\|a b +--R (3b x - 6a b x + 3a )log(----------------------------) +--R b x - a +--R + +--R +---+ +-+ +--R (- 10b x + 6a)\|a b \|x +--R / +--R 4 2 3 2 2 +---+ +--R (8b x - 16a b x + 8a b )\|a b +--R , +--R +-----+ +-+ +--R 2 2 2 \|- a b \|x +-----+ +-+ +--R (- 3b x + 6a b x - 3a )atan(------------) + (- 5b x + 3a)\|- a b \|x +--R a +--R ----------------------------------------------------------------------] +--R 4 2 3 2 2 +-----+ +--R (4b x - 8a b x + 4a b )\|- a b +--R Type: Union(List(Expression(Integer)),...) +--E 82 + +--S 83 of 518 +m0015a:= a0015.1-r0015 +--R +--R +--R +-+ +---+ +-+ +-+ +--R +-+ +-+ - 2a b\|x + (b x + a)\|a b +---+ \|b \|x +--R 3\|a \|b log(----------------------------) + 6\|a b atanh(--------) +--R b x - a +-+ +--R \|a +--R (64) ------------------------------------------------------------------- +--R 2 +-+ +-+ +---+ +--R 8b \|a \|b \|a b +--R Type: Expression(Integer) +--E 83 + +--S 84 of 518 +d0015a:= D(m0015a,x) +--R +--R +--R (65) 0 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 518 +m0015b:= a0015.2-r0015 +--R +--R +--R +-+ +-+ +-----+ +-+ +--R +-----+ \|b \|x +-+ +-+ \|- a b \|x +--R 3\|- a b atanh(--------) - 3\|a \|b atan(------------) +--R +-+ a +--R \|a +--R (66) ------------------------------------------------------ +--R 2 +-----+ +-+ +-+ +--R 4b \|- a b \|a \|b +--R Type: Expression(Integer) +--E 85 + +--S 86 of 518 +d0015b:= D(m0015b,x) +--R +--R +--R (67) 0 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 518 +t0016:= x^(5/2)/(-a+b*x)^2 +--R +--R +--R 2 +-+ +--R x \|x +--R (68) ------------------ +--R 2 2 2 +--R b x - 2a b x + a +--R Type: Expression(Integer) +--E 87 + +--S 88 of 518 +r0016:= 5*a*x^(1/2)/b^3+5/3*x^(3/2)/b^2+x^(5/2)/b/(a-b*x)-_ + 5*a^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (69) +--R +-+ +-+ +--R 2 +-+ \|b \|x 2 2 2 +-+ +-+ +--R (- 15a b x + 15a )\|a atanh(--------) + (2b x + 10a b x - 15a )\|b \|x +--R +-+ +--R \|a +--R ------------------------------------------------------------------------ +--R 4 3 +-+ +--R (3b x - 3a b )\|b +--R Type: Expression(Integer) +--E 88 + +--S 89 of 518 +a0016:= integrate(t0016,x) +--R +--R +--R (70) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 |a \|b +--R (15a b x - 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (4b x + 20a b x - 30a )\|x +--R / +--R 4 3 +--R 6b x - 6a b +--R , +--R +---+ +-+ +--R 2 | a \|x 2 2 2 +-+ +--R (- 15a b x + 15a ) |- - atan(------) + (2b x + 10a b x - 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R -------------------------------------------------------------------] +--R 4 3 +--R 3b x - 3a b +--R Type: Union(List(Expression(Integer)),...) +--E 89 + +--S 90 of 518 +m0016a:= a0016.1-r0016 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 5a |- \|b log(----------------------) + 10a\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (71) -------------------------------------------------------------- +--R 3 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 90 + +--S 91 of 518 +d0016a:= D(m0016a,x) +--R +--R +--R (72) 0 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 518 +m0016b:= a0016.2-r0016 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 5a\|a atanh(--------) - 5a |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (73) ------------------------------------------------ +--R 3 +-+ +--R b \|b +--R Type: Expression(Integer) +--E 92 + +--S 93 of 518 +d0016b:= D(m0016b,x) +--R +--R +--R (74) 0 +--R Type: Expression(Integer) +--E 93 + +--S 94 of 518 +t0017:= x^(5/2)/(-a+b*x)^3 +--R +--R +--R 2 +-+ +--R x \|x +--R (75) ---------------------------- +--R 3 3 2 2 2 3 +--R b x - 3a b x + 3a b x - a +--R Type: Expression(Integer) +--E 94 + +--S 95 of 518 +r0017:= 15/4*x^(1/2)/b^3-1/2*x^(5/2)/b/(a-b*x)^2+_ + 5/4*x^(3/2)/b^2/(a-b*x)-_ + 15/4*a^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/b^(7/2) +--R +--R +--R (76) +--R +-+ +-+ +--R 2 2 2 +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|a atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +-+ +--R (8b x - 25a b x + 15a )\|b \|x +--R / +--R 5 2 4 2 3 +-+ +--R (4b x - 8a b x + 4a b )\|b +--R Type: Expression(Integer) +--E 95 + +--S 96 of 518 +a0017:= integrate(t0017,x) +--R +--R +--R (77) +--R [ +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +--R 2 2 2 |a \|b +--R (15b x - 30a b x + 15a ) |- log(----------------------) +--R \|b b x - a +--R + +--R 2 2 2 +-+ +--R (16b x - 50a b x + 30a )\|x +--R / +--R 5 2 4 2 3 +--R 8b x - 16a b x + 8a b +--R , +--R +---+ +-+ +--R 2 2 2 | a \|x 2 2 2 +-+ +--R (- 15b x + 30a b x - 15a ) |- - atan(------) + (8b x - 25a b x + 15a )\|x +--R \| b +---+ +--R | a +--R |- - +--R \| b +--R ---------------------------------------------------------------------------- +--R 5 2 4 2 3 +--R 4b x - 8a b x + 4a b +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 96 + +--S 97 of 518 +m0017a:= a0017.1-r0017 +--R +--R +--R +-+ +--R |a +-+ +--R +-+ - 2b |- \|x + b x + a +-+ +-+ +--R |a +-+ \|b +-+ \|b \|x +--R 15 |- \|b log(---------------------- + 30\|a atanh(--------) +--R \|b b x - a +-+ +--R \|a +--R (78) ------------------------------------------------------------- +--R 3 +-+ +--R 8b \|b +--R Type: Expression(Integer) +--E 97 + +--S 98 of 518 +d0017a:= D(m0017a,x) +--R +--R +--R (79) 0 +--R Type: Expression(Integer) +--E 98 + +--S 99 of 518 +m0017b:= a0017.2-r0017 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | a +-+ \|x +--R 15\|a atanh(--------) - 15 |- - \|b atan(------) +--R +-+ \| b +---+ +--R \|a | a +--R |- - +--R \| b +--R (80) ------------------------------------------------ +--R 3 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 99 + +--S 100 of 518 +d0017b:= D(m0017b,x) +--R +--R +--R (81) 0 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 518 +t0018:= 1/x^(3/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (82) -------------------------- +--R 2 3 2 2 +-+ +--R (b x - 2a b x + a x)\|x +--R Type: Expression(Integer) +--E 101 + +--S 102 of 518 +r0018:= -2/a/x^(1/2)/(a-b*x)+3*b*x^(1/2)/a^2/(a-b*x)+_ + 3*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-+ +--R (3b x - 3a)\|b \|x atanh(--------) + (- 3b x + 2a)\|a +--R +-+ +--R \|a +--R (83) ------------------------------------------------------ +--R 2 3 +-+ +-+ +--R (a b x - a )\|a \|x +--R Type: Expression(Integer) +--E 102 + +--S 103 of 518 +a0018:= integrate(t0018,x) +--R +--R +--R (84) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R |b +-+ \|a +--R (3b x - 3a) |- \|x log(--------------------) - 6b x + 4a +--R \|a b x - a +--R [--------------------------------------------------------, +--R 2 3 +-+ +--R (2a b x - 2a )\|x +--R +---+ +-+ +--R | b +-+ b\|x +--R (3b x - 3a) |- - \|x atan(-------) - 3b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ----------------------------------------------] +--R 2 3 +-+ +--R (a b x - a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 103 + +--S 104 of 518 +m0018a:= a0018.1-r0018 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 3\|a |- log(--------------------) - 6\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (85) --------------------------------------------------------- +--R 2 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 104 + +--S 105 of 518 +d0018a:= D(m0018a,x) +--R +--R +--R (86) 0 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 518 +m0018b:= a0018.2-r0018 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 3\|b atanh(--------) + 3 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (87) ------------------------------------------------- +--R 2 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 106 + +--S 107 of 518 +d0018b:= D(m0018b,x) +--R +--R +--R (88) 0 +--R Type: Expression(Integer) +--E 107 + +--S 108 of 518 +t0019:= 1/x^(3/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (89) ------------------------------------ +--R 3 4 2 3 2 2 3 +-+ +--R (b x - 3a b x + 3a b x - a x)\|x +--R Type: Expression(Integer) +--E 108 + +--S 109 of 518 +r0019:= 2/a/x^(1/2)/(a-b*x)^2-5/2*b*x^(1/2)/a^2/(a-b*x)^2-_ + 15/4*b*x^(1/2)/a^3/(a-b*x)-_ + 15/4*b^(1/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (90) +--R +-+ +-+ +--R 2 2 2 +-+ +-+ \|b \|x +--R (- 15b x + 30a b x - 15a )\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 2 2 2 +-+ +--R (15b x - 25a b x + 8a )\|a +--R / +--R 3 2 2 4 5 +-+ +-+ +--R (4a b x - 8a b x + 4a )\|a \|x +--R Type: Expression(Integer) +--E 109 + +--S 110 of 518 +a0019:= integrate(t0019,x) +--R +--R +--R (91) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 2 2 2 |b +-+ \|a 2 2 +--R (15b x - 30a b x + 15a ) |- \|x log(----------------------) + 30b x +--R \|a b x - a +--R + +--R 2 +--R - 50a b x + 16a +--R / +--R 3 2 2 4 5 +-+ +--R (8a b x - 16a b x + 8a )\|x +--R , +--R +---+ +-+ +--R 2 2 2 | b +-+ b\|x 2 2 2 +--R (- 15b x + 30a b x - 15a ) |- - \|x atan(-------) + 15b x - 25a b x + 8a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ---------------------------------------------------------------------------] +--R 3 2 2 4 5 +-+ +--R (4a b x - 8a b x + 4a )\|x +--R Type: Union(List(Expression(Integer)),...) +--E 110 + +--S 111 of 518 +m0019a:= a0019.1-r0019 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 15\|a |- log(----------------------) + 30\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (92) ------------------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 111 + +--S 112 of 518 +d0019a:= D(m0019a,x) +--R +--R +--R (93) 0 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 518 +m0019b:= a0019.2-r0019 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 15\|b atanh(--------) - 15 |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (94) ------------------------------------------------- +--R 3 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 113 + +--S 114 of 518 +d0019b:= D(m0019b,x) +--R +--R +--R (95) 0 +--R Type: Expression(Integer) +--E 114 + +--S 115 of 518 +t0020:= 1/x^(5/2)/(-a+b*x)^2 +--R +--R +--R 1 +--R (96) --------------------------- +--R 2 4 3 2 2 +-+ +--R (b x - 2a b x + a x )\|x +--R Type: Expression(Integer) +--E 115 + +--S 116 of 518 +r0020:= -5/3/a^2/x^(3/2)-5*b/a^3/x^(1/2)+1/a/x^(3/2)/(a-b*x)+_ + 5*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (97) +--R +-+ +-+ +--R 2 2 +-+ +-+ \|b \|x 2 2 2 +-+ +--R (15b x - 15a b x)\|b \|x atanh(--------) + (- 15b x + 10a b x + 2a )\|a +--R +-+ +--R \|a +--R -------------------------------------------------------------------------- +--R 3 2 4 +-+ +-+ +--R (3a b x - 3a x)\|a \|x +--R Type: Expression(Integer) +--E 116 + +--S 117 of 518 +a0020:= integrate(t0020,x) +--R +--R +--R (98) +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +--R 2 2 |b +-+ \|a 2 2 2 +--R (15b x - 15a b x) |- \|x log(--------------------) - 30b x + 20a b x + 4a +--R \|a b x - a +--R [---------------------------------------------------------------------------- +--R 3 2 4 +-+ +--R (6a b x - 6a x)\|x +--R , +--R +---+ +-+ +--R 2 2 | b +-+ b\|x 2 2 2 +--R (15b x - 15a b x) |- - \|x atan(-------) - 15b x + 10a b x + 2a +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R ------------------------------------------------------------------] +--R 3 2 4 +-+ +--R (3a b x - 3a x)\|x +--R Type: Union(List(Expression(Integer)),...) +--E 117 + +--S 118 of 518 +m0020a:= a0020.1-r0020 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 5b\|a |- log(--------------------) - 10b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (99) ------------------------------------------------------------ +--R 3 +-+ +--R 2a \|a +--R Type: Expression(Integer) +--E 118 + +--S 119 of 518 +d0020a:= D(m0020a,x) +--R +--R +--R (100) 0 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 518 +m0020b:= a0020.2-r0020 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R - 5b\|b atanh(--------) + 5b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (101) --------------------------------------------------- +--R 3 +-+ +--R a \|a +--R Type: Expression(Integer) +--E 120 + +--S 121 of 518 +d0020b:= D(m0020b,x) +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 518 +t0021:= 1/x^(5/2)/(-a+b*x)^3 +--R +--R +--R 1 +--R (103) ------------------------------------- +--R 3 5 2 4 2 3 3 2 +-+ +--R (b x - 3a b x + 3a b x - a x )\|x +--R Type: Expression(Integer) +--E 122 + +--S 123 of 518 +r0021:= 2/3/a/x^(3/2)/(a-b*x)^2+14/3*b/a^2/x^(1/2)/(a-b*x)^2-_ + 35/6*b^2*x^(1/2)/a^3/(a-b*x)^2-35/4*b^2*x^(1/2)/a^4/(a-b*x)-_ + 35/4*b^(3/2)*atanh(b^(1/2)*x^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (104) +--R +-+ +-+ +--R 3 3 2 2 2 +-+ +-+ \|b \|x +--R (- 105b x + 210a b x - 105a b x)\|b \|x atanh(--------) +--R +-+ +--R \|a +--R + +--R 3 3 2 2 2 3 +-+ +--R (105b x - 175a b x + 56a b x + 8a )\|a +--R / +--R 4 2 3 5 2 6 +-+ +-+ +--R (12a b x - 24a b x + 12a x)\|a \|x +--R Type: Expression(Integer) +--E 123 + +--S 124 of 518 +a0021:= integrate(t0021,x) +--R +--R +--R (105) +--R [ +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +--R 3 3 2 2 2 |b +-+ \|a +--R (105b x - 210a b x + 105a b x) |- \|x log(----------------------) +--R \|a b x - a +--R + +--R 3 3 2 2 2 3 +--R 210b x - 350a b x + 112a b x + 16a +--R / +--R 4 2 3 5 2 6 +-+ +--R (24a b x - 48a b x + 24a x)\|x +--R , +--R +--R +---+ +-+ +--R 3 3 2 2 2 | b +-+ b\|x 3 3 +--R (- 105b x + 210a b x - 105a b x) |- - \|x atan(-------) + 105b x +--R \| a +---+ +--R | b +--R a |- - +--R \| a +--R + +--R 2 2 2 3 +--R - 175a b x + 56a b x + 8a +--R / +--R 4 2 3 5 2 6 +-+ +--R (12a b x - 24a b x + 12a x)\|x +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 124 + +--S 125 of 518 +m0021a:= a0021.1-r0021 +--R +--R +--R +-+ +--R |b +-+ +--R +-+ - 2a |- \|x + b x + a +-+ +-+ +--R +-+ |b \|a +-+ \|b \|x +--R 35b\|a |- log(----------------------) + 70b\|b atanh(--------) +--R \|a b x - a +-+ +--R \|a +--R (106) --------------------------------------------------------------- +--R 4 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 125 + +--S 126 of 518 +d0021a:= D(m0021a,x) +--R +--R +--R (107) 0 +--R Type: Expression(Integer) +--E 126 + +--S 127 of 518 +m0021b:= a0021.2-r0021 +--R +--R +--R +-+ +-+ +---+ +-+ +--R +-+ \|b \|x | b +-+ b\|x +--R 35b\|b atanh(--------) - 35b |- - \|a atan(-------) +--R +-+ \| a +---+ +--R \|a | b +--R a |- - +--R \| a +--R (108) --------------------------------------------------- +--R 4 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 127 + +--S 128 of 518 +d0021b:= D(m0021b,x) +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 128 + +--S 129 of 518 +t0022:= x^(1/2)*(2+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (110) \|x \|b x + 2 +--R Type: Expression(Integer) +--E 129 + +--S 130 of 518 +r0022:= 1/2*x^(1/2)*(2+b*x)^(1/2)/b+1/2*x^(3/2)*(2+b*x)^(1/2)-_ + asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + (b x + 1)\|b \|x \|b x + 2 +--R 2 +--R (111) ---------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 130 + +--S 131 of 518 +--a0022:= integrate(t0022,x) +--E 131 + +--S 132 of 518 +--m0022:= a0022-r0022 +--E 132 + +--S 133 of 518 +--d0022:= D(m0022,x) +--E 133 + +--S 134 of 518 +t0023:= x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (112) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 134 + +--S 135 of 518 +r0023:= x^(1/2)*(2+b*x)^(1/2)/b-2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R - 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (113) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 135 + +--S 136 of 518 +--a0023:= integrate(t0023,x) +--E 136 + +--S 137 of 518 +--m0023:= a0023-r0023 +--E 137 + +--S 138 of 518 +--d0023:= D(m0023,x) +--E 138 + +--S 139 of 518 +t0024:= x^(3/2)/(2+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (114) ---------- +--R +-------+ +--R \|b x + 2 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 518 +r0024:= -3/2*x^(1/2)*(2+b*x)^(1/2)/b^2+1/2*x^(3/2)*(2+b*x)^(1/2)/b+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x - 3)\|b \|x \|b x + 2 +--R 2 +--R (115) -------------------------------------------------- +--R 2 +-+ +--R 2b \|b +--R Type: Expression(Integer) +--E 140 + +--S 141 of 518 +--a0024:= integrate(t0024,x) +--E 141 + +--S 142 of 518 +--m0024:= a0024-r0024 +--E 142 + +--S 143 of 518 +--d0024:= D(m0024,x) +--E 143 + +--S 144 of 518 +t0025:= x^(3/2)/(2+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (116) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 518 +r0025:= -2*x^(3/2)/b/(2+b*x)^(1/2)+3*x^(1/2)*(2+b*x)^(1/2)/b^2-_ + 6*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x +-+ +-+ +--R - 6\|b x + 2 asinh(------------) + (b x + 6)\|b \|x +--R 2 +--R (117) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 518 +--a0025:= integrate(t0025,x) +--E 146 + +--S 147 of 518 +--m0025:= a0025-r0025 +--E 147 + +--S 148 of 518 +--d0025:= D(m0025,x) +--E 148 + +--S 149 of 518 +t0026:= x^(5/2)/(2+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (118) ------------------- +--R +-------+ +--R (b x + 2)\|b x + 2 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 518 +r0026:= 1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)-5*x^(3/2)*b^(3/2)+_ + 30*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2+b*x)^(1/2))/(2+b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R 30\|b x + 2 asinh(------------) + (b x - 5b x - 30)\|b \|x +--R 2 +--R (119) ------------------------------------------------------------ +--R 3 +-+ +-------+ +--R 2b \|b \|b x + 2 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 518 +--a0026:= integrate(t0026,x) +--E 151 + +--S 152 of 518 +--m0026:= a0026-r0026 +--E 152 + +--S 153 of 518 +--d0026:= D(m0026,x) +--E 153 + +--S 154 of 518 +t0027:= x^(5/2)/(2+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (120) --------------------------- +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 518 +r0027:= -2/3*x^(5/2)/b/(2+b*x)^(3/2)-10/3*x^(3/2)/b^2/(2+b*x)^(1/2)+_ + 5*x^(1/2)*(2+b*x)^(1/2)/b^3-_ + 10*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (121) +--R +-+ +-+ +-+ +--R +-------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (- 30b x - 60)\|b x + 2 asinh(------------) + (3b x + 40b x + 60)\|b \|x +--R 2 +--R -------------------------------------------------------------------------- +--R 4 3 +-+ +-------+ +--R (3b x + 6b )\|b \|b x + 2 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 518 +--a0027:= integrate(t0027,x) +--E 156 + +--S 157 of 518 +--m0027:= a0027-r0027 +--E 157 + +--S 158 of 518 +--d0027:= D(m0027,x) +--E 158 + +--S 159 of 518 +t0028:= (2+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (122) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 159 + +--S 160 of 518 +r0028:= x^(1/2)*(2+b*x)^(1/2)+2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 2asinh(------------) + \|b \|x \|b x + 2 +--R 2 +--R (123) ----------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 160 + +--S 161 of 518 +--a0028:= integrate(t0028,x) +--E 161 + +--S 162 of 518 +--m0028:= a0028-r0028 +--E 162 + +--S 163 of 518 +--d0028:= D(m0028,x) +--E 163 + +--S 164 of 518 +t0029:= (2+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (124) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 164 + +--S 165 of 518 +r0029:= 3/2*x^(1/2)*(2+b*x)^(1/2)+1/2*x^(1/2)*(2+b*x)^(3/2)+_ + 3*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +-+ +-+ +-------+ +--R 6asinh(------------) + (b x + 5)\|b \|x \|b x + 2 +--R 2 +--R (125) -------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 165 + +--S 166 of 518 +--a0029:= integrate(t0029,x) +--E 166 + +--S 167 of 518 +--m0029:= a0029-r0029 +--E 167 + +--S 168 of 518 +--d0029:= D(m0029,x) +--E 168 + +--S 169 of 518 +t0030:= 1/x^(1/2)/(2+b*x)^(1/2) +--R +--R +--R 1 +--R (126) -------------- +--R +-+ +-------+ +--R \|x \|b x + 2 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 518 +r0030:= 2*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asinh(------------) +--R 2 +--R (127) -------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 170 + +--S 171 of 518 +--a0030:= integrate(t0030,x) +--E 171 + +--S 172 of 518 +--m0030:= a0030-r0030 +--E 172 + +--S 173 of 518 +--d0030:= D(m0030,x) +--E 173 + +--S 174 of 518 +t0031:= (2+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + 2 +--R (128) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 174 + +--S 175 of 518 +r0031:= -2*(2+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 2\|b \|x asinh(------------) - 2\|b x + 2 +--R 2 +--R (129) ------------------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 175 + +--S 176 of 518 +--a0031:= integrate(t0031,x) +--E 176 + +--S 177 of 518 +--m0031:= a0031-r0031 +--E 177 + +--S 178 of 518 +--d0031:= D(m0031,x) +--E 178 + +--S 179 of 518 +t0032:= (2+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (130) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 179 + +--S 180 of 518 +r0032:= 3*b*x^(1/2)*(2+b*x)^(1/2)-2*(2+b*x)^(3/2)/x^(1/2)+_ + 6*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6\|b \|x asinh(------------) + (b x - 4)\|b x + 2 +--R 2 +--R (131) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 180 + +--S 181 of 518 +--a0032:= integrate(t0032,x) +--E 181 + +--S 182 of 518 +--m0032:= a0032-r0032 +--E 182 + +--S 183 of 518 +--d0032:= D(m0032,x) +--E 183 + +--S 184 of 518 +t0033:= (2+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (132) --------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 184 + +--S 185 of 518 +r0033:= 15/2*b*x^(1/2)*(2+b*x)^(1/2)+5/2*b*x^(1/2)*(2+b*x)^(3/2)-_ + 2*(2+b*x)^(5/2)/x^(1/2)+15*b^(1/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30\|b \|x asinh(------------) + (b x + 9b x - 16)\|b x + 2 +--R 2 +--R (133) ------------------------------------------------------------ +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 185 + +--S 186 of 518 +--a0033:= integrate(t0033,x) +--E 186 + +--S 187 of 518 +--m0033:= a0033-r0033 +--E 187 + +--S 188 of 518 +--d0033:= D(m0033,x) +--E 188 + +--S 189 of 518 +t0034:= (2+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + 2)\|b x + 2 +--R (134) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 189 + +--S 190 of 518 +r0034:= -2*b*(2+b*x)^(1/2)/x^(1/2)-2/3*(2+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +-------+ +--R 6b x\|b \|x asinh(------------) + (- 8b x - 4)\|b x + 2 +--R 2 +--R (135) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 190 + +--S 191 of 518 +--a0034:= integrate(t0034,x) +--E 191 + +--S 192 of 518 +--m0034:= a0034-r0034 +--E 192 + +--S 193 of 518 +--d0034:= D(m0034,x) +--E 193 + +--S 194 of 518 +t0035:= (2+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +-------+ +--R (b x + 4b x + 4)\|b x + 2 +--R (136) --------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 194 + +--S 195 of 518 +r0035:= 1/3*(3*b^2*x^2*(2+b*x)^(1/2)-28*b*x*(2+b*x)^(1/2)-8*(2+b*x)^(1/2)+_ + 30*b^(3/2)*asinh(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +-------+ +--R 30b x\|b \|x asinh(------------) + (3b x - 28b x - 8)\|b x + 2 +--R 2 +--R (137) ---------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 195 + +--S 196 of 518 +--a0035:= integrate(t0035,x) +--E 196 + +--S 197 of 518 +--m0035:= a0035-r0035 +--E 197 + +--S 198 of 518 +--d0035:= D(m0035,x) +--E 198 + +--S 199 of 518 +t0036:= x^(1/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (138) \|x \|b x + a +--R Type: Expression(Integer) +--E 199 + +--S 200 of 518 +r0036:= 1/4*a*x^(1/2)*(a+b*x)^(1/2)/b+1/2*x^(3/2)*(a+b*x)^(1/2)-_ + 1/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + (2b x + a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (139) ---------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 200 + +--S 201 of 518 +--a0036:= integrate(t0036,x) +--E 201 + +--S 202 of 518 +--m0036:= a0036-r0036 +--E 202 + +--S 203 of 518 +--d0036:= D(m0036,x) +--E 203 + +--S 204 of 518 +t0037:= x^(1/2)*(a+b*x)^(3/2) +--R +--R +--R +-+ +-------+ +--R (140) (b x + a)\|x \|b x + a +--R Type: Expression(Integer) +--E 204 + +--S 205 of 518 +r0037:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b-1/12*a*x^(1/2)*(a+b*x)^(3/2)/b+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)/b-_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 3a atanh(----------) + (8b x + 14a b x + 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (141) ------------------------------------------------------------------ +--R +-+ +--R 24b\|b +--R Type: Expression(Integer) +--E 205 + +--S 206 of 518 +--a0037:= integrate(t0037,x) +--E 206 + +--S 207 of 518 +--m0037:= a0037-r0037 +--E 207 + +--S 208 of 518 +--d0037:= D(m0037,x) +--E 208 + +--S 209 of 518 +t0038:= x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (142) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 209 + +--S 210 of 518 +r0038:= x^(1/2)*(a+b*x)^(1/2)/b-a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R - a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (143) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 210 + +--S 211 of 518 +--a0038:= integrate(t0038,x) +--E 211 + +--S 212 of 518 +--m0038:= a0038-r0038 +--E 212 + +--S 213 of 518 +--d0038:= D(m0038,x) +--E 213 + +--S 214 of 518 +t0039:= x^(1/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (144) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 214 + +--S 215 of 518 +r0039:= -2*x^(1/2)/b/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R 2\|b x + a atanh(----------) - 2\|b \|x +--R +-------+ +--R \|b x + a +--R (145) ---------------------------------------- +--R +-+ +-------+ +--R b\|b \|b x + a +--R Type: Expression(Integer) +--E 215 + +--S 216 of 518 +--a0039:= integrate(t0039,x) +--E 216 + +--S 217 of 518 +--m0039:= a0039-r0039 +--E 217 + +--S 218 of 518 +--d0039:= D(m0039,x) +--E 218 + +--S 219 of 518 +t0040:= x^(3/2)*(a+b*x)^(1/2) +--R +--R +--R +-+ +-------+ +--R (146) x\|x \|b x + a +--R Type: Expression(Integer) +--E 219 + +--S 220 of 518 +r0040:= -1/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^2+1/12*a*x^(3/2)*(a+b*x)^(1/2)/b+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)+_ + 1/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 3a atanh(----------) + (8b x + 2a b x - 3a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (147) --------------------------------------------------------------- +--R 2 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 220 + +--S 221 of 518 +--a0040:= integrate(t0040,x) +--E 221 + +--S 222 of 518 +--m0040:= a0040-r0040 +--E 222 + +--S 223 of 518 +--d0040:= D(m0040,x) +--E 223 + +--S 224 of 518 +t0041:= x^(3/2)/(a+b*x)^(1/2) +--R +--R +--R +-+ +--R x\|x +--R (148) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 224 + +--S 225 of 518 +r0041:= -3/4*a*x^(1/2)*(a+b*x)^(1/2)/b^2+1/2*x^(3/2)*(a+b*x)^(1/2)/b+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x - 3a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (149) ---------------------------------------------------- +--R 2 +-+ +--R 4b \|b +--R Type: Expression(Integer) +--E 225 + +--S 226 of 518 +--a0041:= integrate(t0041,x) +--E 226 + +--S 227 of 518 +--m0041:= a0041-r0041 +--E 227 + +--S 228 of 518 +--d0041:= D(m0041,x) +--E 228 + +--S 229 of 518 +t0042:= x^(3/2)/(a+b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (150) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 229 + +--S 230 of 518 +r0042:= -2*x^(3/2)/b/(a+b*x)^(1/2)+3*x^(1/2)*(a+b*x)^(1/2)/b^2-_ + 3*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R - 3a\|b x + a atanh(----------) + (b x + 3a)\|b \|x +--R +-------+ +--R \|b x + a +--R (151) ---------------------------------------------------- +--R 2 +-+ +-------+ +--R b \|b \|b x + a +--R Type: Expression(Integer) +--E 230 + +--S 231 of 518 +--a0042:= integrate(t0042,x) +--E 231 + +--S 232 of 518 +--m0042:= a0042-r0042 +--E 232 + +--S 233 of 518 +--d0042:= D(m0042,x) +--E 233 + +--S 234 of 518 +t0043:= x^(3/2)/(a+b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (152) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 234 + +--S 235 of 518 +r0043:= -2/3*x^(3/2)/b/(a+b*x)^(3/2)-2*x^(1/2)/b^2/(a+b*x)^(1/2)+_ + 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +-------+ \|b \|x +-+ +-+ +--R (6b x + 6a)\|b x + a atanh(----------) + (- 8b x - 6a)\|b \|x +--R +-------+ +--R \|b x + a +--R (153) -------------------------------------------------------------- +--R 3 2 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 235 + +--S 236 of 518 +--a0043:= integrate(t0043,x) +--E 236 + +--S 237 of 518 +--m0043:= a0043-r0043 +--E 237 + +--S 238 of 518 +--d0043:= D(m0043,x) +--E 238 + +--S 239 of 518 +t0044:= x^(5/2)/(a+b*x)^(1/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (154) ---------- +--R +-------+ +--R \|b x + a +--R Type: Expression(Integer) +--E 239 + +--S 240 of 518 +r0044:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)/b^3-5/12*a*x^(3/2)*(a+b*x)^(1/2)/b^2+_ + 1/3*x^(5/2)*(a+b*x)^(1/2)/b-_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R - 15a atanh(----------) + (8b x - 10a b x + 15a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (155) -------------------------------------------------------------------- +--R 3 +-+ +--R 24b \|b +--R Type: Expression(Integer) +--E 240 + +--S 241 of 518 +--a0044:= integrate(t0044,x) +--E 241 + +--S 242 of 518 +--m0044:= a0044-r0044 +--E 242 + +--S 243 of 518 +--d0044:= D(m0044,x) +--E 243 + +--S 244 of 518 +t0045:= x^(5/2)/(a+b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (156) ------------------- +--R +-------+ +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 244 + +--S 245 of 518 +r0045:= 1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)-_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))*(a+b*x)^(1/2))/_ + (a+b*x)^(1/2) +--R +--R +--R +-+ +-+ +--R 2 +-------+ \|b \|x 2 2 2 +-+ +-+ +--R 15a \|b x + a atanh(----------) + (2b x - 5a b x - 15a )\|b \|x +--R +-------+ +--R \|b x + a +--R (157) ----------------------------------------------------------------- +--R 3 +-+ +-------+ +--R 4b \|b \|b x + a +--R Type: Expression(Integer) +--E 245 + +--S 246 of 518 +--a0045:= integrate(t0045,x) +--E 246 + +--S 247 of 518 +--m0045:= a0045-r0045 +--E 247 + +--S 248 of 518 +--d0045:= D(m0045,x) +--E 248 + +--S 249 of 518 +t0046:= x^(5/2)/(a+b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (158) ------------------------------ +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 249 + +--S 250 of 518 +r0046:= -2/3*x^(5/2)/b/(a+b*x)^(3/2)-10/3*x^(3/2)/b^2/(a+b*x)^(1/2)+_ + 5*x^(1/2)*(a+b*x)^(1/2)/b^3-_ + 5*a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(7/2) +--R +--R +--R (159) +--R +-+ +-+ +--R 2 +-------+ \|b \|x +--R (- 15a b x - 15a )\|b x + a atanh(----------) +--R +-------+ +--R \|b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x + 20a b x + 15a )\|b \|x +--R / +--R 4 3 +-+ +-------+ +--R (3b x + 3a b )\|b \|b x + a +--R Type: Expression(Integer) +--E 250 + +--S 251 of 518 +--a0046:= integrate(t0046,x) +--E 251 + +--S 252 of 518 +--m0046:= a0046-r0046 +--E 252 + +--S 253 of 518 +--d0046:= D(m0046,x) +--E 253 + +--S 254 of 518 +t0047:= (a+b*x)^(1/2)/x^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (160) ---------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 254 + +--S 255 of 518 +r0047:= x^(1/2)*(a+b*x)^(1/2)+a*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +-+ +-+ +-------+ +--R a atanh(----------) + \|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (161) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 255 + +--S 256 of 518 +--a0047:= integrate(t0047,x) +--E 256 + +--S 257 of 518 +--m0047:= a0047-r0047 +--E 257 + +--S 258 of 518 +--d0047:= D(m0047,x) +--E 258 + +--S 259 of 518 +t0048:= (a+b*x)^(3/2)/x^(1/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (162) ------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 259 + +--S 260 of 518 +r0048:= 3/4*a*x^(1/2)*(a+b*x)^(1/2)+1/2*x^(1/2)*(a+b*x)^(3/2)+_ + 3/4*a^2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +-+ +-+ +-------+ +--R 3a atanh(----------) + (2b x + 5a)\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (163) ---------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 260 + +--S 261 of 518 +--a0048:= integrate(t0048,x) +--E 261 + +--S 262 of 518 +--m0048:= a0048-r0048 +--E 262 + +--S 263 of 518 +--d0048:= D(m0048,x) +--E 263 + +--S 264 of 518 +t0049:= (a+b*x)^(5/2)/x^(1/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (164) ------------------------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 264 + +--S 265 of 518 +r0049:= 5/8*a^2*x^(1/2)*(a+b*x)^(1/2)+5/12*a*x^(1/2)*(a+b*x)^(3/2)+_ + 1/3*x^(1/2)*(a+b*x)^(5/2)+_ + 5/8*a^3*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 3 \|b \|x 2 2 2 +-+ +-+ +-------+ +--R 15a atanh(----------) + (8b x + 26a b x + 33a )\|b \|x \|b x + a +--R +-------+ +--R \|b x + a +--R (165) ------------------------------------------------------------------ +--R +-+ +--R 24\|b +--R Type: Expression(Integer) +--E 265 + +--S 266 of 518 +--a0049:= integrate(t0049,x) +--E 266 + +--S 267 of 518 +--m0049:= a0049-r0049 +--E 267 + +--S 268 of 518 +--d0049:= D(m0049,x) +--E 268 + +--S 269 of 518 +t0050:= 1/x^(1/2)/(a+b*x)^(1/2) +--R +--R +--R 1 +--R (166) -------------- +--R +-+ +-------+ +--R \|x \|b x + a +--R Type: Expression(Integer) +--E 269 + +--S 270 of 518 +r0050:= 2*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atanh(----------) +--R +-------+ +--R \|b x + a +--R (167) ------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 270 + +--S 271 of 518 +--a0050:= integrate(t0050,x) +--E 271 + +--S 272 of 518 +--m0050:= a0050-r0050 +--E 272 + +--S 273 of 518 +--d0050:= D(m0050,x) +--E 273 + +--S 274 of 518 +t0051:= (a+b*x)^(1/2)/x^(3/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (168) ---------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 274 + +--S 275 of 518 +r0051:= -2*(a+b*x)^(1/2)/x^(1/2)+2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 2\|b \|x atanh(----------) - 2\|b x + a +--R +-------+ +--R \|b x + a +--R (169) ---------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 275 + +--S 276 of 518 +--a0051:= integrate(t0051,x) +--E 276 + +--S 277 of 518 +--m0051:= a0051-r0051 +--E 277 + +--S 278 of 518 +--d0051:= D(m0051,x) +--E 278 + +--S 279 of 518 +t0052:= (a+b*x)^(3/2)/x^(3/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (170) ------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 279 + +--S 280 of 518 +r0052:= 3*b*x^(1/2)*(a+b*x)^(1/2)-2*(a+b*x)^(3/2)/x^(1/2)+_ + 3*a*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 3a\|b \|x atanh(----------) + (b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (171) -------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 280 + +--S 281 of 518 +--a0052:= integrate(t0052,x) +--E 281 + +--S 282 of 518 +--m0052:= a0052-r0052 +--E 282 + +--S 283 of 518 +--d0052:= D(m0052,x) +--E 283 + +--S 284 of 518 +t0053:= (a+b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (172) ------------------------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 284 + +--S 285 of 518 +r0053:= 15/4*a*b*x^(1/2)*(a+b*x)^(1/2)+5/2*b*x^(1/2)*(a+b*x)^(3/2)-_ + 2*(a+b*x)^(5/2)/x^(1/2)+_ + 15/4*a^2*b^(1/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a \|b \|x atanh(----------) + (2b x + 9a b x - 8a )\|b x + a +--R +-------+ +--R \|b x + a +--R (173) ---------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 285 + +--S 286 of 518 +--a0053:= integrate(t0053,x) +--E 286 + +--S 287 of 518 +--m0053:= a0053-r0053 +--E 287 + +--S 288 of 518 +--d0053:= D(m0053,x) +--E 288 + +--S 289 of 518 +t0054:= (a+b*x)^(3/2)/x^(5/2) +--R +--R +--R +-------+ +--R (b x + a)\|b x + a +--R (174) ------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 289 + +--S 290 of 518 +r0054:= -2*b*(a+b*x)^(1/2)/x^(1/2)-2/3*(a+b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +-------+ +--R 6b x\|b \|x atanh(----------) + (- 8b x - 2a)\|b x + a +--R +-------+ +--R \|b x + a +--R (175) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 290 + +--S 291 of 518 +--a0054:= integrate(t0054,x) +--E 291 + +--S 292 of 518 +--m0054:= a0054-r0054 +--E 292 + +--S 293 of 518 +--d0054:= D(m0054,x) +--E 293 + +--S 294 of 518 +t0055:= (a+b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +-------+ +--R (b x + 2a b x + a )\|b x + a +--R (176) ------------------------------ +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 294 + +--S 295 of 518 +r0055:= 5*b^2*x^(1/2)*(a+b*x)^(1/2)-10/3*b*(a+b*x)^(3/2)/x^(1/2)-_ + 2/3*(a+b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atanh(b^(1/2)*x^(1/2)/(a+b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +-------+ +--R 15a b x\|b \|x atanh(----------) + (3b x - 14a b x - 2a )\|b x + a +--R +-------+ +--R \|b x + a +--R (177) -------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 295 + +--S 296 of 518 +--a0055:= integrate(t0055,x) +--E 296 + +--S 297 of 518 +--m0055:= a0055-r0055 +--E 297 + +--S 298 of 518 +--d0055:= D(m0055,x) +--E 298 + +--S 299 of 518 +t0056:= x^(1/2)*(2-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (178) \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 299 + +--S 300 of 518 +r0056:= -1/2*x^(1/2)*(2-b*x)^(1/2)/b+1/2*x^(3/2)*(2-b*x)^(1/2)+_ + asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + (b x - 1)\|- b x + 2 \|b \|x +--R 2 +--R (179) --------------------------------------------------- +--R +-+ +--R 2b\|b +--R Type: Expression(Integer) +--E 300 + +--S 301 of 518 +--a0056:= integrate(t0056,x) +--E 301 + +--S 302 of 518 +--m0056:= a0056-r0056 +--E 302 + +--S 303 of 518 +--d0056:= D(m0056,x) +--E 303 + +--S 304 of 518 +t0057:= x^(1/2)/(1-x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (180) ---------- +--R +-------+ +--R \|- x + 1 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 518 +r0057:= -(1-x)^(1/2)*x^(1/2)-asin((1-x)^(1/2)) +--R +--R +--R +-------+ +-------+ +-+ +--R (181) - asin(\|- x + 1 ) - \|- x + 1 \|x +--R Type: Expression(Integer) +--E 305 + +--S 306 of 518 +--a0057:= integrate(t0057,x) +--E 306 + +--S 307 of 518 +--m0057:= a0057-r0057 +--E 307 + +--S 308 of 518 +--d0057:= D(m0057,x) +--E 308 + +--S 309 of 518 +t0058:= x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (182) ------------ +--R +---------+ +--R \|- b x + 2 +--R Type: Expression(Integer) +--E 309 + +--S 310 of 518 +r0058:= -x^(1/2)*(2-b*x)^(1/2)/b+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) - \|- b x + 2 \|b \|x +--R 2 +--R (183) ------------------------------------------ +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 310 + +--S 311 of 518 +--a0058:= integrate(t0058,x) +--E 311 + +--S 312 of 518 +--m0058:= a0058-r0058 +--E 312 + +--S 313 of 518 +--d0058:= D(m0058,x) +--E 313 + +--S 314 of 518 +t0059:= x^(3/2)/(2-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (184) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 314 + +--S 315 of 518 +r0059:= 2*x^(3/2)/b/(2-b*x)^(1/2)+3*x^(1/2)*(2-b*x)^(1/2)/b^2-_ + 6*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x +-+ +-+ +--R - 6\|- b x + 2 asin(------------) + (- b x + 6)\|b \|x +--R 2 +--R (185) ------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 315 + +--S 316 of 518 +--a0059:= integrate(t0059,x) +--E 316 + +--S 317 of 518 +--m0059:= a0059-r0059 +--E 317 + +--S 318 of 518 +--d0059:= D(m0059,x) +--E 318 + +--S 319 of 518 +t0060:= x^(5/2)/(2-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (186) - --------------------- +--R +---------+ +--R (b x - 2)\|- b x + 2 +--R Type: Expression(Integer) +--E 319 + +--S 320 of 518 +r0060:= -1/2/b^(7/2)*(x^(5/2)*b^(5/2)-30*x^(1/2)*b^(1/2)+5*x^(3/2)*b^(3/2)+_ + 30*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*(2-b*x)^(1/2))/(2-b*x)^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R - 30\|- b x + 2 asin(------------) + (- b x - 5b x + 30)\|b \|x +--R 2 +--R (187) ----------------------------------------------------------------- +--R 3 +---------+ +-+ +--R 2b \|- b x + 2 \|b +--R Type: Expression(Integer) +--E 320 + +--S 321 of 518 +--a0060:= integrate(t0060,x) +--E 321 + +--S 322 of 518 +--m0060:= a0060-r0060 +--E 322 + +--S 323 of 518 +--d0060:= D(m0060,x) +--E 323 + +--S 324 of 518 +t0061:= x^(5/2)/(2-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (188) ----------------------------- +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R Type: Expression(Integer) +--E 324 + +--S 325 of 518 +r0061:= 2/3*x^(5/2)/b/(2-b*x)^(3/2)-10/3*x^(3/2)/b^2/(2-b*x)^(1/2)-_ + 5*x^(1/2)*(2-b*x)^(1/2)/b^3+_ + 10*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(7/2) +--R +--R +--R (189) +--R +-+ +-+ +-+ +--R +---------+ \|2 \|b \|x 2 2 +-+ +-+ +--R (30b x - 60)\|- b x + 2 asin(------------) + (3b x - 40b x + 60)\|b \|x +--R 2 +--R ------------------------------------------------------------------------- +--R 4 3 +---------+ +-+ +--R (3b x - 6b )\|- b x + 2 \|b +--R Type: Expression(Integer) +--E 325 + +--S 326 of 518 +--a0061:= integrate(t0061,x) +--E 326 + +--S 327 of 518 +--m0061:= a0061-r0061 +--E 327 + +--S 328 of 518 +--d0061:= D(m0061,x) +--E 328 + +--S 329 of 518 +t0062:= (2-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (190) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 329 + +--S 330 of 518 +r0062:= x^(1/2)*(2-b*x)^(1/2)+2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 2asin(------------) + \|- b x + 2 \|b \|x +--R 2 +--R (191) ------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 330 + +--S 331 of 518 +--a0062:= integrate(t0062,x) +--E 331 + +--S 332 of 518 +--m0062:= a0062-r0062 +--E 332 + +--S 333 of 518 +--d0062:= D(m0062,x) +--E 333 + +--S 334 of 518 +t0063:= (2-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (192) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 334 + +--S 335 of 518 +r0063:= 3/2*x^(1/2)*(2-b*x)^(1/2)+1/2*x^(1/2)*(2-b*x)^(3/2)+_ + 3*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +---------+ +-+ +-+ +--R 6asin(------------) + (- b x + 5)\|- b x + 2 \|b \|x +--R 2 +--R (193) ----------------------------------------------------- +--R +-+ +--R 2\|b +--R Type: Expression(Integer) +--E 335 + +--S 336 of 518 +--a0063:= integrate(t0063,x) +--E 336 + +--S 337 of 518 +--m0063:= a0063-r0063 +--E 337 + +--S 338 of 518 +--d0063:= D(m0063,x) +--E 338 + +--S 339 of 518 +t0064:= 1/x^(1/2)/(2-b*x)^(1/2) +--R +--R +--R 1 +--R (194) ---------------- +--R +---------+ +-+ +--R \|- b x + 2 \|x +--R Type: Expression(Integer) +--E 339 + +--S 340 of 518 +r0064:= 2*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +-+ +--R \|2 \|b \|x +--R 2asin(------------) +--R 2 +--R (195) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 340 + +--S 341 of 518 +--a0064:= integrate(t0064,x) +--E 341 + +--S 342 of 518 +--m0064:= a0064-r0064 +--E 342 + +--S 343 of 518 +--d0064:= D(m0064,x) +--E 343 + +--S 344 of 518 +t0065:= (2-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + 2 +--R (196) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 344 + +--S 345 of 518 +r0065:= -2*(2-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 2\|b \|x asin(------------) - 2\|- b x + 2 +--R 2 +--R (197) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 345 + +--S 346 of 518 +--a0065:= integrate(t0065,x) +--E 346 + +--S 347 of 518 +--m0065:= a0065-r0065 +--E 347 + +--S 348 of 518 +--d0065:= D(m0065,x) +--E 348 + +--S 349 of 518 +t0066:= (2-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (198) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 518 +r0066:= -3*b*x^(1/2)*(2-b*x)^(1/2)-2*(2-b*x)^(3/2)/x^(1/2)-_ + 6*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R - 6\|b \|x asin(------------) + (- b x - 4)\|- b x + 2 +--R 2 +--R (199) ------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 350 + +--S 351 of 518 +--a0066:= integrate(t0066,x) +--E 351 + +--S 352 of 518 +--m0066:= a0066-r0066 +--E 352 + +--S 353 of 518 +--d0066:= D(m0066,x) +--E 353 + +--S 354 of 518 +t0067:= (2-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (200) ----------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 518 +r0067:= -15/2*b*x^(1/2)*(2-b*x)^(1/2)-5/2*b*x^(1/2)*(2-b*x)^(3/2)-_ + 2*(2-b*x)^(5/2)/x^(1/2)-15*b^(1/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R - 30\|b \|x asin(------------) + (b x - 9b x - 16)\|- b x + 2 +--R 2 +--R (201) --------------------------------------------------------------- +--R +-+ +--R 2\|x +--R Type: Expression(Integer) +--E 355 + +--S 356 of 518 +--a0067:= integrate(t0067,x) +--E 356 + +--S 357 of 518 +--m0067:= a0067-r0067 +--E 357 + +--S 358 of 518 +--d0067:= D(m0067,x) +--E 358 + +--S 359 of 518 +t0068:= (2-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + 2)\|- b x + 2 +--R (202) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 359 + +--S 360 of 518 +r0068:= 2*b*(2-b*x)^(1/2)/x^(1/2)-2/3*(2-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2)) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x +---------+ +--R 6b x\|b \|x asin(------------) + (8b x - 4)\|- b x + 2 +--R 2 +--R (203) ------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 360 + +--S 361 of 518 +--a0068:= integrate(t0068,x) +--E 361 + +--S 362 of 518 +--m0068:= a0068-r0068 +--E 362 + +--S 363 of 518 +--d0068:= D(m0068,x) +--E 363 + +--S 364 of 518 +t0069:= (2-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 +---------+ +--R (b x - 4b x + 4)\|- b x + 2 +--R (204) ----------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 364 + +--S 365 of 518 +r0069:= 1/3*(3*b^2*x^2*(2-b*x)^(1/2)+28*b*x*(2-b*x)^(1/2)-8*(2-b*x)^(1/2)+_ + 30*b^(3/2)*asin(1/2*b^(1/2)*x^(1/2)*2^(1/2))*x^(3/2))/x^(3/2) +--R +--R +--R +-+ +-+ +-+ +--R +-+ +-+ \|2 \|b \|x 2 2 +---------+ +--R 30b x\|b \|x asin(------------) + (3b x + 28b x - 8)\|- b x + 2 +--R 2 +--R (205) ----------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 365 + +--S 366 of 518 +--a0069:= integrate(t0069,x) +--E 366 + +--S 367 of 518 +--m0069:= a0069-r0069 +--E 367 + +--S 368 of 518 +--d0069:= D(m0069,x) +--E 368 + +--S 369 of 518 +t0070:= x^(1/2)*(a-b*x)^(1/2) +--R +--R +--R +---------+ +-+ +--R (206) \|- b x + a \|x +--R Type: Expression(Integer) +--E 369 + +--S 370 of 518 +r0070:= -1/4*a*x^(1/2)*(a-b*x)^(1/2)/b+1/2*x^(3/2)*(a-b*x)^(1/2)+_ + 1/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + (2b x - a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (207) ----------------------------------------------------- +--R +-+ +--R 4b\|b +--R Type: Expression(Integer) +--E 370 + +--S 371 of 518 +--a0070:= integrate(t0070,x) +--E 371 + +--S 372 of 518 +--m0070:= a0070-r0070 +--E 372 + +--S 373 of 518 +--d0070:= D(m0070,x) +--E 373 + +--S 374 of 518 +t0071:= x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R +-+ +--R \|x +--R (208) ------------ +--R +---------+ +--R \|- b x + a +--R Type: Expression(Integer) +--E 374 + +--S 375 of 518 +r0071:= -x^(1/2)*(a-b*x)^(1/2)/b+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) - \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (209) ------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 375 + +--S 376 of 518 +--a0071:= integrate(t0071,x) +--E 376 + +--S 377 of 518 +--m0071:= a0071-r0071 +--E 377 + +--S 378 of 518 +--d0071:= D(m0071,x) +--E 378 + +--S 379 of 518 +t0072:= x^(1/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R \|x +--R (210) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 379 + +--S 380 of 518 +r0072:= 2*x^(1/2)/b/(a-b*x)^(1/2)-2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(3/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 2\|- b x + a atan(------------) + 2\|b \|x +--R +---------+ +--R \|- b x + a +--R (211) --------------------------------------------- +--R +---------+ +-+ +--R b\|- b x + a \|b +--R Type: Expression(Integer) +--E 380 + +--S 381 of 518 +--a0072:= integrate(t0072,x) +--E 381 + +--S 382 of 518 +--m0072:= a0072-r0072 +--E 382 + +--S 383 of 518 +--d0072:= D(m0072,x) +--E 383 + +--S 384 of 518 +t0073:= x^(3/2)/(a-b*x)^(3/2) +--R +--R +--R +-+ +--R x\|x +--R (212) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 384 + +--S 385 of 518 +r0073:= 2*x^(3/2)/b/(a-b*x)^(1/2)+3*x^(1/2)*(a-b*x)^(1/2)/b^2-_ + 3*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R - 3a\|- b x + a atan(------------) + (- b x + 3a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (213) --------------------------------------------------------- +--R 2 +---------+ +-+ +--R b \|- b x + a \|b +--R Type: Expression(Integer) +--E 385 + +--S 386 of 518 +--a0073:= integrate(t0073,x) +--E 386 + +--S 387 of 518 +--m0073:= a0073-r0073 +--E 387 + +--S 388 of 518 +--d0073:= D(m0073,x) +--E 388 + +--S 389 of 518 +t0074:= x^(3/2)/(a-b*x)^(5/2) +--R +--R +--R +-+ +--R x\|x +--R (214) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 518 +r0074:= 2/3*x^(3/2)/b/(a-b*x)^(3/2)-2*x^(1/2)/b^2/(a-b*x)^(1/2)+_ + 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(5/2) +--R +--R +--R +-+ +-+ +--R +---------+ \|b \|x +-+ +-+ +--R (6b x - 6a)\|- b x + a atan(------------) + (- 8b x + 6a)\|b \|x +--R +---------+ +--R \|- b x + a +--R (215) ----------------------------------------------------------------- +--R 3 2 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 390 + +--S 391 of 518 +--a0074:= integrate(t0074,x) +--E 391 + +--S 392 of 518 +--m0074:= a0074-r0074 +--E 392 + +--S 393 of 518 +--d0074:= D(m0074,x) +--E 393 + +--S 394 of 518 +t0075:= x^(5/2)/(a-b*x)^(3/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (216) - --------------------- +--R +---------+ +--R (b x - a)\|- b x + a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 518 +r0075:= -1/4/b^(7/2)*(2*x^(5/2)*b^(5/2)-15*a^2*x^(1/2)*b^(1/2)+_ + 5*a*x^(3/2)*b^(3/2)+_ + 15*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))*(a-b*x)^(1/2))/(a-b*x)^(1/2) +--R +--R +--R (217) +--R +-+ +-+ +--R 2 +---------+ \|b \|x 2 2 2 +-+ +-+ +--R - 15a \|- b x + a atan(------------) + (- 2b x - 5a b x + 15a )\|b \|x +--R +---------+ +--R \|- b x + a +--R ------------------------------------------------------------------------ +--R 3 +---------+ +-+ +--R 4b \|- b x + a \|b +--R Type: Expression(Integer) +--E 395 + +--S 396 of 518 +--a0075:= integrate(t0075,x) +--E 396 + +--S 397 of 518 +--m0075:= a0075-r0075 +--E 397 + +--S 398 of 518 +--d0075:= D(m0075,x) +--E 398 + +--S 399 of 518 +t0076:= x^(5/2)/(a-b*x)^(5/2) +--R +--R +--R 2 +-+ +--R x \|x +--R (218) -------------------------------- +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 518 +r0076:= 2/3*x^(5/2)/b/(a-b*x)^(3/2)-10/3*x^(3/2)/b^2/(a-b*x)^(1/2)-_ + 5*x^(1/2)*(a-b*x)^(1/2)/b^3+_ + 5*a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(7/2) +--R +--R +--R (219) +--R +-+ +-+ +--R 2 +---------+ \|b \|x +--R (15a b x - 15a )\|- b x + a atan(------------) +--R +---------+ +--R \|- b x + a +--R + +--R 2 2 2 +-+ +-+ +--R (3b x - 20a b x + 15a )\|b \|x +--R / +--R 4 3 +---------+ +-+ +--R (3b x - 3a b )\|- b x + a \|b +--R Type: Expression(Integer) +--E 400 + +--S 401 of 518 +--a0076:= integrate(t0076,x) +--E 401 + +--S 402 of 518 +--m0076:= a0076-r0076 +--E 402 + +--S 403 of 518 +--d0076:= D(m0076,x) +--E 403 + +--S 404 of 518 +t0077:= (a-b*x)^(1/2)/x^(1/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (220) ------------ +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 404 + +--S 405 of 518 +r0077:= x^(1/2)*(a-b*x)^(1/2)+a*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +---------+ +-+ +-+ +--R a atan(------------) + \|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (221) ------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 405 + +--S 406 of 518 +--a0077:= integrate(t0077,x) +--E 406 + +--S 407 of 518 +--m0077:= a0077-r0077 +--E 407 + +--S 408 of 518 +--d0077:= D(m0077,x) +--E 408 + +--S 409 of 518 +t0078:= (a-b*x)^(3/2)/x^(1/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (222) ----------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 409 + +--S 410 of 518 +r0078:= 3/4*a*x^(1/2)*(a-b*x)^(1/2)+1/2*x^(1/2)*(a-b*x)^(3/2)+_ + 3/4*a^2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R 2 \|b \|x +---------+ +-+ +-+ +--R 3a atan(------------) + (- 2b x + 5a)\|- b x + a \|b \|x +--R +---------+ +--R \|- b x + a +--R (223) --------------------------------------------------------- +--R +-+ +--R 4\|b +--R Type: Expression(Integer) +--E 410 + +--S 411 of 518 +--a0078:= integrate(t0078,x) +--E 411 + +--S 412 of 518 +--m0078:= a0078-r0078 +--E 412 + +--S 413 of 518 +--d0078:= D(m0078,x) +--E 413 + +--S 414 of 518 +t0079:= 1/x^(1/2)/(a-b*x)^(1/2) +--R +--R +--R 1 +--R (224) ---------------- +--R +---------+ +-+ +--R \|- b x + a \|x +--R Type: Expression(Integer) +--E 414 + +--S 415 of 518 +r0079:= 2*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2))/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|b \|x +--R 2atan(------------) +--R +---------+ +--R \|- b x + a +--R (225) ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 415 + +--S 416 of 518 +--a0079:= integrate(t0079,x) +--E 416 + +--S 417 of 518 +--m0079:= a0079-r0079 +--E 417 + +--S 418 of 518 +--d0079:= D(m0079,x) +--E 418 + +--S 419 of 518 +t0080:= (a-b*x)^(1/2)/x^(3/2) +--R +--R +--R +---------+ +--R \|- b x + a +--R (226) ------------ +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 518 +r0080:= -2*(a-b*x)^(1/2)/x^(1/2)-2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 2\|b \|x atan(------------) - 2\|- b x + a +--R +---------+ +--R \|- b x + a +--R (227) --------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 420 + +--S 421 of 518 +--a0080:= integrate(t0080,x) +--E 421 + +--S 422 of 518 +--m0080:= a0080-r0080 +--E 422 + +--S 423 of 518 +--d0080:= D(m0080,x) +--E 423 + +--S 424 of 518 +t0081:= (a-b*x)^(3/2)/x^(3/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (228) ----------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 424 + +--S 425 of 518 +r0081:= -3*b*x^(1/2)*(a-b*x)^(1/2)-2*(a-b*x)^(3/2)/x^(1/2)-_ + 3*a*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R - 3a\|b \|x atan(------------) + (- b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (229) --------------------------------------------------------- +--R +-+ +--R \|x +--R Type: Expression(Integer) +--E 425 + +--S 426 of 518 +--a0081:= integrate(t0081,x) +--E 426 + +--S 427 of 518 +--m0081:= a0081-r0081 +--E 427 + +--S 428 of 518 +--d0081:= D(m0081,x) +--E 428 + +--S 429 of 518 +t0082:= (a-b*x)^(5/2)/x^(3/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (230) -------------------------------- +--R +-+ +--R x\|x +--R Type: Expression(Integer) +--E 429 + +--S 430 of 518 +r0082:= -15/4*a*b*x^(1/2)*(a-b*x)^(1/2)-5/2*b*x^(1/2)*(a-b*x)^(3/2)-_ + 2*(a-b*x)^(5/2)/x^(1/2)-_ + 15/4*a^2*b^(1/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (231) +--R +-+ +-+ +--R 2 +-+ +-+ \|b \|x 2 2 2 +---------+ +--R - 15a \|b \|x atan(------------) + (2b x - 9a b x - 8a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R --------------------------------------------------------------------- +--R +-+ +--R 4\|x +--R Type: Expression(Integer) +--E 430 + +--S 431 of 518 +--a0082:= integrate(t0082,x) +--E 431 + +--S 432 of 518 +--m0082:= a0082-r0082 +--E 432 + +--S 433 of 518 +--d0082:= D(m0082,x) +--E 433 + +--S 434 of 518 +t0083:= (a-b*x)^(3/2)/x^(5/2) +--R +--R +--R +---------+ +--R (- b x + a)\|- b x + a +--R (232) ----------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 434 + +--S 435 of 518 +r0083:= 2*b*(a-b*x)^(1/2)/x^(1/2)-2/3*(a-b*x)^(3/2)/x^(3/2)+_ + 2*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ +-+ \|b \|x +---------+ +--R 6b x\|b \|x atan(------------) + (8b x - 2a)\|- b x + a +--R +---------+ +--R \|- b x + a +--R (233) -------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 435 + +--S 436 of 518 +--a0083:= integrate(t0083,x) +--E 436 + +--S 437 of 518 +--m0083:= a0083-r0083 +--E 437 + +--S 438 of 518 +--d0083:= D(m0083,x) +--E 438 + +--S 439 of 518 +t0084:= (a-b*x)^(5/2)/x^(5/2) +--R +--R +--R 2 2 2 +---------+ +--R (b x - 2a b x + a )\|- b x + a +--R (234) -------------------------------- +--R 2 +-+ +--R x \|x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 518 +r0084:= 5*b^2*x^(1/2)*(a-b*x)^(1/2)+10/3*b*(a-b*x)^(3/2)/x^(1/2)-_ + 2/3*(a-b*x)^(5/2)/x^(3/2)+_ + 5*a*b^(3/2)*atan(b^(1/2)*x^(1/2)/(a-b*x)^(1/2)) +--R +--R +--R (235) +--R +-+ +-+ +--R +-+ +-+ \|b \|x 2 2 2 +---------+ +--R 15a b x\|b \|x atan(------------) + (3b x + 14a b x - 2a )\|- b x + a +--R +---------+ +--R \|- b x + a +--R ----------------------------------------------------------------------- +--R +-+ +--R 3x\|x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 518 +--a0084:= integrate(t0084,x) +--E 441 + +--S 442 of 518 +--m0084:= a0084-r0084 +--E 442 + +--S 443 of 518 +--d0084:= D(m0084,x) +--E 443 + +--S 444 of 518 +t0085:= x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 3 +--R x +--R (236) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 444 + +--S 445 of 518 +r0085:= -2/3*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 5/8*(b*c+a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 5/12*(b*c+a*d)*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/3*x^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d+_ + 3/2*a*c*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(5/2)/d^(5/2)-5/8*(b*c+a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2) +--R +--R +--R (237) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (- 15a d - 9a b c d - 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +--R (8b d x + (- 10a b d - 10b c d)x + 15a d + 14a b c d + 15b c )\|b +--R * +--R +-+ +-------+ +-------+ +--R \|d \|b x + a \|d x + c +--R / +--R 3 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 445 + +--S 446 of 518 +--a0085:= integrate(t0085,x) +--E 446 + +--S 447 of 518 +--m0085:= a0085-r0085 +--E 447 + +--S 448 of 518 +--d0085:= D(m0085,x) +--E 448 + +--S 449 of 518 +t0086:= x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +--R x +--R (238) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 449 + +--S 450 of 518 +r0086:= -3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + a*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/_ + d^(3/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (239) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (3a d + 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x - 3a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression(Integer) +--E 450 + +--S 451 of 518 +--a0086:= integrate(t0086,x) +--E 451 + +--S 452 of 518 +--m0086:= a0086-r0086 +--E 452 + +--S 453 of 518 +--d0086:= D(m0086,x) +--E 453 + +--S 454 of 518 +t0087:= x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R x +--R (240) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 454 + +--S 455 of 518 +r0087:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d-_ + (b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (- a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (241) ----------------------------------------------------------------- +--R +-+ +-+ +--R b d\|b \|d +--R Type: Expression(Integer) +--E 455 + +--S 456 of 518 +--a0087:= integrate(t0087,x) +--E 456 + +--S 457 of 518 +--m0087:= a0087-r0087 +--E 457 + +--S 458 of 518 +--d0087:= D(m0087,x) +--E 458 + +--S 459 of 518 +t0088:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (242) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 459 + +--S 460 of 518 +r0088:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (243) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 460 + +--S 461 of 518 +--a0088:= integrate(t0088,x) +--E 461 + +--S 462 of 518 +--m0088:= a0088-r0088 +--E 462 + +--S 463 of 518 +--d0088:= D(m0088,x) +--E 463 + +--S 464 of 518 +t0089:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (244) --------------------- +--R +-------+ +-------+ +--R x\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 464 + +--S 465 of 518 +r0089:= -2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(1/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R (245) - ---------------------- +--R +-+ +-+ +--R \|a \|c +--R Type: Expression(Integer) +--E 465 + +--S 466 of 518 +--a0089:= integrate(t0089,x) +--E 466 + +--S 467 of 518 +--m0089:= a0089-r0089 +--E 467 + +--S 468 of 518 +--d0089:= D(m0089,x) +--E 468 + +--S 469 of 518 +t0090:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (246) ---------------------- +--R 2 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 469 + +--S 470 of 518 +r0090:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x+_ + (b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(3/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d + b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (247) ----------------------------------------------------------------- +--R +-+ +-+ +--R a c x\|a \|c +--R Type: Expression(Integer) +--E 470 + +--S 471 of 518 +--a0090:= integrate(t0090,x) +--E 471 + +--S 472 of 518 +--m0090:= a0090-r0090 +--E 472 + +--S 473 of 518 +--d0090:= D(m0090,x) +--E 473 + +--S 474 of 518 +t0091:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (248) ---------------------- +--R 3 +-------+ +-------+ +--R x \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 474 + +--S 475 of 518 +r0091:= -1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c/x^2+_ + 3/4*(b*c+a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(3/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (249) +--R +-+ +-------+ +--R 2 2 2 2 2 \|c \|b x + a +--R (- 3a d - 2a b c d - 3b c )x atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R ((3a d + 3b c)x - 2a c)\|a \|c \|b x + a \|d x + c +--R / +--R 2 2 2 +-+ +-+ +--R 4a c x \|a \|c +--R Type: Expression(Integer) +--E 475 + +--S 476 of 518 +--a0091:= integrate(t0091,x) +--E 476 + +--S 477 of 518 +--m0091:= a0091-r0091 +--E 477 + +--S 478 of 518 +--d0091:= D(m0091,x) +--E 478 + +--S 479 of 518 +t0092:= x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (250) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 479 + +--S 480 of 518 +r0092:= -2*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 7/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^3-_ + 3/4*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^2+_ + 1/2*x*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2+_ + 3*c^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(7/2)+3/4*(b*c+a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (251) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 +-------+ \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 2 2 2 3 2 2 2 2 2 +--R (2a b d - 2b c d )x + (- 3a d - 2a b c d + 5b c d)x - 3a c d +--R + +--R 2 2 3 +--R - 4a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 4 3 3 +-+ +-+ +-------+ +--R (4a b d - 4b c d )\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 480 + +--S 481 of 518 +--a0092:= integrate(t0092,x) +--E 481 + +--S 482 of 518 +--m0092:= a0092-r0092 +--E 482 + +--S 483 of 518 +--d0092:= D(m0092,x) +--E 483 + +--S 484 of 518 +t0093:= x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (252) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 484 + +--S 485 of 518 +r0093:= 2*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-_ + 3*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/_ + d^(5/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2) +--R +--R +--R (253) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|d \|b x + a +--R (- a d - 2a b c d + 3b c )\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((a d - b c d)x + a c d - 3b c )\|b \|d \|b x + a +--R / +--R 3 2 2 +-+ +-+ +-------+ +--R (a b d - b c d )\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 485 + +--S 486 of 518 +--a0093:= integrate(t0093,x) +--E 486 + +--S 487 of 518 +--m0093:= a0093-r0093 +--E 487 + +--S 488 of 518 +--d0093:= D(m0093,x) +--E 488 + +--S 489 of 518 +t0094:= x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R x +--R (254) ----------------------------- +--R +-------+ +-------+ +--R (d x + c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 489 + +--S 490 of 518 +r0094:= -2*c*(a+b*x)^(1/2)/d/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +-+ +-+ +-------+ +--R (2a d - 2b c)\|d x + c atanh(--------------) + 2c\|b \|d \|b x + a +--R +-+ +-------+ +--R \|b \|d x + c +--R (255) ------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a d - b c d)\|b \|d \|d x + c +--R Type: Expression(Integer) +--E 490 + +--S 491 of 518 +--a0094:= integrate(t0094,x) +--E 491 + +--S 492 of 518 +--m0094:= a0094-r0094 +--E 492 + +--S 493 of 518 +--d0094:= D(m0094,x) +--E 493 + +--S 494 of 518 +t0095:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (256) -------------------------------- +--R 2 +-------+ +-------+ +--R (d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 494 + +--S 495 of 518 +r0095:= -2*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R (257) +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +-+ +-+ +-------+ +--R (- 2a d + 2b c)\|d x + c atanh(--------------) + 2d\|a \|c \|b x + a +--R +-+ +-------+ +--R \|a \|d x + c +--R --------------------------------------------------------------------- +--R 2 +-+ +-+ +-------+ +--R (a c d - b c )\|a \|c \|d x + c +--R Type: Expression(Integer) +--E 495 + +--S 496 of 518 +--a0095:= integrate(t0095,x) +--E 496 + +--S 497 of 518 +--m0095:= a0095-r0095 +--E 497 + +--S 498 of 518 +--d0095:= D(m0095,x) +--E 498 + +--S 499 of 518 +t0096:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (258) --------------------------------- +--R 3 2 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 499 + +--S 500 of 518 +r0096:= 2*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(3/2)+_ + 3*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (259) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ \|c \|b x + a +--R (3a d - 2a b c d - b c )x\|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 +-+ +-+ +-------+ +--R ((- 3a d + b c d)x - a c d + b c )\|a \|c \|b x + a +--R / +--R 2 2 3 +-+ +-+ +-------+ +--R (a c d - a b c )x\|a \|c \|d x + c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 518 +--a0096:= integrate(t0096,x) +--E 501 + +--S 502 of 518 +--m0096:= a0096-r0096 +--E 502 + +--S 503 of 518 +--d0096:= D(m0096,x) +--E 503 + +--S 504 of 518 +t0097:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (260) --------------------------------- +--R 4 3 +-------+ +-------+ +--R (d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 504 + +--S 505 of 518 +r0097:= -2*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^2/x^2+_ + 3/4*b*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a^2/c^2/x+_ + 7/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x-_ + 3*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/_ + c^(7/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (261) +--R 3 3 2 2 2 2 3 3 2 +-------+ +--R (- 15a d + 9a b c d + 3a b c d + 3b c )x \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 2 2 2 2 2 2 3 +--R (15a d - 4a b c d - 3b c d)x + (5a c d - 2a b c d - 3b c )x +--R + +--R 2 2 3 +--R - 2a c d + 2a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 2 4 2 +-+ +-+ +-------+ +--R (4a c d - 4a b c )x \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 505 + +--S 506 of 518 +--a0097:= integrate(t0097,x) +--E 506 + +--S 507 of 518 +--m0097:= a0097-r0097 +--E 507 + +--S 508 of 518 +--d0097:= D(m0097,x) +--E 508 + +--S 509 of 518 +t0098:= x^5/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 5 +--R x +--R (262) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 509 + +--S 510 of 518 +r0098:= -2/3*a^5*(a+b*x)^(1/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 20/3*a^3*(a+b*x)^(3/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a^4*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)-_ + 20/3*a^2*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(7/2)/b^5/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(9/2)/b^5/d/(c+d*x)^(3/2)+_ + 20*a^3*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 4/3*a^5*(a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 100/3*a^2*(a+b*x)^(3/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 70/3*a*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 6*(a+b*x)^(7/2)/b^4/d^2/(c+d*x)^(1/2)+_ + 50*a^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 175/4*a*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 105/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^5-_ + 175/6*a*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 35/4*(b*c-a*d)*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^3/d^4+_ + 7*(a+b*x)^(5/2)*(c+d*x)^(1/2)/b^3/d^3-_ + 20*a^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/_ + d^(5/2)-50*a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(7/2)-_ + 175/4*a*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(9/2)-_ + 105/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(11/2) +--R +--R +--R (263) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R - 15a d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 5 +--R - 315b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 15a c d - 15a b c d - 30a b c d - 150a b c d + 525a b c d +--R + +--R 5 6 +--R - 315b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 6 3 5 4 2 4 4 +--R (8a b d - 16a b c d + 8b c d )x +--R + +--R 3 6 2 2 5 3 2 4 4 3 3 3 +--R (- 10a b d + 2a b c d + 26a b c d - 18b c d )x +--R + +--R 4 6 2 2 2 4 3 3 3 4 4 2 2 +--R (15a d + 18a b c d - 96a b c d + 63b c d )x +--R + +--R 4 5 3 2 4 2 2 3 3 3 4 2 4 5 +--R (30a c d + 30a b c d + 62a b c d - 574a b c d + 420b c d)x +--R + +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 6 +--R 15a c d + 20a b c d + 38a b c d - 420a b c d + 315b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 3 8 4 7 5 2 6 2 3 7 4 2 6 +--R (24a b d - 48a b c d + 24b c d )x + 24a b c d - 48a b c d +--R + +--R 5 3 5 +--R 24b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression(Integer) +--E 510 + +--S 511 of 518 +--a0098:= integrate(t0098,x) +--E 511 + +--S 512 of 518 +--m0098:= a0098-r0098 +--E 512 + +--S 513 of 518 +--d0098:= D(m0098,x) +--E 513 + +--S 514 of 518 +t0099:= x^4/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 4 +--R x +--R (264) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 514 + +--S 515 of 518 +r0099:= 2/3*a^4*(a+b*x)^(1/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4*a^2*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(3/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(5/2)/b^4/d/(c+d*x)^(3/2)-_ + 2/3*(a+b*x)^(7/2)/b^4/d/(c+d*x)^(3/2)-_ + 12*a^2*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)+4/3*a^4*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)^2/(c+d*x)^(1/2)+40/3*a*(a+b*x)^(3/2)/b^3/d^2/_ + (c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 20*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^2/d^4+_ + 35/6*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d^3+_ + 12*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)+20*a*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2)+35/4*(b*c-a*d)^2*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(9/2) +--R +--R +--R (265) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (9a d + 12a b c d + 54a b c d - 180a b c d + 105b c d)x + 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 54a b c d - 180a b c d + 105b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 5 2 4 3 2 3 3 +--R (6a b d - 12a b c d + 6b c d )x +--R + +--R 3 5 2 4 2 2 3 3 3 2 2 +--R (- 9a d - 3a b c d + 33a b c d - 21b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 3 2 3 +--R (- 18a c d - 24a b c d + 198a b c d - 140b c d)x - 9a c d +--R + +--R 2 3 2 2 4 3 5 +--R - 15a b c d + 145a b c d - 105b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 2 7 3 6 4 2 5 2 2 6 3 2 5 +--R (12a b d - 24a b c d + 12b c d )x + 12a b c d - 24a b c d +--R + +--R 4 3 4 +--R 12b c d +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|d x + c +--R Type: Expression(Integer) +--E 515 + +--S 516 of 518 +--a0099:= integrate(t0099,x) +--E 516 + +--S 517 of 518 +--m0099:= a0099-r0099 +--E 517 + +--S 518 of 518 +--d0099:= D(m0099,x) +--E 518 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic000-099.input.pdf b/src/axiom-website/CATS/richalgebraic000-099.input.pdf new file mode 100644 index 0000000..0ea2edb Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic000-099.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet b/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet new file mode 100644 index 0000000..e4f1350 --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic100-199.input.pamphlet @@ -0,0 +1,13567 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic100-199.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic100-199.output +)spool richalgebraic100-199.output +)set message test on +)set message auto off +)clear all + +--S 1 of 512 +t0100:= x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 3 +--R x +--R (1) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 1 + +--S 2 of 512 +r0100:= -2/3*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*c^3*(a+b*x)^(1/2)/d^3/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 6*c^2*(a+b*x)^(1/2)/d^3/(b*c-a*d)/(c+d*x)^(1/2)+(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(1/2)/d^(7/2)-a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (2) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 3a d - 9a b c d + 27a b c d - 15b c d)x - 3a c d - 9a b c d +--R + +--R 2 3 3 4 +--R 27a b c d - 15b c +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 4 3 2 2 2 2 2 3 2 2 2 3 +--R (3a d - 6a b c d + 3b c d )x + (6a c d - 30a b c d + 20b c d)x +--R + +--R 2 2 2 3 2 4 +--R 3a c d - 22a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +--R \|b \|d \|b x + a +--R / +--R 2 6 2 5 3 2 4 2 5 2 2 4 3 3 3 +-+ +--R ((3a b d - 6a b c d + 3b c d )x + 3a b c d - 6a b c d + 3b c d )\|b +--R * +--R +-+ +-------+ +--R \|d \|d x + c +--R Type: Expression(Integer) +--E 2 + +--S 3 of 512 +--a0100:= integrate(t0100,x) +--E 3 + +--S 4 of 512 +--m0100:= a0100-r0100 +--E 4 + +--S 5 of 512 +--d0100:= D(m0100,x) +--E 5 + +--S 6 of 512 +t0101:= x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 2 +--R x +--R (3) ---------------------------------------- +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 6 + +--S 7 of 512 +r0101:= 2/3*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*c^2*(a+b*x)^(1/2)/d^2/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 4*c*(a+b*x)^(1/2)/d^2/(b*c-a*d)/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(5/2) +--R +--R +--R (4) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((6a d - 12a b c d + 6b c d)x + 6a c d - 12a b c d + 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|d \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 3 +-+ +-+ +-------+ +--R ((12a c d - 8b c d)x + 10a c d - 6b c )\|b \|d \|b x + a +--R / +--R 2 5 4 2 2 3 2 4 2 3 2 3 2 +-+ +-+ +--R ((3a d - 6a b c d + 3b c d )x + 3a c d - 6a b c d + 3b c d )\|b \|d +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 7 + +--S 8 of 512 +--a0101:= integrate(t0101,x) +--E 8 + +--S 9 of 512 +--m0101:= a0101-r0101 +--E 9 + +--S 10 of 512 +--d0101:= D(m0101,x) +--E 10 + +--S 11 of 512 +t0102:= 1/x/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (5) ------------------------------------------ +--R 2 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 11 + +--S 12 of 512 +r0102:= -2/3*d*(a+b*x)^(1/2)/c/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d*(a+b*x)^(1/2)/c/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 2*d*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(5/2) +--R +--R +--R (6) +--R 2 3 2 2 2 2 2 2 2 3 +--R ((- 6a d + 12a b c d - 6b c d)x - 6a c d + 12a b c d - 6b c ) +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 2 2 +-+ +-+ +-------+ +--R ((6a d - 10b c d )x + 8a c d - 12b c d)\|a \|c \|b x + a +--R / +--R 2 2 3 3 2 2 4 2 3 2 4 2 5 +-+ +-+ +--R ((3a c d - 6a b c d + 3b c d)x + 3a c d - 6a b c d + 3b c )\|a \|c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 12 + +--S 13 of 512 +--a0102:= integrate(t0102,x) +--E 13 + +--S 14 of 512 +--m0102:= a0102-r0102 +--E 14 + +--S 15 of 512 +--d0102:= D(m0102,x) +--E 15 + +--S 16 of 512 +t0103:= 1/x^2/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (7) ------------------------------------------- +--R 2 4 3 2 2 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 16 + +--S 17 of 512 +r0103:= 2/3*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)/(c+d*x)^(3/2)+_ + 4/3*b*d^2*(a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 4*d^2*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(1/2)-_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x+_ + b*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2)+_ + 5*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(7/2) +--R +--R +--R (8) +--R 3 4 2 3 2 2 2 3 3 2 +--R (15a d - 27a b c d + 9a b c d + 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 +--R (15a c d - 27a b c d + 9a b c d + 3b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 3 2 2 2 2 +--R (- 15a d + 22a b c d - 3b c d )x +--R + +--R 2 3 2 2 2 3 2 2 2 3 2 4 +--R (- 20a c d + 30a b c d - 6b c d)x - 3a c d + 6a b c d - 3b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 3 3 3 2 4 2 2 5 2 3 4 2 2 5 2 6 +--R ((3a c d - 6a b c d + 3a b c d)x + (3a c d - 6a b c d + 3a b c )x) +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 17 + +--S 18 of 512 +--a0103:= integrate(t0103,x) +--E 18 + +--S 19 of 512 +--m0103:= a0103-r0103 +--E 19 + +--S 20 of 512 +--d0103:= D(m0103,x) +--E 20 + +--S 21 of 512 +t0104:= 1/x^3/(a+b*x)^(1/2)/(c+d*x)^(5/2) +--R +--R +--R 1 +--R (9) ------------------------------------------- +--R 2 5 4 2 3 +-------+ +-------+ +--R (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 21 + +--S 22 of 512 +r0104:= -2/3*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)/(c+d*x)^(3/2)-_ + 4/3*b*d^3*(a+b*x)^(1/2)/c^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 6*d^3*(a+b*x)^(1/2)/c^4/(b*c-a*d)/(c+d*x)^(1/2)-_ + 1/2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^3/x^2+3/4*b*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/a^2/c^3/x+11/4*d*(a+b*x)^(1/2)*(c+d*x)^(1/2)/a/c^4/x-_ + b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)-8*d^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(1/2)/c^(9/2)-3/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/_ + a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(9/2) +--R +--R +--R (10) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 3 +--R (- 105a d + 180a b c d - 54a b c d - 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 2 +--R (- 105a c d + 180a b c d - 54a b c d - 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 4 2 2 3 3 3 2 3 +--R (105a d - 145a b c d + 15a b c d + 9b c d )x +--R + +--R 3 4 2 2 3 2 3 2 3 4 2 +--R (140a c d - 198a b c d + 24a b c d + 18b c d)x +--R + +--R 3 2 3 2 3 2 2 4 3 5 3 3 2 2 4 +--R (21a c d - 33a b c d + 3a b c d + 9b c )x - 6a c d + 12a b c d +--R + +--R 2 5 +--R - 6a b c +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|b x + a +--R / +--R 4 4 3 3 5 2 2 2 6 3 +--R (12a c d - 24a b c d + 12a b c d)x +--R + +--R 4 5 2 3 6 2 2 7 2 +--R (12a c d - 24a b c d + 12a b c )x +--R * +--R +-+ +-+ +-------+ +--R \|a \|c \|d x + c +--R Type: Expression(Integer) +--E 22 + +--S 23 of 512 +--a0104:= integrate(t0104,x) +--E 23 + +--S 24 of 512 +--m0104:= a0104-r0104 +--E 24 + +--S 25 of 512 +--d0104:= D(m0104,x) +--E 25 + +--S 26 of 512 +t0105:= x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 3 +--R x +--R (11) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 26 + +--S 27 of 512 +r0105:= 2*a*c/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 2*a*c*(b*c+a*d)/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^2/b^3/d^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/4*(b*c+a*d)^3/b^3/d^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 3/2*(b*c+a*d)*x/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+x^2/b/d/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)-4*a*c*(b*c+a*d)*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+3/2*(b*c+a*d)^3*(c+d*x)^(1/2)/b^2/d^3/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-3*(b*c+a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (12) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (- 3a d + 3a b c d + 3a b c d - 3b c )\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (a b d - 2a b c d + b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (3a d - a b c d - a b c d + 3b c )x + 3a c d - 2a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 2 2 4 3 3 4 2 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d )\|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 27 + +--S 28 of 512 +--a0105:= integrate(t0105,x) +--E 28 + +--S 29 of 512 +--m0105:= a0105-r0105 +--E 29 + +--S 30 of 512 +--d0105:= D(m0105,x) +--E 30 + +--S 31 of 512 +t0106:= x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 2 +--R x +--R (13) ------------------------------------------------- +--R 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 31 + +--S 32 of 512 +r0106:= 1/2*(b*c+a*d)/b^2/d^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+_ + 1/2*(b*c+a*d)^2/b^2/d^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + x/b/d/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)^2*(c+d*x)^(1/2)/b/d^2/_ + (b*c-a*d)^2/(a+b*x)^(1/2)+2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(3/2) +--R +--R +--R (14) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|d \|b x + a +--R (2a d - 4a b c d + 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((- 2a d - 2b c )x - 2a c d - 2a b c )\|b \|d +--R / +--R 2 3 2 2 3 2 +-+ +-+ +-------+ +-------+ +--R (a b d - 2a b c d + b c d)\|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 32 + +--S 33 of 512 +--a0106:= integrate(t0106,x) +--E 33 + +--S 34 of 512 +--m0106:= a0106-r0106 +--E 34 + +--S 35 of 512 +--d0106:= D(m0106,x) +--E 35 + +--S 36 of 512 +t0107:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (15) ---------------------------------------------------- +--R 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 512 +r0107:= 1/a/c/(a+b*x)^(1/2)/(c+d*x)^(1/2)-(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(1/2)/(c+d*x)^(1/2)+2*b*(b*c+a*d)*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(3/2)/c^(3/2) +--R +--R +--R (16) +--R +-+ +-------+ +--R 2 2 2 2 +-------+ +-------+ \|c \|b x + a +--R (- 2a d + 4a b c d - 2b c )\|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 +-+ +-+ +--R ((2a b d + 2b c d)x + 2a d + 2b c )\|a \|c +--R / +--R 3 2 2 2 2 3 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )\|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 37 + +--S 38 of 512 +--a0107:= integrate(t0107,x) +--E 38 + +--S 39 of 512 +--m0107:= a0107-r0107 +--E 39 + +--S 40 of 512 +--d0107:= D(m0107,x) +--E 40 + +--S 41 of 512 +t0108:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (17) ----------------------------------------------------- +--R 4 3 2 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 41 + +--S 42 of 512 +r0108:= -4*b*d/a/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-3/2*(b*c+a*d)/_ + a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/c^2/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + a^(5/2)/c^(5/2) +--R +--R +--R (18) +--R 3 3 2 2 2 2 3 3 +-------+ +-------+ +--R (3a d - 3a b c d - 3a b c d + 3b c )x\|b x + a \|d x + c +--R * +--R +-+ +-------+ +--R \|c \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 3 2 2 3 2 2 +--R (- 3a b d + 2a b c d - 3b c d)x +--R + +--R 3 3 2 2 2 2 3 3 3 2 2 2 2 3 +--R (- 3a d + a b c d + a b c d - 3b c )x - a c d + 2a b c d - a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 2 3 3 2 2 4 +-+ +-+ +-------+ +-------+ +--R (a c d - 2a b c d + a b c )x\|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 42 + +--S 43 of 512 +--a0108:= integrate(t0108,x) +--E 43 + +--S 44 of 512 +--m0108:= a0108-r0108 +--E 44 + +--S 45 of 512 +--d0108:= D(m0108,x) +--E 45 + +--S 46 of 512 +t0109:= 1/x^3/(a+b*x)^(3/2)/(c+d*x)^(3/2) +--R +--R +--R 1 +--R (19) ----------------------------------------------------- +--R 5 4 3 +-------+ +-------+ +--R (b d x + (a d + b c)x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 46 + +--S 47 of 512 +r0109:= -3/2*b*d/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)+13/2*b*d*(b*c+a*d)/_ + a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+15/8*(b*c+a*d)^2/_ + a^3/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)-15/8*(b*c+a*d)^3/a^3/c^3/_ + (b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/2/a/c/x^2/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/4*(b*c+a*d)/a^2/c^2/x/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 13*b^2*d*(b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 15/4*b*(b*c+a*d)^3*(c+d*x)^(1/2)/a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 3*b*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/_ + c^(5/2)-15/4*(b*c+a*d)^2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (20) +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +-------+ +--R (- 15a d + 12a b c d + 6a b c d + 12a b c d - 15b c )x \|b x + a +--R * +--R +-+ +-------+ +--R +-------+ \|c \|b x + a +--R \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 4 2 2 3 3 2 2 4 3 3 +--R (15a b d - 7a b c d - 7a b c d + 15b c d)x +--R + +--R 4 4 3 3 2 2 2 2 3 3 4 4 2 +--R (15a d - 2a b c d - 10a b c d - 2a b c d + 15b c )x +--R + +--R 4 3 3 2 2 2 2 3 3 4 4 2 2 3 3 +--R (5a c d - 5a b c d - 5a b c d + 5a b c )x - 2a c d + 4a b c d +--R + +--R 2 2 4 +--R - 2a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 2 4 4 3 2 5 2 +-+ +-+ +-------+ +-------+ +--R (4a c d - 8a b c d + 4a b c )x \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 47 + +--S 48 of 512 +--a0109:= integrate(t0109,x) +--E 48 + +--S 49 of 512 +--m0109:= a0109-r0109 +--E 49 + +--S 50 of 512 +--d0109:= D(m0109,x) +--E 50 + +--S 51 of 512 +t0110:= x^5/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (21) +--R 5 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 51 + +--S 52 of 512 +r0110:= 2*a^5/b^5/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^5*d*_ + (a+b*x)^(1/2)/b^5/(b*c-a*d)^2/(c+d*x)^(3/2)+10/3*a^4*(a+b*x)^(1/2)/_ + b^5/(b*c-a*d)/(c+d*x)^(3/2)-20/3*a^2*(a+b*x)^(3/2)/b^5/d/_ + (c+d*x)^(3/2)-20/3*a^3*(a+b*x)^(3/2)/b^5/(b*c-a*d)/(c+d*x)^(3/2)+_ + 10/3*a*(a+b*x)^(5/2)/b^5/d/(c+d*x)^(3/2)-2/3*(a+b*x)^(7/2)/b^5/d/_ + (c+d*x)^(3/2)-20*a^2*(a+b*x)^(1/2)/b^4/d^2/(c+d*x)^(1/2)+16/3*a^5*_ + d*(a+b*x)^(1/2)/b^4/(b*c-a*d)^3/(c+d*x)^(1/2)+20/3*a^4*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(1/2)+50/3*a*(a+b*x)^(3/2)/_ + b^4/d^2/(c+d*x)^(1/2)-14/3*(a+b*x)^(5/2)/b^4/d^2/(c+d*x)^(1/2)-_ + 25*a*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3-35/4*(b*c-a*d)*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4+35/6*(a+b*x)^(3/2)*_ + (c+d*x)^(1/2)/b^3/d^3+20*a^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)+25*a*(b*c-a*d)*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+35/4*_ + (b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2) +--R +--R +--R (22) +--R 5 6 4 5 3 2 2 4 2 3 3 3 4 4 2 +--R 45a d - 45a b c d - 30a b c d - 90a b c d + 225a b c d +--R + +--R 5 5 +--R - 105b c d +--R * +--R x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 5 6 +--R 45a c d - 45a b c d - 30a b c d - 90a b c d + 225a b c d - 105b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 2 6 2 3 5 4 2 4 5 3 3 4 +--R (6a b d - 18a b c d + 18a b c d - 6b c d )x +--R + +--R 4 6 3 2 5 2 3 2 4 4 3 3 5 4 2 3 +--R (- 15a b d + 24a b c d + 18a b c d - 48a b c d + 21b c d )x +--R + +--R 5 6 3 2 2 4 2 3 3 3 4 4 2 5 5 2 +--R (- 45a d + 66a b c d + 12a b c d - 237a b c d + 140b c d)x +--R + +--R 5 5 4 2 4 3 2 3 3 2 3 4 2 4 5 +--R - 90a c d + 45a b c d + 84a b c d - 222a b c d - 50a b c d +--R + +--R 5 6 +--R 105b c +--R * +--R x +--R + +--R 5 2 4 4 3 3 3 2 4 2 2 3 5 4 6 +--R - 45a c d + 30a b c d + 36a b c d - 190a b c d + 105a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 3 8 2 4 7 5 2 6 6 3 5 3 3 7 +--R (12a b d - 36a b c d + 36a b c d - 12b c d )x + 12a b c d +--R + +--R 2 4 2 6 5 3 5 6 4 4 +--R - 36a b c d + 36a b c d - 12b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 52 + +--S 53 of 512 +--a0110:= integrate(t0110,x) +--E 53 + +--S 54 of 512 +--m0110:= a0110-r0110 +--E 54 + +--S 55 of 512 +--d0110:= D(m0110,x) +--E 55 + +--S 56 of 512 +t0111:= x^4/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (23) +--R 4 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 56 + +--S 57 of 512 +r0111:= -2*a^4/b^4/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*a^4*d*_ + (a+b*x)^(1/2)/b^4/(b*c-a*d)^2/(c+d*x)^(3/2)-8/3*a^3*(a+b*x)^(1/2)/_ + b^4/(b*c-a*d)/(c+d*x)^(3/2)+8/3*a*(a+b*x)^(3/2)/b^4/d/(c+d*x)^(3/2)+_ + 4*a^2*(a+b*x)^(3/2)/b^4/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(5/2)/_ + b^4/d/(c+d*x)^(3/2)+8*a*(a+b*x)^(1/2)/b^3/d^2/(c+d*x)^(1/2)-_ + 16/3*a^4*d*(a+b*x)^(1/2)/b^3/(b*c-a*d)^3/(c+d*x)^(1/2)-_ + 16/3*a^3*(a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(1/2)-_ + 10/3*(a+b*x)^(3/2)/b^3/d^2/(c+d*x)^(1/2)+5*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d^3-5*c*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(3/2)/d^(7/2)-3*a*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/d^(5/2) +--R +--R +--R (24) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 4 4 +--R (- 9a d + 12a b c d + 18a b c d - 36a b c d + 15b c d)x - 9a c d +--R + +--R 3 2 3 2 2 3 2 3 4 4 5 +--R 12a b c d + 18a b c d - 36a b c d + 15b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (9a d - 3a b c d - 9a b c d + 39a b c d - 20b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (18a c d - 15a b c d + 33a b c d + 11a b c d - 15b c )x + 9a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R - 9a b c d + 31a b c d - 15a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 2 7 2 3 6 4 2 5 5 3 4 3 2 6 2 3 2 5 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 4 3 4 5 4 3 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 57 + +--S 58 of 512 +--a0111:= integrate(t0111,x) +--E 58 + +--S 59 of 512 +--m0111:= a0111-r0111 +--E 59 + +--S 60 of 512 +--d0111:= D(m0111,x) +--E 60 + +--S 61 of 512 +t0112:= x^3/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (25) +--R 3 +--R x +--R -------------------------------------------------------------------------- +--R 2 3 2 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 61 + +--S 62 of 512 +r0112:= 2*a^3/b^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*a^3*d*_ + (a+b*x)^(1/2)/b^3/(b*c-a*d)^2/(c+d*x)^(3/2)+2*a^2*(a+b*x)^(1/2)/_ + b^3/(b*c-a*d)/(c+d*x)^(3/2)-2/3*(a+b*x)^(3/2)/b^3/d/(c+d*x)^(3/2)-_ + 2*a*(a+b*x)^(3/2)/b^3/(b*c-a*d)/(c+d*x)^(3/2)-2*(a+b*x)^(1/2)/_ + b^2/d^2/(c+d*x)^(1/2)+16/3*a^3*d*(a+b*x)^(1/2)/b^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+4*a^2*(a+b*x)^(1/2)/b^2/(b*c-a*d)^2/(c+d*x)^(1/2)+_ + 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (26) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 18a b c d + 18a b c d - 6b c d)x + 6a c d - 18a b c d +--R + +--R 2 3 3 4 +--R 18a b c d - 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|d \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 4 2 2 2 3 3 2 +--R (- 6a d - 18a b c d + 8b c d)x +--R + +--R 3 3 2 2 2 2 3 3 4 3 2 2 2 3 +--R (- 12a c d - 18a b c d - 8a b c d + 6b c )x - 6a c d - 16a b c d +--R + +--R 2 4 +--R 6a b c +--R * +--R +-+ +-+ +--R \|b \|d +--R / +--R 3 6 2 2 5 3 2 4 4 3 3 3 5 2 2 2 4 +--R (3a b d - 9a b c d + 9a b c d - 3b c d )x + 3a b c d - 9a b c d +--R + +--R 3 3 3 4 4 2 +--R 9a b c d - 3b c d +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 62 + +--S 63 of 512 +--a0112:= integrate(t0112,x) +--E 63 + +--S 64 of 512 +--m0112:= a0112-r0112 +--E 64 + +--S 65 of 512 +--d0112:= D(m0112,x) +--E 65 + +--S 66 of 512 +t0113:= 1/x/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (27) +--R 1 +--R ---------------------------------------------------------------------------- +--R 2 4 2 3 2 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 66 + +--S 67 of 512 +r0113:= 2*d/c/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)+8/3*d^2*(a+b*x)^(1/2)/_ + c/(b*c-a*d)^2/(c+d*x)^(3/2)+1/a/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+16/3*b*d^2*_ + (a+b*x)^(1/2)/c/(b*c-a*d)^3/(c+d*x)^(1/2)+2*b*(b*c+a*d)*_ + (c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-2*atanh(c^(1/2)*_ + (a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/c^(5/2) +--R +--R +--R (28) +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (- 6a d + 18a b c d - 18a b c d + 6b c d)x - 6a c d + 18a b c d +--R + +--R 2 3 3 4 +--R - 18a b c d + 6b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 4 2 3 3 2 2 2 +--R (6a b d - 16a b c d - 6b c d )x +--R + +--R 3 4 2 3 2 2 2 3 3 3 3 2 2 2 +--R (6a d - 8a b c d - 18a b c d - 12b c d)x + 8a c d - 18a b c d +--R + +--R 3 4 +--R - 6b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 4 2 4 3 3 3 2 2 4 2 3 5 4 3 3 3 4 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x + 3a c d - 9a b c d +--R + +--R 2 2 5 3 6 +--R 9a b c d - 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 67 + +--S 68 of 512 +--a0113:= integrate(t0113,x) +--E 68 + +--S 69 of 512 +--m0113:= a0113-r0113 +--E 69 + +--S 70 of 512 +--d0113:= D(m0113,x) +--E 70 + +--S 71 of 512 +t0114:= 1/x^2/(a+b*x)^(3/2)/(c+d*x)^(5/2) +--R +--R +--R (29) +--R 1 +--R ----------------------------------------------------------------------------- +--R 2 5 2 4 2 3 2 2 +-------+ +-------+ +--R (b d x + (a d + 2b c d)x + (2a c d + b c )x + a c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 71 + +--S 72 of 512 +r0114:= -2*d^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(3/2)-8/3*d^3*_ + (a+b*x)^(1/2)/c^2/(b*c-a*d)^2/(c+d*x)^(3/2)-d/a/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-4*b*d/a/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + 3/2*(b*c+a*d)/a^2/c^3/(a+b*x)^(1/2)/(c+d*x)^(1/2)+d*(b*c+a*d)/a/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+3/2*(b*c+a*d)^2/a^2/_ + c^3/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)-1/a/c^2/x/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)-16/3*b*d^3*(a+b*x)^(1/2)/c^2/(b*c-a*d)^3/_ + (c+d*x)^(1/2)+8*b^2*d*(c+d*x)^(1/2)/a/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*b*d*(b*c+a*d)*(c+d*x)^(1/2)/a/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 3*b*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+_ + 2*d*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(3/2)/_ + c^(7/2)+3*(b*c+a*d)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/_ + (c+d*x)^(1/2))/a^(5/2)/c^(7/2) +--R +--R +--R (30) +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (15a d - 36a b c d + 18a b c d + 12a b c d - 9b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 +--R (15a c d - 36a b c d + 18a b c d + 12a b c d - 9b c )x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 5 2 2 4 3 2 3 4 3 2 3 +--R (- 15a b d + 31a b c d - 9a b c d + 9b c d )x +--R + +--R 4 5 3 4 2 2 2 3 3 3 2 4 4 2 +--R (- 15a d + 11a b c d + 33a b c d - 15a b c d + 18b c d)x +--R + +--R 4 4 3 2 3 2 2 3 2 3 4 4 5 4 2 3 +--R (- 20a c d + 39a b c d - 9a b c d - 3a b c d + 9b c )x - 3a c d +--R + +--R 3 3 2 2 2 4 3 5 +--R 9a b c d - 9a b c d + 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 5 3 4 4 4 3 3 2 5 2 2 3 6 2 +--R (3a c d - 9a b c d + 9a b c d - 3a b c d)x +--R + +--R 5 4 3 4 5 2 3 2 6 2 3 7 +--R (3a c d - 9a b c d + 9a b c d - 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 72 + +--S 73 of 512 +--a0114:= integrate(t0114,x) +--E 73 + +--S 74 of 512 +--m0114:= a0114-r0114 +--E 74 + +--S 75 of 512 +--d0114:= D(m0114,x) +--E 75 + +--S 76 of 512 +t0115:= 1/x/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (31) +--R 1 +--R / +--R 2 2 5 2 2 4 2 2 2 2 3 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 76 + +--S 77 of 512 +r0115:= 1/3/a/c/(a+b*x)^(3/2)/(c+d*x)^(3/2)-1/3*(b*c+a*d)/a/c/(b*c-a*d)/_ + (a+b*x)^(3/2)/(c+d*x)^(3/2)-2*b*(b*c+a*d)/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+1/a^2/c^2/(a+b*x)^(1/2)/(c+d*x)^(1/2)-_ + (b*c+a*d)/a^2/c^2/(b*c-a*d)/(a+b*x)^(1/2)/(c+d*x)^(1/2)+8/3*b^2*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/(a+b*x)^(3/2)-16/3*b^2*d*_ + (b*c+a*d)*(c+d*x)^(1/2)/a/c/(b*c-a*d)^4/(a+b*x)^(1/2)+2*b*_ + (b*c+a*d)*(c+d*x)^(1/2)/a^2/c^2/(b*c-a*d)^2/(a+b*x)^(1/2)-_ + 2*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(5/2)/c^(5/2) +--R +--R +--R (32) +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (- 6a b d + 24a b c d - 36a b c d + 24a b c d - 6b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (- 6a d + 18a b c d - 12a b c d - 12a b c d + 18a b c d - 6b c )x +--R + +--R 5 4 4 2 3 3 2 3 2 2 3 4 4 5 +--R - 6a c d + 24a b c d - 36a b c d + 24a b c d - 6a b c +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 3 +--R (6a b d - 22a b c d - 22a b c d + 6b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 2 +--R (12a b d - 36a b c d - 48a b c d - 36a b c d + 12b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R (6a d - 6a b c d - 48a b c d - 48a b c d - 6a b c d + 6b c )x +--R + +--R 5 4 4 2 3 2 3 4 4 5 +--R 8a c d - 24a b c d - 24a b c d + 8a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 6 2 5 5 2 3 4 4 3 4 3 3 4 5 2 2 5 6 2 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 7 2 5 6 3 4 5 2 4 3 4 3 5 2 3 4 6 2 5 7 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 7 3 4 6 4 3 5 2 5 2 4 3 6 3 4 7 +--R 3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 77 + +--S 78 of 512 +--a0115:= integrate(t0115,x) +--E 78 + +--S 79 of 512 +--m0115:= a0115-r0115 +--E 79 + +--S 80 of 512 +--d0115:= D(m0115,x) +--E 80 + +--S 81 of 512 +t0116:= 1/x^2/(a+b*x)^(5/2)/(c+d*x)^(5/2) +--R +--R +--R (33) +--R 1 +--R / +--R 2 2 6 2 2 5 2 2 2 2 4 +--R b d x + (2a b d + 2b c d)x + (a d + 4a b c d + b c )x +--R + +--R 2 2 3 2 2 2 +--R (2a c d + 2a b c )x + a c x +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 81 + +--S 82 of 512 +r0116:= -8/3*b*d/a/c/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 5/6*(b*c+a*d)/a^2/c^2/(a+b*x)^(3/2)/(c+d*x)^(3/2)+_ + 5/6*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)/(a+b*x)^(3/2)/(c+d*x)^(3/2)-_ + 1/a/c/x/(a+b*x)^(3/2)/(c+d*x)^(3/2)-16*b^2*d/a/c/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)+5*b*(b*c+a*d)^2/a^2/c^2/(b*c-a*d)^2/_ + (a+b*x)^(3/2)/(c+d*x)^(1/2)-5/2*(b*c+a*d)/a^3/c^3/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+5/2*(b*c+a*d)^2/a^3/c^3/(b*c-a*d)/(a+b*x)^(1/2)/_ + (c+d*x)^(1/2)+64/3*b^3*d*(c+d*x)^(1/2)/a/c/(b*c-a*d)^3/_ + (a+b*x)^(3/2)-20/3*b^2*(b*c+a*d)^2*(c+d*x)^(1/2)/a^2/c^2/_ + (b*c-a*d)^3/(a+b*x)^(3/2)-128/3*b^3*d^2*(c+d*x)^(1/2)/a/c/_ + (b*c-a*d)^4/(a+b*x)^(1/2)+40/3*b^2*d*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^2/c^2/(b*c-a*d)^4/(a+b*x)^(1/2)-5*b*(b*c+a*d)^2*(c+d*x)^(1/2)/_ + a^3/c^3/(b*c-a*d)^2/(a+b*x)^(1/2)+5*(b*c+a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(7/2)/c^(7/2) +--R +--R +--R (34) +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R 15a b d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 6 5 +--R 15b c d +--R * +--R 3 +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R 15a d - 30a b c d - 15a b c d + 60a b c d - 15a b c d +--R + +--R 5 5 6 6 +--R - 30a b c d + 15b c +--R * +--R 2 +--R x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R 15a c d - 45a b c d + 30a b c d + 30a b c d - 45a b c d +--R + +--R 5 6 +--R 15a b c +--R * +--R x +--R * +--R +-+ +-------+ +--R +-------+ +-------+ \|c \|b x + a +--R \|b x + a \|d x + c atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 6 4 2 4 +--R (- 15a b d + 40a b c d - 18a b c d + 40a b c d - 15b c d )x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 5 4 2 +--R - 30a b d + 60a b c d + 18a b c d + 18a b c d + 60a b c d +--R + +--R 6 5 +--R - 30b c d +--R * +--R 3 +--R x +--R + +--R 6 6 4 2 2 4 3 3 3 3 2 4 4 2 6 6 2 +--R (- 15a d + 87a b c d - 48a b c d + 87a b c d - 15b c )x +--R + +--R 6 5 5 2 4 4 2 3 3 3 3 4 2 2 4 5 +--R - 20a c d + 48a b c d - 12a b c d - 12a b c d + 48a b c d +--R + +--R 5 6 +--R - 20a b c +--R * +--R x +--R + +--R 6 2 4 5 3 3 4 2 4 2 3 3 5 2 4 6 +--R - 3a c d + 12a b c d - 18a b c d + 12a b c d - 3a b c +--R * +--R +-+ +-+ +--R \|a \|c +--R / +--R 7 3 5 6 2 4 4 5 3 5 3 4 4 6 2 3 5 7 3 +--R (3a b c d - 12a b c d + 18a b c d - 12a b c d + 3a b c d)x +--R + +--R 8 3 5 7 4 4 6 2 5 3 5 3 6 2 4 4 7 3 5 8 2 +--R (3a c d - 9a b c d + 6a b c d + 6a b c d - 9a b c d + 3a b c )x +--R + +--R 8 4 4 7 5 3 6 2 6 2 5 3 7 4 4 8 +--R (3a c d - 12a b c d + 18a b c d - 12a b c d + 3a b c )x +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|a \|c \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 82 + +--S 83 of 512 +--a0116:= integrate(t0116,x) +--E 83 + +--S 84 of 512 +--m0116:= a0116-r0116 +--E 84 + +--S 85 of 512 +--d0116:= D(m0116,x) +--E 858 + +--S 86 of 512 +t0117:= x^3*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 5 4 2 3 +-------+ +-------+ +--R (35) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 86 + +--S 87 of 512 +r0117:= -33/1024*(b*c-a*d)^6*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^6/d^4-_ + 11/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^5/d^4-_ + 11/640*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^4/d^4-_ + 33/2240*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^3/d^4-_ + 11/840*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b^2/d^4-_ + 1/84*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(11/2)/b/d^4+5/64*c^3*_ + (b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(7/2)/d^(9/2)-21/128*c^2*(b*c-a*d)^5*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(9/2)+_ + 63/512*c*(b*c-a*d)^6*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(11/2)/d^(9/2)+1/7*(a+b*x)^(1/2)*_ + (c+d*x)^(13/2)/d^4-1/4*c^3*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^4+_ + 3/5*c^2*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^4-1/2*c*(a+b*x)^(1/2)*_ + (c+d*x)^(11/2)/d^4-33/1024*(b*c-a*d)^7*atanh(d^(1/2)*_ + (a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(13/2)/d^(9/2)+_ + 5/64*c^3*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^4-_ + 21/128*c^2*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^4+_ + 63/512*c*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^4+_ + 5/96*c^3*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^4-_ + 7/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^4+_ + 21/256*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^4+_ + 1/24*c^3*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^4-_ + 7/80*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^4+_ + 21/320*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^4-_ + 3/40*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^4+_ + 9/160*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^4+_ + 1/20*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/b/d^4 +--R +--R +--R (36) +--R 7 7 6 6 5 2 2 5 4 3 3 4 3 4 4 3 +--R 3465a d - 11025a b c d + 11025a b c d - 2625a b c d - 525a b c d +--R + +--R 2 5 5 2 6 6 7 7 +--R - 315a b c d - 525a b c d + 525b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 6 6 6 5 6 6 5 5 +--R 15360b d x + (1280a b d + 37120b c d )x +--R + +--R 2 4 6 5 5 6 2 4 4 +--R (- 1408a b d + 3840a b c d + 23680b c d )x +--R + +--R 3 3 6 2 4 5 5 2 4 6 3 3 3 +--R (1584a b d - 4336a b c d + 3280a b c d + 240b c d )x +--R + +--R 4 2 6 3 3 5 2 4 2 4 5 3 3 +--R - 1848a b d + 5088a b c d - 3888a b c d + 160a b c d +--R + +--R 6 4 2 +--R - 280b c d +--R * +--R 2 +--R x +--R + +--R 5 6 4 2 5 3 3 2 4 2 4 3 3 +--R 2310a b d - 6426a b c d + 5004a b c d - 260a b c d +--R + +--R 5 4 2 6 5 +--R - 210a b c d + 350b c d +--R * +--R x +--R + +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 3465a d + 9870a b c d - 8043a b c d + 660a b c d + 385a b c d +--R + +--R 5 5 6 6 +--R 350a b c d - 525b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 6 4 +-+ +-+ +--R 107520b d \|b \|d +--R Type: Expression(Integer) +--E 87 + +--S 88 of 512 +--a0117:= integrate(t0117,x) +--E 88 + +--S 89 of 512 +--m0117:= a0117-r0117 +--E 89 + +--S 90 of 512 +--d0117:= D(m0117,x) +--E 90 + +--S 91 of 512 +t0118:= x^2*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 4 3 2 2 +-------+ +-------+ +--R (37) (d x + 2c d x + c x )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 91 + +--S 92 of 512 +r0118:= -5/64*c^2*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^3+_ + 7/64*c*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^3-_ + 21/512*(b*c-a*d)^5*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^5/d^3-_ + 5/96*c^2*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^3+_ + 7/96*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^3-_ + 7/256*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^4/d^3-_ + 1/24*c^2*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^3+_ + 7/120*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^3-_ + 7/320*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^3/d^3+_ + 1/4*c^2*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^3+1/20*c*_ + (b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(7/2)/b/d^3-3/160*(b*c-a*d)^2*_ + (a+b*x)^(1/2)*(c+d*x)^(7/2)/b^2/d^3-2/5*c*(a+b*x)^(1/2)*_ + (c+d*x)^(9/2)/d^3-1/60*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(9/2)/_ + b/d^3+1/6*(a+b*x)^(1/2)*(c+d*x)^(11/2)/d^3-5/64*c^2*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(7/2)+_ + 7/64*c*(b*c-a*d)^5*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(9/2)/d^(7/2)-21/512*(b*c-a*d)^6*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(11/2)/d^(7/2) +--R +--R +--R (38) +--R 6 6 5 5 4 2 2 4 3 3 3 3 2 4 4 2 +--R - 315a d + 1050a b c d - 1125a b c d + 300a b c d + 75a b c d +--R + +--R 5 5 6 6 +--R 90a b c d - 75b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 5 5 5 4 5 5 4 4 +--R 1280b d x + (128a b d + 3200b c d )x +--R + +--R 2 3 5 4 4 5 2 3 3 +--R (- 144a b d + 416a b c d + 2160b c d )x +--R + +--R 3 2 5 2 3 4 4 2 3 5 3 2 2 +--R (168a b d - 488a b c d + 408a b c d + 40b c d )x +--R + +--R 4 5 3 2 4 2 3 2 3 4 3 2 5 4 +--R (- 210a b d + 616a b c d - 524a b c d + 40a b c d - 50b c d)x +--R + +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 5 5 +--R 315a d - 945a b c d + 838a b c d - 90a b c d - 65a b c d + 75b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 5 3 +-+ +-+ +--R 7680b d \|b \|d +--R Type: Expression(Integer) +--E 92 + +--S 93 of 512 +--a0118:= integrate(t0118,x) +--E 93 + +--S 94 of 512 +--m0118:= a0118-r0118 +--E 94 + +--S 95 of 512 +--d0118:= D(m0118,x) +--E 95 + +--S 96 of 512 +t0119:= x*(a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 3 2 2 +-------+ +-------+ +--R (39) (d x + 2c d x + c x)\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 96 + +--S 97 of 512 +r0119:= 5/64*c*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d^2-_ + 7/128*(b*c-a*d)^4*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^4/d^2+_ + 5/96*c*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d^2-_ + 7/192*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^3/d^2+_ + 1/24*c*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d^2-_ + 7/240*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b^2/d^2-_ + 11/40*c*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d^2+1/40*a*(a+b*x)^(1/2)*_ + (c+d*x)^(7/2)/b/d+1/5*(a+b*x)^(1/2)*(c+d*x)^(9/2)/d^2+_ + 5/64*c*(b*c-a*d)^4*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(7/2)/d^(5/2)-7/128*(b*c-a*d)^5*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(9/2)/d^(5/2) +--R +--R +--R (40) +--R 5 5 4 4 3 2 2 3 2 3 3 2 4 4 +--R 105a d - 375a b c d + 450a b c d - 150a b c d - 75a b c d +--R + +--R 5 5 +--R 45b c +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 4 4 4 3 4 4 3 3 +--R 384b d x + (48a b d + 1008b c d )x +--R + +--R 2 2 4 3 3 4 2 2 2 +--R (- 56a b d + 176a b c d + 744b c d )x +--R + +--R 3 4 2 2 3 3 2 2 4 3 4 4 +--R (70a b d - 222a b c d + 218a b c d + 30b c d)x - 105a d +--R + +--R 3 3 2 2 2 2 3 3 4 4 +--R 340a b c d - 346a b c d + 60a b c d - 45b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 4 2 +-+ +-+ +--R 1920b d \|b \|d +--R Type: Expression(Integer) +--E 97 + +--S 98 of 512 +--a0119:= integrate(t0119,x) +--E 98 + +--S 99 of 512 +--m0119:= a0119-r0119 +--E 99 + +--S 100 of 512 +--d0119:= D(m0119,x) +--E 100 + +--S 101 of 512 +t0120:= (a+b*x)^(1/2)*(c+d*x)^(5/2) +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (41) (d x + 2c d x + c )\|b x + a \|d x + c +--R Type: Expression(Integer) +--E 101 + +--S 102 of 512 +r0120:= -5/64*(b*c-a*d)^3*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b^3/d-_ + 5/96*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(3/2)/b^2/d-_ + 1/24*(b*c-a*d)*(a+b*x)^(1/2)*(c+d*x)^(5/2)/b/d+_ + 1/4*(a+b*x)^(1/2)*(c+d*x)^(7/2)/d-5/64*(b*c-a*d)^4*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(7/2)/d^(3/2) +--R +--R +--R (42) +--R 4 4 3 3 2 2 2 2 3 3 4 4 +--R (- 15a d + 60a b c d - 90a b c d + 60a b c d - 15b c ) +--R * +--R +-+ +-------+ +--R \|d \|b x + a +--R atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 3 3 3 2 3 3 2 2 +--R 48b d x + (8a b d + 136b c d )x +--R + +--R 2 3 2 2 3 2 3 3 2 2 +--R (- 10a b d + 36a b c d + 118b c d)x + 15a d - 55a b c d +--R + +--R 2 2 3 3 +--R 73a b c d + 15b c +--R * +--R +-+ +-+ +-------+ +-------+ +--R \|b \|d \|b x + a \|d x + c +--R / +--R 3 +-+ +-+ +--R 192b d\|b \|d +--R Type: Expression(Integer) +--E 102 + +--S 103 of 512 +--a0120:= integrate(t0120,x) +--E 103 + +--S 104 of 512 +--m0120:= a0120-r0120 +--E 104 + +--S 105 of 512 +--d0120:= D(m0120,x) +--E 105 + +--S 106 of 512 +t0121:= (a+b*x)^(1/2)*(c+d*x)^(5/2)/x +--R +--R +--R 2 2 2 +-------+ +-------+ +--R (d x + 2c d x + c )\|b x + a \|d x + c +--R (43) ---------------------------------------- +--R x +--R Type: Expression(Integer) +--E 106 + +--S 107 of 512 +r0121:= 1/24/b^(5/2)*(-3*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a^2*d^(5/2)*b^(1/2)+_ + 45*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a*b^2*d*c^2-_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^2*b*d^2*c+_ + 15*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*b^3*c^3+_ + 3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))*a^3*d^3+_ + 14*(a+b*x)^(1/2)*(c+d*x)^(1/2)*a*d^(3/2)*b^(3/2)*c+33*c^2*_ + (a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(1/2)-48*a^(1/2)*c^(5/2)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))*b^(5/2)*d^(1/2)+_ + 2*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(3/2)*a*x+_ + 26*(a+b*x)^(1/2)*(c+d*x)^(1/2)*b^(5/2)*d^(3/2)*c*x+_ + 8*(a+b*x)^(1/2)*(c+d*x)^(1/2)*d^(5/2)*b^(5/2)*x^2)/d^(1/2) +--R +--R +--R (44) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d - 15a b c d + 45a b c d + 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-------+ +--R 2 2 +-+ +-+ +-+ +-+ \|c \|b x + a +--R - 48b c \|a \|b \|c \|d atanh(--------------) +--R +-+ +-------+ +--R \|a \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d + 26b c d)x - 3a d + 14a b c d + 33b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 24b \|b \|d +--R Type: Expression(Integer) +--E 107 + +--S 108 of 512 +--a0121:= integrate(t0121,x) +--E 108 + +--S 109 of 512 +--m0121:= a0121-r0121 +--E 109 + +--S 110 of 512 +--d0121:= D(m0121,x) +--E 110 + +--S 111 of 512 +t0122:= x^3*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 3 +-----+ +--R x \|x + 1 +--R (45) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 512 +r0122:= -6*(1+x)^(1/2)/(1-x)^(1/2)-3*(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)-1/2*x*(1-x^2)^(1/2)+11/2*asin(x) +--R +--R +--R (46) +--R 2 +-----+ +--R (18x - 74x + 52)\|x + 1 +--R + +--R +--------+ +--R 2 | 2 +-------+ +--R ((- 3x + 3x)\|- x + 1 + (33x - 33)asin(x))\|- x + 1 +--R / +--R +-------+ +--R (6x - 6)\|- x + 1 +--R Type: Expression(Integer) +--E 112 + +--S 113 of 512 +--a0122:= integrate(t0122,x) +--E 113 + +--S 114 of 512 +--m0122:= a0122-r0122 +--E 114 + +--S 115 of 512 +--d0122:= D(m0122,x) +--E 115 + +--S 116 of 512 +t0123:= x^2*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R 2 +-----+ +--R x \|x + 1 +--R (47) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 512 +r0123:= -4*(1+x)^(1/2)/(1-x)^(1/2)-(1-x)^(1/2)*(1+x)^(1/2)+_ + 1/3*(1+x)^(3/2)/(1-x)^(3/2)+3*asin(x) +--R +--R +--R 2 +-----+ +-------+ +--R (3x - 19x + 14)\|x + 1 + (9x - 9)asin(x)\|- x + 1 +--R (48) ---------------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 117 + +--S 118 of 512 +--a0123:= integrate(t0123,x) +--E 118 + +--S 119 of 512 +--m0123:= a0123-r0123 +--E 119 + +--S 120 of 512 +--d0123:= D(m0123,x) +--E 120 + +--S 121 of 512 +t0124:= x*(1+x)^(1/2)/(1-x)^(5/2) +--R +--R +--R +-----+ +--R x\|x + 1 +--R (49) ----------------------- +--R 2 +-------+ +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 121 + +--S 122 of 512 +r0124:= -2*(1+x)^(1/2)/(1-x)^(1/2)+1/3*(1+x)^(3/2)/(1-x)^(3/2)+asin(x) +--R +--R +--R +-----+ +-------+ +--R (- 7x + 5)\|x + 1 + (3x - 3)asin(x)\|- x + 1 +--R (50) ---------------------------------------------- +--R +-------+ +--R (3x - 3)\|- x + 1 +--R Type: Expression(Integer) +--E 122 + +--S 123 of 512 +--a0124:= integrate(t0124,x) +--E 123 + +--S 124 of 512 +--m0124:= a0124-r0124 +--E 124 + +--S 125 of 512 +--d0124:= D(m0124,x) +--E 125 + +--S 126 of 512 +t0125:= x^2*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 2 +-------+ +--R x \|b x + a +--R (51) ------------ +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 512 +r0125:= 3/2*a*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/b/d^2-1/2*a^2*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b^2/d+5/8*(b*c-a*d)^2*(a+b*x)^(1/2)*(c+d*x)^(1/2)/_ + b^2/d^3-5/12*c*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d^2-7/12*a*_ + (a+b*x)^(3/2)*(c+d*x)^(1/2)/b^2/d+1/3*(a+b*x)^(5/2)*(c+d*x)^(1/2)/_ + b^2/d-a^2*(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(3/2)-3/2*a*(b*c-a*d)^2*_ + atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(5/2)/_ + d^(5/2)-5/8*(b*c-a*d)^3*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/b^(5/2)/d^(7/2) +--R +--R +--R (52) +--R +-+ +-------+ +--R 3 3 2 2 2 2 3 3 \|d \|b x + a +--R (3a d + 3a b c d + 9a b c d - 15b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R 2 2 2 2 2 2 2 2 2 +-+ +-+ +--R (8b d x + (2a b d - 10b c d)x - 3a d - 4a b c d + 15b c )\|b \|d +--R * +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R / +--R 2 3 +-+ +-+ +--R 24b d \|b \|d +--R Type: Expression(Integer) +--E 127 + +--S 128 of 512 +--a0125:= integrate(t0125,x) +--E 128 + +--S 129 of 512 +--m0125:= a0125-r0125 +--E 129 + +--S 130 of 512 +--d0125:= D(m0125,x) +--E 130 + +--S 131 of 512 +t0126:= x*(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R x\|b x + a +--R (53) ----------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 512 +r0126:= -3/4*c*(a+b*x)^(1/2)*(c+d*x)^(1/2)/d^2-1/4*a*(a+b*x)^(1/2)*_ + (c+d*x)^(1/2)/b/d+1/2*(a+b*x)^(3/2)*(c+d*x)^(1/2)/b/d+a*_ + (b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/_ + b^(3/2)/d^(3/2)+3/4*(b*c-a*d)^2*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(3/2)/d^(5/2) +--R +--R +--R (54) +--R +-+ +-------+ +--R 2 2 2 2 \|d \|b x + a +--R (- a d - 2a b c d + 3b c )atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R + +--R +-+ +-+ +-------+ +-------+ +--R (2b d x + a d - 3b c)\|b \|d \|b x + a \|d x + c +--R / +--R 2 +-+ +-+ +--R 4b d \|b \|d +--R Type: Expression(Integer) +--E 132 + +--S 133 of 512 +--a0126:= integrate(t0126,x) +--E 133 + +--S 134 of 512 +--m0126:= a0126-r0126 +--E 134 + +--S 135 of 512 +--d0126:= D(m0126,x) +--E 135 + +--S 136 of 512 +t0127:= (a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (55) ---------- +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 136 + +--S 137 of 512 +r0127:= (a+b*x)^(1/2)*(c+d*x)^(1/2)/d-(b*c-a*d)*atanh(d^(1/2)*(a+b*x)^(1/2)/_ + b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)atanh(--------------) + \|b \|d \|b x + a \|d x + c +--R +-+ +-------+ +--R \|b \|d x + c +--R (56) --------------------------------------------------------------- +--R +-+ +-+ +--R d\|b \|d +--R Type: Expression(Integer) +--E 137 + +--S 138 of 512 +--a0127:= integrate(t0127,x) +--E 138 + +--S 139 of 512 +--m0127:= a0127-r0127 +--E 139 + +--S 140 of 512 +--d0127:= D(m0127,x) +--E 140 + +--S 141 of 512 +t0128:= (a+b*x)^(1/2)/x/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (57) ----------- +--R +-------+ +--R x\|d x + c +--R Type: Expression(Integer) +--E 141 + +--S 142 of 512 +r0128:= -2*a^(1/2)*atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/_ + c^(1/2)+2*b^(1/2)*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/_ + (c+d*x)^(1/2))/d^(1/2) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R +-+ +-+ \|d \|b x + a +-+ +-+ \|c \|b x + a +--R 2\|b \|c atanh(--------------) - 2\|a \|d atanh(--------------) +--R +-+ +-------+ +-+ +-------+ +--R \|b \|d x + c \|a \|d x + c +--R (58) --------------------------------------------------------------- +--R +-+ +-+ +--R \|c \|d +--R Type: Expression(Integer) +--E 142 + +--S 143 of 512 +--a0128:= integrate(t0128,x) +--E 143 + +--S 144 of 512 +--m0128:= a0128-r0128 +--E 144 + +--S 145 of 512 +--d0128:= D(m0128,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 145 + +--S 146 of 512 +t0129:= (a+b*x)^(1/2)/x^2/(c+d*x)^(1/2) +--R +--R +--R +-------+ +--R \|b x + a +--R (59) ------------ +--R 2 +-------+ +--R x \|d x + c +--R Type: Expression(Integer) +--E 146 + +--S 147 of 512 +r0129:= -(a+b*x)^(1/2)*(c+d*x)^(1/2)/c/x-(b*c-a*d)*_ + atanh(c^(1/2)*(a+b*x)^(1/2)/a^(1/2)/(c+d*x)^(1/2))/a^(1/2)/c^(3/2) +--R +--R +--R +-+ +-------+ +--R \|c \|b x + a +-+ +-+ +-------+ +-------+ +--R (a d - b c)x atanh(--------------) - \|a \|c \|b x + a \|d x + c +--R +-+ +-------+ +--R \|a \|d x + c +--R (60) ----------------------------------------------------------------- +--R +-+ +-+ +--R c x\|a \|c +--R Type: Expression(Integer) +--E 147 + +--S 148 of 512 +--a0129:= integrate(t0129,x) +--E 148 + +--S 149 of 512 +--m0129:= a0129-r0129 +--E 149 + +--S 150 of 512 +--d0129:= D(m0129,x) +--E 150 + +--S 151 of 512 +t0130:= x^2/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 2 +--R x +--R (61) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 512 +r0130:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 + acosh(x) +--R (62) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 152 + +--S 153 of 512 +--a0130:= integrate(t0130,x) +--E 153 + +--S 154 of 512 +--m0130:= a0130-r0130 +--E 154 + +--S 155 of 512 +--d0130:= D(m0130,x) +--E 155 + +--S 156 of 512 +t0131:= 1/(-1+x)^(1/2)/(1+x)^(1/2) +--R +--R +--R 1 +--R (63) ---------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 512 +r0131:= acosh(x) +--R +--R +--R (64) acosh(x) +--R Type: Expression(Integer) +--E 157 + + +-- +-----+ +-----+ +-- (65) - log(- \|x - 1 \|x + 1 + x) +-- Type: Union(Expression(Integer),...) + +--S 158 of 512 ok to fail. seems there are 2 answers (see above) +a0131:= integrate(t0131,x) +--R +--R +--R +-----+ +-----+ +--R (65) - 2log(\|x + 1 - \|x - 1 ) +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 512 ok to fail. due to 2 answers (see above) +m0131:= a0131-r0131 +--R +--R +--R +-----+ +-----+ +--R (66) - 2log(\|x + 1 - \|x - 1 ) - acosh(x) +--R Type: Expression(Integer) +--E 159 + +--S 160 of 512 +d0131:= D(m0131,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (67) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 512 +t0132:= 1/(-1+x)^(1/2)/x/(1+x)^(1/2) +--R +--R +--R 1 +--R (68) ----------------- +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 512 +r0132:= 2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x - 1 +--R (69) 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 162 + + + +-- +-----+ +-----+ +-- 220\|x - 1 \|x + 1 - 21 +-- (70) atan(------------------------) +-- +-----+ +-----+ +-- 21\|x - 1 \|x + 1 + 220 +-- Type: Union(Expression(Integer),...) + +--S 163 of 512 ok to fail. seems there are 2 answers (see above) +a0132:= integrate(t0132,x) +--R +--R +--R +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 +--R (70) - atan(------------------------) +--R +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 512ok to fail. due to 2 answers (see above) +m0132:= a0132-r0132 +--R +--R +--R +-----+ +-----+ +-----+ +--R 416\|x - 1 \|x + 1 + 87 \|x - 1 +--R (71) - atan(------------------------) - 2atan(--------) +--R +-----+ +-----+ +-----+ +--R 87\|x - 1 \|x + 1 - 416 \|x + 1 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 512 +d0132:= D(m0132,x) +--R +--R +--R (72) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 512 +t0133:= x^2*(-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R 2 +-----+ +-----+ +--R (73) x \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 512 +r0133:= -1/8*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/4*(-1+x)^(1/2)*x^3*(1+x)^(1/2)-_ + 1/8*acosh(x) +--R +--R +--R 3 +-----+ +-----+ +--R (2x - x)\|x - 1 \|x + 1 - acosh(x) +--R (74) ------------------------------------ +--R 8 +--R Type: Expression(Integer) +--E 167 + + + +-- +-----+ +-----+ 3 +-----+ +-----+ +-- - log(- \|x - 1 \|x + 1 - x) + (2x - x)\|x - 1 \|x + 1 +-- (75) --------------------------------------------------------- +-- 8 +-- Type: Union(Expression(Integer),...) + +--S 168 of 512 ok to fail. seems there are 2 answers (see above) +a0133:= integrate(t0133,x) +--R +--R +--R +-----+ +-----+ 3 +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + (2x - x)\|x - 1 \|x + 1 +--R (75) ------------------------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 512 ok to fail. due to 2 answers (see above) +m0133:= a0133-r0133 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 + x) + acosh(x) +--R (76) -------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 512 +d0133:= D(m0133,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (77) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 8\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 512 +t0134:= (-1+x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-----+ +-----+ +--R (78) \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 171 + +--S 172 of 512 +r0134:= 1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)-1/2*acosh(x) +--R +--R +--R +-----+ +-----+ +--R x\|x - 1 \|x + 1 - acosh(x) +--R (79) ---------------------------- +--R 2 +--R Type: Expression(Integer) +--E 172 + + + +-- +-----+ +-----+ +-----+ +-----+ +-- - log(\|x - 1 \|x + 1 + x) + x\|x - 1 \|x + 1 +-- (80) ----------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 173 of 512 ok to fail. seems there are 2 answers (see above) +a0134:= integrate(t0134,x) +--R +--R +--R (80) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (4x\|x - 1 \|x + 1 - 4x + 2)log(\|x + 1 - \|x - 1 ) +--R + +--R 3 +-----+ +-----+ 4 2 +--R (- 2x + x)\|x - 1 \|x + 1 + 2x - 2x +--R / +--R +-----+ +-----+ 2 +--R 4x\|x - 1 \|x + 1 - 4x + 2 +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 512 ok to fail. due to 2 answers, see above +m0134:= a0134-r0134 +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 1 - \|x - 1 ) + acosh(x) +--R (81) ------------------------------------ +--R 2 +--R Type: Expression(Integer) +--E 174 + +--S 175 of 512 +d0134:= D(m0134,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R - \|x - 1 + \|x - 1 \|x + 1 +--R (82) ------------------------------ +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 175 + +--S 176 of 512 +t0135:= (-1+x)^(1/2)*(1+x)^(1/2)/x^2 +--R +--R +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R (83) ---------------- +--R 2 +--R x +--R Type: Expression(Integer) +--E 176 + +--S 177 of 512 +r0135:= -(-1+x)^(1/2)*(1+x)^(1/2)/x+acosh(x) +--R +--R +--R +-----+ +-----+ +--R - \|x - 1 \|x + 1 + x acosh(x) +--R (84) ------------------------------- +--R x +--R Type: Expression(Integer) +--E 177 + + + +-- +-----+ +-----+ +-----+ +-----+ +-- - 16x log(- \|x - 1 \|x + 1 + x) - 16\|x - 1 \|x + 1 + 19x +-- (85) ------------------------------------------------------------ +-- 16x +-- Type: Union(Expression(Integer),...) + +--S 178 of 512 ok to fail. seems there are 2 answers (see above) +a0135:= integrate(t0135,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ +--R - x log(\|x - 1 \|x + 1 - x) - \|x - 1 \|x + 1 + x +--R (85) ---------------------------------------------------- +--R x +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 512 ok to fail. due to 2 answers (see above) +m0135:= a0135-r0135 +--R +--R +--R +-----+ +-----+ +--R (86) - log(\|x - 1 \|x + 1 - x) - acosh(x) + 1 +--R Type: Expression(Integer) +--E 179 + +--S 180 of 512 +d0135:= D(m0135,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (87) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 180 + +--S 181 of 512 +t0136:= 1/(1+2*x)^(1/2)/(3+2*x)^(1/2) +--R +--R +--R 1 +--R (88) ------------------ +--R +------+ +------+ +--R \|2x + 1 \|2x + 3 +--R Type: Expression(Integer) +--E 181 + +--S 182 of 512 +r0136:= asinh(1/2*(1+2*x)^(1/2)*2^(1/2)) +--R +--R +--R +-+ +------+ +--R \|2 \|2x + 1 +--R (89) asinh(-------------) +--R 2 +--R Type: Expression(Integer) +--E 182 + + + +-- +------+ +------+ +-- log(- \|2x + 1 \|2x + 3 + 2x + 2) +-- (90) - ---------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 183 of 512 ok to fail. seems there are 2 answers (see above) +a0136:= integrate(t0136,x) +--R +--R +--R +------+ +------+ +--R (90) - log(\|2x + 3 - \|2x + 1 ) +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 512 ok to fail. due to 2 answers (see above) +m0136:= a0136-r0136 +--R +--R +--R +-+ +------+ +--R +------+ +------+ \|2 \|2x + 1 +--R (91) - log(\|2x + 3 - \|2x + 1 ) - asinh(-------------) +--R 2 +--R Type: Expression(Integer) +--E 184 + +--S 185 of 512 +d0136:= D(m0136,x) +--R +--R +--R (92) 0 +--R Type: Expression(Integer) +--E 185 + +--S 186 of 512 +t0137:= 1/x/(-2+3*x)^(1/2)/(3+5*x)^(1/2) +--R +--R +--R 1 +--R (93) ------------------- +--R +------+ +------+ +--R x\|3x - 2 \|5x + 3 +--R Type: Expression(Integer) +--E 186 + +--S 187 of 512 +r0137:= 1/3*6^(1/2)*atan(1/2*6^(1/2)*(-2+3*x)^(1/2)/(3+5*x)^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R \|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R (94) ----------------------- +--R 3 +--R Type: Expression(Integer) +--E 187 + + + +-- +-+ +-+ +------+ +------+ +-+ +-+ +-- +-+ +-+ 3192\|2 \|3 \|3x - 2 \|5x + 3 + (67x + 804)\|2 \|3 +-- \|2 \|3 atan(----------------------------------------------------) +-- +------+ +------+ +-- 804\|3x - 2 \|5x + 3 - 1596x - 19152 +-- (95) - ------------------------------------------------------------------ +-- 6 +-- Type: Union(Expression(Integer),...) + +--S 188 of 512 ok to fail. seems there are 2 answers (see above) +a0137:= integrate(t0137,x) +--R +--R +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R (95) - ------------------------------------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 512 ok to fail. due to 2 answers (see above) +m0137:= a0137-r0137 +--R +--R +--R (96) +--R +-+ +-+ +------+ +------+ +-+ +-+ +--R +-+ +-+ 912\|2 \|3 \|3x - 2 \|5x + 3 + (337x + 4044)\|2 \|3 +--R - \|2 \|3 atan(-----------------------------------------------------) +--R +------+ +------+ +--R 4044\|3x - 2 \|5x + 3 - 456x - 5472 +--R + +--R +-+ +------+ +--R +-+ \|6 \|3x - 2 +--R - 2\|6 atan(-------------) +--R +------+ +--R 2\|5x + 3 +--R / +--R 6 +--R Type: Expression(Integer) +--E 189 + +--S 190 of 512 +d0137:= D(m0137,x) +--R +--R +--R (97) 0 +--R Type: Expression(Integer) +--E 190 + +--S 191 of 512 +t0138:= 1/(-1+x)^(3/2)/x/(1+x)^(3/2) +--R +--R +--R 1 +--R (98) ------------------------ +--R 3 +-----+ +-----+ +--R (x - x)\|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 191 + +--S 192 of 512 +r0138:= -1/(-1+x)^(1/2)/(1+x)^(1/2)-2*atan((-1+x)^(1/2)/(1+x)^(1/2)) +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R - 2\|x - 1 \|x + 1 atan(--------) - 1 +--R +-----+ +--R \|x + 1 +--R (99) ------------------------------------- +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 +--R Type: Expression(Integer) +--E 192 + + + +-- (100) +-- +-----+ +-----+ +-- 2 416\|x - 1 \|x + 1 + 87 +-----+ +-----+ 2 +-- (24x - 24)atan(------------------------) - 24\|x - 1 \|x + 1 + 19x - 19 +-- +-----+ +-----+ +-- 87\|x - 1 \|x + 1 - 416 +-- -------------------------------------------------------------------------- +-- 2 +-- 24x - 24 +-- Type: Union(Expression(Integer),...) + +--S 193 of 512 ok to fail. seems there are 2 answers (see above) +a0138:= integrate(t0138,x) +--R +--R +--R (100) +--R +-----+ +-----+ 2 +-----+ +-----+ +--R (- 2x\|x - 1 \|x + 1 + 2x - 2)atan(\|x - 1 \|x + 1 - x) +--R + +--R +-----+ +-----+ +--R \|x - 1 \|x + 1 - x +--R / +--R +-----+ +-----+ 2 +--R x\|x - 1 \|x + 1 - x + 1 +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 512 ok to fail. due to 2 answers (see above) +m0138:= a0138-r0138 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x - 1 +--R (101) - 2atan(\|x - 1 \|x + 1 - x) + 2atan(--------) +--R +-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 194 + +--S 195 of 512 +d0138:= D(m0138,x) +--R +--R +--R (102) 0 +--R Type: Expression(Integer) +--E 195 + +--S 196 of 512 +t0139:= x*(1-x)^(1/2)*(1+x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (103) x\|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 512 +r0139:= -1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R (x - 1)\|- x + 1 +--R (104) ------------------- +--R 3 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 512 +a0139:= integrate(t0139,x) +--R +--R +--R 2 +-------+ +-----+ +--R (x - 1)\|- x + 1 \|x + 1 +--R (105) -------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 512 +m0139:= a0139-r0139 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (106) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 512 +d0139:= D(m0139,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (107) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 512 +t0140:= x*(1+(1-x)^(1/2)*(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (108) x\|- x + 1 \|x + 1 + x +--R Type: Expression(Integer) +--E 201 + +--S 202 of 512 +r0140:= 1/2*x^2-1/3*(1-x^2)^(3/2) +--R +--R +--R +--------+ +--R 2 | 2 2 +--R (2x - 2)\|- x + 1 + 3x +--R (109) -------------------------- +--R 6 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 512 +a0140:= integrate(t0140,x) +--R +--R +--R 2 +-------+ +-----+ 2 +--R (2x - 2)\|- x + 1 \|x + 1 + 3x +--R (110) --------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 512 +m0140:= a0140-r0140 +--R +--R +--R +--------+ +--R 2 +-------+ +-----+ 2 | 2 +--R (x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 +--R (111) -------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 512 +d0140:= D(m0140,x) +--R +--R +--R +--------+ +--R 3 +-------+ +-----+ 3 | 2 +--R (x - x)\|- x + 1 \|x + 1 + (- x + x)\|- x + 1 +--R (112) -------------------------------------------------- +--R +--------+ +--R | 2 +-------+ +-----+ +--R \|- x + 1 \|- x + 1 \|x + 1 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 512 +t0141:= x*(1+1/(2+x)^(1/2)/(3+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R x\|x + 2 \|x + 3 + x +--R (113) --------------------- +--R +-----+ +-----+ +--R \|x + 2 \|x + 3 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 512 +r0141:= 1/2*x^2+(2+x)^(1/2)*(3+x)^(1/2)-5*asinh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +-----+ 2 +--R - 10asinh(\|x + 2 ) + 2\|x + 2 \|x + 3 + x +--R (114) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 207 + + + +-- (115) +-- +-----+ +-----+ 2 +-- ((- 640x - 1600)\|x + 2 \|x + 3 - 640x - 3200x - 3920) +-- * +-- +-----+ +-----+ +-- log(\|x + 3 + \|x + 2 ) +-- + +-- 3 2 +-----+ +-----+ 4 3 2 +-- (64x + 288x + 232x - 236)\|x + 2 \|x + 3 + 64x + 448x + 944x + 328x +-- + +-- - 579 +-- / +-- +-----+ +-----+ 2 +-- (128x + 320)\|x + 2 \|x + 3 + 128x + 640x + 784 +-- Type: Union(Expression(Integer),...) + +--S 208 of 512 ok to fail. seems there are 2 answers (see above) +a0141:= integrate(t0141,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 2\|x + 2 \|x + 3 + x +--R (115) ------------------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 512 ok to fail. due to 2 answers (see above) +m0141:= a0141-r0141 +--R +--R +--R +-----+ +-----+ +-----+ +--R - 5log(- 2\|x + 2 \|x + 3 - 2x - 5) + 10asinh(\|x + 2 ) +--R (116) -------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 512 +d0141:= D(m0141,x) +--R +--R +--R (117) 0 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 512 +t0142:= x^(-3+n)/((a+b*x)^n) +--R +--R +--R n - 3 +--R x +--R (118) ---------- +--R n +--R (b x + a) +--R Type: Expression(Integer) +--E 211 + +--S 212 of 512 +r0142:= 1/a^2/(-1+n)/(-2+n)*(a+b*x)^(-n)*(-x^(-2+n)*a^2+x^(-2+n)*a^2*n+_ + x^(-1+n)*a*n*b+x^n*b^2) +--R +--R +--R 2 n n - 1 2 2 n - 2 - n +--R (b x + a b n x + (a n - a )x )(b x + a) +--R (119) ---------------------------------------------------- +--R 2 2 2 2 +--R a n - 3a n + 2a +--R Type: Expression(Integer) +--E 212 + +--S 213 of 512 +a0142:= integrate(t0142,x) +--R +--R +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R (120) ---------------------------------------------- +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 512 +m0142:= a0142-r0142 +--R +--R +--R (121) +--R 2 n n - 1 2 2 n - 2 - n n log(b x + a) +--R (- b x - a b n x + (- a n + a )x )(b x + a) %e +--R + +--R 2 3 2 2 2 (n - 3)log(x) +--R (b x + a b n x + (a n - a )x)%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression(Integer) +--E 214 + +--S 215 of 512 +d0142:= D(m0142,x) +--R +--R +--R (122) +--R 2 n - 1 2 n - 2 +--R - b n x + (- a b n + a b n)x +--R + +--R 2 2 2 2 n - 3 +--R (- a n + 3a n - 2a )x +--R * +--R - n +--R (b x + a) +--R + +--R 3 n 2 2 n - 1 2 2 2 n - 2 - n - 1 +--R (b n x + a b n x + (a b n - a b n)x )(b x + a) +--R * +--R n log(b x + a) +--R %e +--R + +--R 2 2 2 2 (n - 3)log(x) +--R (a n - 3a n + 2a )%e +--R / +--R 2 2 2 2 n log(b x + a) +--R (a n - 3a n + 2a )%e +--R Type: Expression(Integer) +--E 215 + +--S 216 of 512 +t0143:= (a+b*x^(1/2))^3 +--R +--R +--R 3 2 +-+ 2 3 +--R (123) (b x + 3a b)\|x + 3a b x + a +--R Type: Expression(Integer) +--E 216 + +--S 217 of 512 +r0143:= 1/10*(a+b*x^(1/2))^4*(-a+4*b*x^(1/2))/b^2 +--R +--R +--R 5 2 2 3 +-+ 4 2 3 2 5 +--R (4b x + 20a b x)\|x + 15a b x + 10a b x - a +--R (124) ----------------------------------------------- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 217 + +--S 218 of 512 +a0143:= integrate(t0143,x) +--R +--R +--R 3 2 2 +-+ 2 2 3 +--R (4b x + 20a b x)\|x + 15a b x + 10a x +--R (125) ---------------------------------------- +--R 10 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 512 +m0143:= a0143-r0143 +--R +--R +--R 5 +--R a +--R (126) ---- +--R 2 +--R 10b +--R Type: Expression(Integer) +--E 219 + +--S 220 of 512 +d0143:= D(m0143,x) +--R +--R +--R (127) 0 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 512 +t0144:= (a+b*x^(1/2))^4 +--R +--R +--R 3 3 +-+ 4 2 2 2 4 +--R (128) (4a b x + 4a b)\|x + b x + 6a b x + a +--R Type: Expression(Integer) +--E 221 + +--S 222 of 512 +r0144:= 1/15*(a+b*x^(1/2))^5*(-a+5*b*x^(1/2))/b^2 +--R +--R +--R 5 2 3 3 +-+ 6 3 2 4 2 4 2 6 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a b x - a +--R (129) ---------------------------------------------------------- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 222 + +--S 223 of 512 +a0144:= integrate(t0144,x) +--R +--R +--R 3 2 3 +-+ 4 3 2 2 2 4 +--R (24a b x + 40a b x)\|x + 5b x + 45a b x + 15a x +--R (130) --------------------------------------------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 512 +m0144:= a0144-r0144 +--R +--R +--R 6 +--R a +--R (131) ---- +--R 2 +--R 15b +--R Type: Expression(Integer) +--E 224 + +--S 225 of 512 +d0144:= D(m0144,x) +--R +--R +--R (132) 0 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 512 +t0145:= (a+b*x^(1/2))^5 +--R +--R +--R 5 2 2 3 4 +-+ 4 2 3 2 5 +--R (133) (b x + 10a b x + 5a b)\|x + 5a b x + 10a b x + a +--R Type: Expression(Integer) +--E 226 + +--S 227 of 512 +r0145:= 1/21*(a+b*x^(1/2))^6*(-a+6*b*x^(1/2))/b^2 +--R +--R +--R (134) +--R 7 3 2 5 2 4 3 +-+ 6 3 3 4 2 5 2 7 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a b x - a +--R ---------------------------------------------------------------------- +--R 2 +--R 21b +--R Type: Expression(Integer) +--E 227 + +--S 228 of 512 +a0145:= integrate(t0145,x) +--R +--R +--R 5 3 2 3 2 4 +-+ 4 3 3 2 2 5 +--R (6b x + 84a b x + 70a b x)\|x + 35a b x + 105a b x + 21a x +--R (135) --------------------------------------------------------------- +--R 21 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 512 +m0145:= a0145-r0145 +--R +--R +--R 7 +--R a +--R (136) ---- +--R 2 +--R 21b +--R Type: Expression(Integer) +--E 229 + +--S 230 of 512 +d0145:= D(m0145,x) +--R +--R +--R (137) 0 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 512 +t0146:= (a+b*x^(1/2))^6 +--R +--R +--R 5 2 3 3 5 +-+ 6 3 2 4 2 4 2 6 +--R (138) (6a b x + 20a b x + 6a b)\|x + b x + 15a b x + 15a b x + a +--R Type: Expression(Integer) +--E 231 + +--S 232 of 512 +r0146:= 1/28*(a+b*x^(1/2))^7*(-a+7*b*x^(1/2))/b^2 +--R +--R +--R (139) +--R 7 3 3 5 2 5 3 +-+ 8 4 2 6 3 4 4 2 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x +--R + +--R 6 2 8 +--R 28a b x - a +--R / +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 232 + +--S 233 of 512 +a0146:= integrate(t0146,x) +--R +--R +--R (140) +--R 5 3 3 3 2 5 +-+ 6 4 2 4 3 4 2 2 6 +--R (48a b x + 224a b x + 112a b x)\|x + 7b x + 140a b x + 210a b x + 28a x +--R ----------------------------------------------------------------------------- +--R 28 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 512 +m0146:= a0146-r0146 +--R +--R +--R 8 +--R a +--R (141) ---- +--R 2 +--R 28b +--R Type: Expression(Integer) +--E 234 + +--S 235 of 512 +d0146:= D(m0146,x) +--R +--R +--R (142) 0 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 512 +t0147:= (a+b*x^(1/2))^7 +--R +--R +--R (143) +--R 7 3 2 5 2 4 3 6 +-+ 6 3 3 4 2 5 2 7 +--R (b x + 21a b x + 35a b x + 7a b)\|x + 7a b x + 35a b x + 21a b x + a +--R Type: Expression(Integer) +--E 236 + +--S 237 of 512 +r0147:= 1/36*(a+b*x^(1/2))^8*(-a+8*b*x^(1/2))/b^2 +--R +--R +--R (144) +--R 9 4 2 7 3 4 5 2 6 3 +-+ 8 4 3 6 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 4 2 7 2 9 +--R 378a b x + 36a b x - a +--R / +--R 2 +--R 36b +--R Type: Expression(Integer) +--E 237 + +--S 238 of 512 +a0147:= integrate(t0147,x) +--R +--R +--R (145) +--R 7 4 2 5 3 4 3 2 6 +-+ 6 4 3 4 3 +--R (8b x + 216a b x + 504a b x + 168a b x)\|x + 63a b x + 420a b x +--R + +--R 5 2 2 7 +--R 378a b x + 36a x +--R / +--R 36 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 512 +m0147:= a0147-r0147 +--R +--R +--R 9 +--R a +--R (146) ---- +--R 2 +--R 36b +--R Type: Expression(Integer) +--E 239 + +--S 240 of 512 +d0147:= D(m0147,x) +--R +--R +--R (147) 0 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 512 +t0148:= (a+b*x^(1/2))^8 +--R +--R +--R (148) +--R 7 3 3 5 2 5 3 7 +-+ 8 4 2 6 3 4 4 2 +--R (8a b x + 56a b x + 56a b x + 8a b)\|x + b x + 28a b x + 70a b x +--R + +--R 6 2 8 +--R 28a b x + a +--R Type: Expression(Integer) +--E 241 + +--S 242 of 512 +r0148:= 1/45*(a+b*x^(1/2))^9*(-a+9*b*x^(1/2))/b^2 +--R +--R +--R (149) +--R 9 4 3 7 3 5 5 2 7 3 +-+ 10 5 2 8 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 6 3 6 4 2 8 2 10 +--R 1050a b x + 630a b x + 45a b x - a +--R / +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 242 + +--S 243 of 512 +a0148:= integrate(t0148,x) +--R +--R +--R (150) +--R 7 4 3 5 3 5 3 2 7 +-+ 8 5 2 6 4 +--R (80a b x + 720a b x + 1008a b x + 240a b x)\|x + 9b x + 315a b x +--R + +--R 4 4 3 6 2 2 8 +--R 1050a b x + 630a b x + 45a x +--R / +--R 45 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 512 +m0148:= a0148-r0148 +--R +--R +--R 10 +--R a +--R (151) ---- +--R 2 +--R 45b +--R Type: Expression(Integer) +--E 244 + +--S 245 of 512 +d0148:= D(m0148,x) +--R +--R +--R (152) 0 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 512 +t0149:= 1/(4+b*x)^(1/2)/(-4+b*x)^(1/2) +--R +--R +--R 1 +--R (153) -------------------- +--R +-------+ +-------+ +--R \|b x - 4 \|b x + 4 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 512 +r0149:= acosh(1/4*b*x)/b +--R +--R +--R b x +--R acosh(---) +--R 4 +--R (154) ---------- +--R b +--R Type: Expression(Integer) +--E 247 + +--S 248 of 512 +--a0149:= integrate(t0149,x) +--E 248 + +--S 249 of 512 +--m0149:= a0149-r0149 +--E 249 + +--S 250 of 512 +--d0149:= D(m0149,x) +-- >> Error detected within library code: +-- integrate: implementation incomplete (non-algebraic residues) +--E 250 + +--S 251 of 512 +t0150:= 1/((-b+b*c)/d+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (155) ---------------------------- +--R +---------------+ +--R |b d x + b c - b +-------+ +--R |--------------- \|d x + c +--R \| d +--R Type: Expression(Integer) +--E 251 + +--S 252 of 512 +r0150:= 2*asinh(d^(1/2)*(b*(-1+c+d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x + b c - b +--R \|d |--------------- +--R \| d +--R 2asinh(----------------------) +--R +-+ +--R \|b +--R (156) ------------------------------ +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 252 + +--S 253 of 512 +--a0150:= integrate(t0150,x) +--E 253 + +--S 254 of 512 +--m0150:= a0150-r0150 +--E 254 + +--S 255 of 512 +--d0150:= D(m0150,x) +--E 255 + +--S 256 of 512 +t0151:= 1/x^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (157) ------------- +--R +-+ +------+ +--R \|x \|2x - 3 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 512 +r0151:= 2^(1/2)*asinh(1/3*(-3+2*x)^(1/2)*3^(1/2)) +--R +--R +--R +-+ +------+ +--R +-+ \|3 \|2x - 3 +--R (158) \|2 asinh(-------------) +--R 3 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 512 +--a0151:= integrate(t0151,x) +--E 258 + +--S 259 of 512 +--m0151:= a0151-r0151 +--E 259 + +--S 260 of 512 +--d0151:= D(m0151,x) +--E 260 + +--S 261 of 512 +t0152:= 1/(2+3*x)^(1/2)/(-3+2*x)^(1/2) +--R +--R +--R 1 +--R (159) ------------------ +--R +------+ +------+ +--R \|2x - 3 \|3x + 2 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 512 +r0152:= 1/3*6^(1/2)*asinh(1/13*39^(1/2)*(-3+2*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +-+ \|39 \|2x - 3 +--R \|6 asinh(--------------) +--R 13 +--R (160) ------------------------- +--R 3 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 512 +--a0152:= integrate(t0152,x) +--E 263 + +--S 264 of 512 +--m0152:= a0152-r0152 +--E 264 + +--S 265 of 512 +--d0152:= D(m0152,x) +--E 265 + +--S 266 of 512 +t0153:= 1/(a+b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (161) -------------------- +--R +-------+ +-------+ +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 266 + +--S 267 of 512 +r0153:= 2*atanh(d^(1/2)*(a+b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +-+ +-------+ +--R \|d \|b x + a +--R 2atanh(--------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (162) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 267 + +--S 268 of 512 +--a0153:= integrate(t0153,x) +--E 268 + +--S 269 of 512 +--m0153:= a0153-r0153 +--E 269 + +--S 270 of 512 +--d0153:= D(m0153,x) +--E 270 + +--S 271 of 512 +t0154:= 1/((b-b*c)/d+b*x)^(1/2)/(c-d*x)^(1/2) +--R +--R +--R 1 +--R (163) ------------------------------ +--R +---------------+ +--R +---------+ |b d x - b c + b +--R \|- d x + c |--------------- +--R \| d +--R Type: Expression(Integer) +--E 271 + +--S 272 of 512 +r0154:= 2*asin(d^(1/2)*(-b*(-1+c-d*x)/d)^(1/2)/b^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------------+ +--R +-+ |b d x - b c + b +--R \|d |--------------- +--R \| d +--R 2asin(----------------------) +--R +-+ +--R \|b +--R (164) ----------------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 272 + +--S 273 of 512 +--a0154:= integrate(t0154,x) +--E 273 + +--S 274 of 512 +--m0154:= a0154-r0154 +--E 274 + +--S 275 of 512 +--d0154:= D(m0154,x) +--E 275 + +--S 276 of 512 +t0155:= 1/(4-x)^(1/2)/x^(1/2) +--R +--R +--R 1 +--R (165) -------------- +--R +-------+ +-+ +--R \|- x + 4 \|x +--R Type: Expression(Integer) +--E 276 + +--S 277 of 512 +r0155:= 2*asin(1/2*x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (166) 2asin(----) +--R 2 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 512 +--a0155:= integrate(t0155,x) +--E 278 + +--S 279 of 512 +--m0155:= a0155-r0155 +--E 279 + +--S 280 of 512 +--d0155:= D(m0155,x) +--E 280 + +--S 281 of 512 +t0156:= 1/x^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (167) --------------- +--R +--------+ +-+ +--R \|- 2x + 3 \|x +--R Type: Expression(Integer) +--E 281 + +--S 282 of 512 +r0156:= 2^(1/2)*asin(1/3*6^(1/2)*x^(1/2)) +--R +--R +--R +-+ +-+ +--R +-+ \|6 \|x +--R (168) \|2 asin(--------) +--R 3 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 512 +--a0156:= integrate(t0156,x) +--E 283 + +--S 284 of 512 +--m0156:= a0156-r0156 +--E 284 + +--S 285 of 512 +--d0156:= D(m0156,x) +--E 285 + +--S 286 of 512 +t0157:= 1/(3+5*x)^(1/2)/(3-2*x)^(1/2) +--R +--R +--R 1 +--R (169) -------------------- +--R +--------+ +------+ +--R \|- 2x + 3 \|5x + 3 +--R Type: Expression(Integer) +--E 286 + +--S 287 of 512 +r0157:= 1/5*10^(1/2)*asin(1/21*42^(1/2)*(3+5*x)^(1/2)) +--R +--R +--R +--+ +------+ +--R +--+ \|42 \|5x + 3 +--R \|10 asin(--------------) +--R 21 +--R (170) ------------------------- +--R 5 +--R Type: Expression(Integer) +--E 287 + +--S 288 of 512 +--a0157:= integrate(t0157,x) +--E 288 + +--S 289 of 512 +--m0157:= a0157-r0157 +--E 289 + +--S 290 of 512 +--d0157:= D(m0157,x) +--E 290 + +--S 291 of 512 +t0158:= 1/(a-b*x)^(1/2)/(c+d*x)^(1/2) +--R +--R +--R 1 +--R (171) ---------------------- +--R +---------+ +-------+ +--R \|- b x + a \|d x + c +--R Type: Expression(Integer) +--E 291 + +--S 292 of 512 +r0158:= -2*atan(d^(1/2)*(a-b*x)^(1/2)/b^(1/2)/(c+d*x)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +---------+ +-+ +--R \|- b x + a \|d +--R 2atan(----------------) +--R +-+ +-------+ +--R \|b \|d x + c +--R (172) - ----------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 292 + +--S 293 of 512 +--a0158:= integrate(t0158,x) +--E 293 + +--S 294 of 512 +--m0158:= a0158-r0158 +--E 294 + +--S 295 of 512 +--d0158:= D(m0158,x) +--E 295 + +--S 296 of 512 +t0159:= 1/(a+b*(c+d*x)^(1/2)) +--R +--R +--R 1 +--R (173) --------------- +--R +-------+ +--R b\|d x + c + a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 512 +r0159:= -2*(-b*(c+d*x)^(1/2)+a*log(a+b*(c+d*x)^(1/2)))/b^2/d +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (174) ---------------------------------------- +--R 2 +--R b d +--R Type: Expression(Integer) +--E 297 + +--S 298 of 512 +a0159:= integrate(t0159,x) +--R +--R +--R +-------+ +-------+ +--R - 2a log(b\|d x + c + a) + 2b\|d x + c +--R (175) ---------------------------------------- +--R 2 +--R b d +--R Type: Union(Expression(Integer),...) +--E 298 + +--S 299 of 512 +m0159:= a0159-r0159 +--R +--R +--R (176) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 512 +d0159:= D(m0159,x) +--R +--R +--R (177) 0 +--R Type: Expression(Integer) +--E 300 + +--S 301 of 512 +t0160:= x^(1/2)/(1-x^2) +--R +--R +--R +-+ +--R \|x +--R (178) - ------ +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 301 + +--S 302 of 512 +r0160:= -atan(x^(1/2))+atanh(x^(1/2)) +--R +--R +--R +-+ +-+ +--R (179) atanh(\|x ) - atan(\|x ) +--R Type: Expression(Integer) +--E 302 + +--S 303 of 512 +a0160:= integrate(t0160,x) +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atan(\|x ) +--R (180) ------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 303 + +--S 304 of 512 +m0160:= a0160-r0160 +--R +--R +--R +-+ +-+ +-+ +--R log(\|x + 1) - log(\|x - 1) - 2atanh(\|x ) +--R (181) -------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 512 +d0160:= D(m0160,x) +--R +--R +--R (182) 0 +--R Type: Expression(Integer) +--E 305 + +--S 306 of 512 +t0161:= x^(1/2)/(a-b*x^2) +--R +--R +--R +-+ +--R \|x +--R (183) - -------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 306 + +--S 307 of 512 +r0161:= -(atan(b^(1/4)*x^(1/2)/a^(1/4))-_ + atanh(b^(1/4)*x^(1/2)/a^(1/4)))/a^(1/4)/b^(3/4) +--R +--R +--R 4+-+ +-+ 4+-+ +-+ +--R \|b \|x \|b \|x +--R atanh(--------) - atan(--------) +--R 4+-+ 4+-+ +--R \|a \|a +--R (184) -------------------------------- +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression(Integer) +--E 307 + +--S 308 of 512 +a0161:= integrate(t0161,x) +--R +--R +--R (185) +--R +------+ +------+3 +------+ +------+3 +--R | 1 +-+ 2 | 1 | 1 +-+ 2 | 1 +--R |------ log(\|x + 8a b |------ ) - |------ log(\|x - 8a b |------ ) +--R 4| 3 4| 3 4| 3 4| 3 +--R \|16a b \|16a b \|16a b \|16a b +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R +------+ 4| 3 +--R | 1 \|16a b +--R 2 |------ atan(---------------) +--R 4| 3 +-+ +--R \|16a b \|x +--R Type: Union(Expression(Integer),...) +--E 308 + +--S 309 of 512 +m0161:= a0161-r0161 +--R +--R +--R (186) +--R +------+ +------+3 +--R | 1 4+-+4+-+3 +-+ 2 | 1 +--R |------ \|a \|b log(\|x + 8a b |------ ) +--R 4| 3 4| 3 +--R \|16a b \|16a b +--R + +--R +------+ +------+3 4+-+ +-+ +--R | 1 4+-+4+-+3 +-+ 2 | 1 \|b \|x +--R - |------ \|a \|b log(\|x - 8a b |------ ) - atanh(--------) +--R 4| 3 4| 3 4+-+ +--R \|16a b \|16a b \|a +--R + +--R +------+3 +--R 2 | 1 +--R 8a b |------ +--R 4+-+ +-+ +------+ 4| 3 +--R \|b \|x | 1 4+-+4+-+3 \|16a b +--R atan(--------) + 2 |------ \|a \|b atan(---------------) +--R 4+-+ 4| 3 +-+ +--R \|a \|16a b \|x +--R / +--R 4+-+4+-+3 +--R \|a \|b +--R Type: Expression(Integer) +--E 309 + +--S 310 of 512 +d0161:= D(m0161,x) +--R +--R +--R (187) 0 +--R Type: Expression(Integer) +--E 310 + +--S 311 of 512 +t0162:= (2+3*x)^(1/2)/(a+b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (188) --------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 311 + +--S 312 of 512 +r0162:= -(-(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/(-3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2))+_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)*_ + atanh((-b)^(1/2)*(2+3*x)^(1/2)/_ + (3*a^(1/2)*(-b)^(1/2)-2*b)^(1/2)))/a^(1/2)/b +--R +--R +--R (189) +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R \|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - \|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 512 +a0162:= integrate(t0162,x) +--R +--R +--R (190) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 313 + +--S 314 of 512 +m0162:= a0162-r0162 +--R +--R +--R (191) +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 1 +--R |- 6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |-------------------- + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R | | 3 +--R +-+ | \| 4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 1 +--R |6a b |- ----- - 2 +--R +-------+ | | 3 +--R 2 | 1 | \| 4a b +------+ +--R log(- 2a b |- ----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +------------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R - 2\|- 3\|- b \|a - 2b atanh(---------------------) +--R +------------------+ +--R | +---+ +-+ +--R \|- 3\|- b \|a - 2b +--R + +--R +----------------+ +---+ +------+ +--R | +---+ +-+ \|- b \|3x + 2 +--R 2\|3\|- b \|a - 2b atanh(-------------------) +--R +----------------+ +--R | +---+ +-+ +--R \|3\|- b \|a - 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 314 + +--S 315 of 512 +d0162:= D(m0162,x) +--R +--R +--R (192) 0 +--R Type: Expression(Integer) +--E 315 + +--S 316 of 512 +t0163:= (2+3*x)^(1/2)/(a-b*x^2) +--R +--R +--R +------+ +--R \|3x + 2 +--R (193) - --------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 316 + +--S 317 of 512 +r0163:= -(-3*a^(1/2)*b^(1/2)+2*b)^(1/2)*atanh(b^(1/2)*(2+3*x)^(1/2)/_ + (-3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b+_ + (3*a^(1/2)*b^(1/2)+2*b)^(1/2)*_ + atanh(b^(1/2)*(2+3*x)^(1/2)/(3*a^(1/2)*b^(1/2)+2*b)^(1/2))/a^(1/2)/b +--R +--R +--R (194) +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - \|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R \|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 512 +a0163:= integrate(t0163,x) +--R +--R +--R (195) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R | \|4a b 2 | 1 | \|4a b +------+ +--R - |---------------- log(- 2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 318 + +--S 319 of 512 +m0163:= a0163-r0163 +--R +--R +--R (196) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 1 | | 1 +--R |6a b |----- + 2 |6a b |----- + 2 +--R | | 3 +-----+ | | 3 +--R +-+ | \|4a b 2 | 1 | \|4a b +------+ +--R b\|a |---------------- log(2a b |----- |---------------- + \|3x + 2 ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 1 +--R |- 6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |------------------ + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 1 +--R |6a b |----- + 2 +--R +-----+ | | 3 +--R 2 | 1 | \|4a b +------+ +--R log(- 2a b |----- |---------------- + \|3x + 2 ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R 2\|- 3\|a \|b + 2b atanh(-------------------) +--R +----------------+ +--R | +-+ +-+ +--R \|- 3\|a \|b + 2b +--R + +--R +--------------+ +-+ +------+ +--R | +-+ +-+ \|b \|3x + 2 +--R - 2\|3\|a \|b + 2b atanh(-----------------) +--R +--------------+ +--R | +-+ +-+ +--R \|3\|a \|b + 2b +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 512 +d0163:= D(m0163,x) +--R +--R +--R (197) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 512 +t0164:= (c+d*x)^(1/2)/(1+x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (198) ---------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 321 + +--S 322 of 512 +r0164:= d*((c-(-d^2)^(1/2))^(1/2)*atanh((c+d*x)^(1/2)/_ + (c-(-d^2)^(1/2))^(1/2))-(c+(-d^2)^(1/2))^(1/2)*_ + atanh((c+d*x)^(1/2)/(c+(-d^2)^(1/2))^(1/2)))/(-d^2)^(1/2) +--R +--R +--R (199) +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R \|- d +--R Type: Expression(Integer) +--E 322 + +--S 323 of 512 +a0164:= integrate(t0164,x) +--R +--R +--R (200) +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +-------+ atan(-----) +--R 4| 2 2 c +--R 2\|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 323 + +--S 324 of 512 +m0164:= a0164-r0164 +--R +--R +--R (201) +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|- d \|d + c cos(-----------) +--R 2 +--R * +--R log +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R d \|d + c sin(-----------) +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 +-------+ c +--R - 2\|d \|d + c \|d x + c sin(-----------) +--R 2 +--R + +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c 2 +--R d \|d + c cos(-----------) + d x + c d +--R 2 +--R + +--R - +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) - d\|d x + c +--R 2 +--R + +--R +--+ +--R | 2 +--R \|d +--R +----+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R 2\|- d \|d + c sin(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R atan(---------------------------------------------) +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+ atan(-----) +--R | 2 4| 2 2 c +-------+ +--R \|d \|d + c sin(-----------) + d\|d x + c +--R 2 +--R + +--R +-------------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R - 2d\|- \|- d + c atanh(----------------) +--R +-------------+ +--R | +----+ +--R | | 2 +--R \|- \|- d + c +--R + +--R +-----------+ +--R | +----+ +-------+ +--R | | 2 \|d x + c +--R 2d\|\|- d + c atanh(--------------) +--R +-----------+ +--R | +----+ +--R | | 2 +--R \|\|- d + c +--R / +--R +----+ +--R | 2 +--R 2\|- d +--R Type: Expression(Integer) +--E 324 + +--S 325 of 512 +d0164:= D(m0164,x) +--R +--R +--R (202) +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (6d + 12c d + 6c d )x + (12c d + 24c d + 12c d)x + 6c d +--R + +--R 4 2 6 +--R 12c d + 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ +--+ 9 +--R | 2 | 2 +--R \|d \|d +--R +--+ +-------+2 atan(-----) atan(-----) +--R | 2 4| 2 2 c c +--R \|d \|d + c cos(-----------)sin(-----------) +--R 2 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 6d - 18c d - 18c d - 6c d)x - 6c d - 18c d - 18c d - 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (12d + 24c d + 12c d )x + (24c d + 48c d + 24c d)x + 12c d +--R + +--R 4 2 6 +--R 24c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 15d - 30c d - 15c d )x + (- 45c d - 90c d - 45c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 45c d - 90c d - 45c d)x - 15c d - 30c d - 15c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 7 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- 4d - 12c d - 12c d - 4c d)x - 4c d - 12c d - 12c d - 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x + 8c d +--R + +--R 4 2 6 +--R 16c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 8d - 16c d - 8c d )x + (- 24c d - 48c d - 24c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 24c d - 48c d - 24c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (20d + 20c d )x + (80c d + 80c d )x + (120c d + 120c d )x +--R + +--R 3 3 5 4 2 6 +--R (80c d + 80c d)x + 20c d + 20c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 12d - 12c d )x + (- 36c d - 36c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 48c d - 36c d)x + (- 36c d - 48c d - 12c )x +--R + +--R 2 3 4 3 2 5 +--R (- 36c d - 36c d)x - 12c d - 12c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 6 6 3 4 5 2 7 +--R ((- d - 3c d - 3c d - c d)x - c d - 3c d - 3c d - c ) +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x + 4c d +--R + +--R 4 2 6 +--R 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- 4d - 8c d - 4c d )x + (- 12c d - 24c d - 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 12c d - 24c d - 12c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 8d - 8c d )x + (- 32c d - 32c d )x + (- 48c d - 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 32c d - 32c d)x - 8c d - 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 15d - 15c d )x + (- 75c d - 75c d )x + (- 150c d - 150c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 150c d - 150c d )x + (- 75c d - 75c d)x - 15c d - 15c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (8d + 8c d )x + (32c d + 32c d )x + (8d + 56c d + 48c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (32c d + 64c d + 32c d)x + (48c d + 56c d + 8c )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 2 5 3 3 5 2 4 4 2 +--R (2d + 4c d + 2c d )x + (4c d + 8c d + 4c d)x + 2c d + 4c d +--R + +--R 6 +--R 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (4d + 8c d + 4c d )x + (12c d + 24c d + 12c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (12c d + 24c d + 12c d)x + 4c d + 8c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (8d + 8c d )x + (32c d + 32c d )x + (48c d + 48c d )x +--R + +--R 3 3 5 4 2 6 +--R (32c d + 32c d)x + 8c d + 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (12d + 12c d )x + (60c d + 60c d )x + (120c d + 120c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (120c d + 120c d )x + (60c d + 60c d)x + 12c d + 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 +--R 6d x + 36c d x + 90c d x + 120c d x + 90c d x + 36c d x +--R + +--R 6 +--R 6c +--R * +--R +-------+2 +--R 4| 2 2 +--R \|d + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 2d - 2c d )x + (- 6c d - 6c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 8c d - 6c d)x + (- 6c d - 8c d - 2c )x +--R + +--R 2 3 4 3 2 5 +--R (- 6c d - 6c d)x - 2c d - 2c +--R * +--R +--+ 5 +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 28c d - 24c d )x + (- 16c d - 32c d - 16c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 24c d - 28c d - 4c )x + (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 3 +--R | 2 +--R \|d +--R +--+ atan(-----) +--R | 2 c +--R \|d cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 2d x - 10c d x + (- 2d - 20c d )x + (- 10c d - 20c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 20c d - 10c d)x + (- 20c d - 2c )x - 10c d x - 2c +--R * +--R +--+ +--R | 2 +--R \|d +--R +--+ +-------+2 atan(-----) +--R | 2 4| 2 2 c +--R \|d \|d + c cos(-----------) +--R 2 +--R * +--R +--+ +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 7 2 5 4 3 3 6 3 4 5 2 2 +--R (- d - 2c d - c d )x + (- 3c d - 6c d - 3c d )x +--R + +--R 2 5 4 3 6 3 4 5 2 7 +--R (- 3c d - 6c d - 3c d)x - c d - 2c d - c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 2 4 4 5 3 3 3 2 4 4 2 2 +--R (- 4d - 4c d )x + (- 16c d - 16c d )x + (- 24c d - 24c d )x +--R + +--R 3 3 5 4 2 6 +--R (- 16c d - 16c d)x - 4c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 2 5 5 6 3 4 4 2 5 4 3 3 +--R (- 6d - 6c d )x + (- 30c d - 30c d )x + (- 60c d - 60c d )x +--R + +--R 3 4 5 2 2 4 3 6 5 2 7 +--R (- 60c d - 60c d )x + (- 30c d - 30c d)x - 6c d - 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 6 6 5 5 2 4 4 3 3 3 4 2 2 5 6 +--R (- 4d x - 24c d x - 60c d x - 80c d x - 60c d x - 24c d x - 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 c +--R \|d + c cos(-----------) +--R 2 +--R + +--R 7 7 6 6 2 5 5 3 4 4 4 3 3 5 2 2 6 7 +--R - d x - 7c d x - 21c d x - 35c d x - 35c d x - 21c d x - 7c d x - c +--R / +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 12 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 6d - 12c d - 6c d)x + (- 6c d - 12c d - 6c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 6d - 12c d - 6c d)x - 6c d - 12c d - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 10 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((6d + 18c d + 18c d + 6c )x + 6d + 18c d + 18c d + 6c ) +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 12d - 24c d - 12c d)x + (- 12c d - 24c d - 12c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 12d - 24c d - 12c d)x - 12c d - 24c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 30c d + 15c d )x + (30c d + 60c d + 30c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (15d + 45c d + 45c d + 15c )x + (30c d + 60c d + 30c d)x +--R + +--R 2 4 4 2 6 +--R 15c d + 30c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +--R ((4d + 12c d + 12c d + 4c )x + 4d + 12c d + 12c d + 4c ) +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 16c d - 8c d)x + (- 8c d - 16c d - 8c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 8d - 16c d - 8c d)x - 8c d - 16c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (8d + 16c d + 8c d )x + (16c d + 32c d + 16c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (8d + 24c d + 24c d + 8c )x + (16c d + 32c d + 16c d)x +--R + +--R 2 4 4 2 6 +--R 8c d + 16c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 20d - 20c d )x + (- 60c d - 60c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 20d - 80c d - 60c d)x + (- 60c d - 80c d - 20c )x +--R + +--R 2 3 4 3 2 5 +--R (- 60c d - 60c d)x - 20c d - 20c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 6 2 6 2 4 4 2 6 +-------+ +--R ((d + 3c d + 3c d + c )x + d + 3c d + 3c d + c )\|d x + c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R cos(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 4d - 8c d - 4c d)x + (- 4c d - 8c d - 4c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 4d - 8c d - 4c d)x - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (4d + 8c d + 4c d )x + (8c d + 16c d + 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (4d + 12c d + 12c d + 4c )x + (8c d + 16c d + 8c d)x +--R + +--R 2 4 4 2 6 +--R 4c d + 8c d + 4c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (8d + 8c d )x + (24c d + 24c d )x + (8d + 32c d + 24c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (24c d + 32c d + 8c )x + (24c d + 24c d)x + 8c d + 8c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (15d + 15c d )x + (60c d + 60c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (15d + 105c d + 90c d )x + (60c d + 120c d + 60c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (90c d + 105c d + 15c )x + (60c d + 60c d)x + 15c d + 15c +--R * +--R +-------+ +--R \|d x + c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 2d - 4c d - 2c d)x + (- 2c d - 4c d - 2c )x +--R + +--R 5 2 3 4 4 3 2 5 +--R (- 2d - 4c d - 2c d)x - 2c d - 4c d - 2c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 4d - 8c d - 4c d )x + (- 8c d - 16c d - 8c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 +--R (- 4d - 12c d - 12c d - 4c )x + (- 8c d - 16c d - 8c d)x +--R + +--R 2 4 4 2 6 +--R - 4c d - 8c d - 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 +--R (- 8d - 8c d )x + (- 24c d - 24c d )x +--R + +--R 5 2 3 4 3 4 3 2 5 2 +--R (- 8d - 32c d - 24c d)x + (- 24c d - 32c d - 8c )x +--R + +--R 2 3 4 3 2 5 +--R (- 24c d - 24c d)x - 8c d - 8c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 +--R (- 12d - 12c d )x + (- 48c d - 48c d )x +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (- 12d - 84c d - 72c d )x + (- 48c d - 96c d - 48c d)x +--R + +--R 2 4 4 2 6 2 3 3 5 4 2 6 +--R (- 72c d - 84c d - 12c )x + (- 48c d - 48c d)x - 12c d - 12c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R - 6d x - 30c d x + (- 6d - 60c d )x + (- 30c d - 60c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (- 60c d - 30c d)x + (- 60c d - 6c )x - 30c d x - 6c +--R * +--R +-------+2 +--R 4| 2 2 +-------+ +--R \|d + c \|d x + c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R atan(-----) +--R c +--R sin(-----------) +--R 2 +--R + +--R 6 2 4 4 2 4 5 3 3 5 3 +--R (d + 2c d + c d )x + (2c d + 4c d + 2c d)x +--R + +--R 6 2 4 4 2 6 2 5 3 3 5 2 4 4 2 +--R (d + 3c d + 3c d + c )x + (2c d + 4c d + 2c d)x + c d + 2c d +--R + +--R 6 +--R c +--R * +--R +--+ 8 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 2 3 5 4 3 2 4 5 2 3 4 3 +--R (4d + 4c d )x + (12c d + 12c d )x + (4d + 16c d + 12c d)x +--R + +--R 4 3 2 5 2 2 3 4 3 2 5 +--R (12c d + 16c d + 4c )x + (12c d + 12c d)x + 4c d + 4c +--R * +--R +--+ 6 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 2 4 6 5 3 3 5 6 2 4 4 2 4 +--R (6d + 6c d )x + (24c d + 24c d )x + (6d + 42c d + 36c d )x +--R + +--R 5 3 3 5 3 2 4 4 2 6 2 +--R (24c d + 48c d + 24c d)x + (36c d + 42c d + 6c )x +--R + +--R 3 3 5 4 2 6 +--R (24c d + 24c d)x + 6c d + 6c +--R * +--R +--+ 4 +--R | 2 +--R \|d +--R atan(-----) +--R +-------+ c +--R \|d x + c cos(-----------) +--R 2 +--R + +--R 5 7 4 6 5 2 3 5 4 3 2 4 +--R 4d x + 20c d x + (4d + 40c d )x + (20c d + 40c d )x +--R + +--R 2 3 4 3 3 2 5 2 4 5 +--R (40c d + 20c d)x + (40c d + 4c )x + 20c d x + 4c +--R * +--R +--+ 2 +--R | 2 +--R \|d +--R +-------+2 atan(-----) +--R 4| 2 2 +-------+ c +--R \|d + c \|d x + c cos(-----------) +--R 2 +--R + +--R 6 8 5 7 6 2 4 6 5 3 3 5 +--R d x + 6c d x + (d + 15c d )x + (6c d + 20c d )x +--R + +--R 2 4 4 2 4 3 3 5 3 4 2 6 2 5 6 +--R (15c d + 15c d )x + (20c d + 6c d)x + (15c d + c )x + 6c d x + c +--R * +--R +-------+ +--R \|d x + c +--R Type: Expression(Integer) +--E 325 + +--S 326 of 512 +t0165:= (c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (203) ---------- +--R 2 +--R b x + a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 512 +r0165:= -(-(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))+_ + (b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2)))/_ + a^(1/2)/(-b)^(1/2)/b^(1/2) +--R +--R +--R (204) +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R \|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - \|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R \|- b \|a \|b +--R Type: Expression(Integer) +--E 327 + +--S 328 of 512 +a0165:= integrate(t0165,x) +--R +--R +--R (205) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R | \| 4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 328 + +--S 329 of 512 +m0165:= a0165-r0165 +--R +--R +--R (206) +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |- 2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |-------------------- +--R \| a b +--R * +--R +--------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |- 2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |-------------------- + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R - +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R |2a b |- ----- - c +--R | | 3 +--R +---+ +-+ +-+ | \| 4a b +--R \|- b \|a \|b |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-------+ +--R | | 2 +--R | | d +--R +-------+ |2a b |- ----- - c +--R | 2 | | 3 +--R 2 | d | \| 4a b +-------+ +--R log(- 2a b |- ----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \| 4a b +--R + +--R +-------------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R - 2\|- d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-----------------+ +-+ +-------+ +--R | +---+ +-+ \|b \|d x + c +--R 2\|d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +---+ +-+ +-+ +--R 2\|- b \|a \|b +--R Type: Expression(Integer) +--E 329 + +--S 330 of 512 +d0165:= D(m0165,x) +--R +--R +--R (207) 0 +--R Type: Expression(Integer) +--E 330 + +--S 331 of 512 +t0166:= (c+d*x)^(1/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R \|d x + c +--R (208) - ---------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 512 +r0166:= -(b*c-a^(1/2)*b^(1/2)*d)^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b+_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*b^(1/2)*d)^(1/2))/a^(1/2)/b +--R +--R +--R (209) +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - \|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R \|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R b\|a +--R Type: Expression(Integer) +--E 332 + +--S 333 of 512 +a0166:= integrate(t0166,x) +--R +--R +--R (210) +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R |---------------- log(2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R | \|4a b +--R |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +----------------+ +----------------+ +--R | +-----+ | +-----+ +--R | | 2 | | 2 +--R | | d | | d +--R |2a b |----- + c +-----+ |2a b |----- + c +--R | | 3 | 2 | | 3 +--R | \|4a b 2 | d | \|4a b +-------+ +--R - |---------------- log(- 2a b |----- |---------------- + d\|d x + c ) +--R \| a b | 3 \| a b +--R \|4a b +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 333 + +--S 334 of 512 +m0166:= a0166-r0166 +--R +--R +--R (211) +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |- 2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |------------------ +--R \| a b +--R * +--R +------------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |- 2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |------------------ + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R - +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R |2a b |----- + c +--R | | 3 +--R +-+ | \|4a b +--R b\|a |---------------- +--R \| a b +--R * +--R +----------------+ +--R | +-----+ +--R | | 2 +--R | | d +--R +-----+ |2a b |----- + c +--R | 2 | | 3 +--R 2 | d | \|4a b +-------+ +--R log(- 2a b |----- |---------------- + d\|d x + c ) +--R | 3 \| a b +--R \|4a b +--R + +--R +-----------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R 2\|- d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +---------------+ +-+ +-------+ +--R | +-+ +-+ \|b \|d x + c +--R - 2\|d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-+ +--R 2b\|a +--R Type: Expression(Integer) +--E 334 + +--S 335 of 512 +d0166:= D(m0166,x) +--R +--R +--R (212) 0 +--R Type: Expression(Integer) +--E 335 + +--S 336 of 512 +t0167:= 1/(c+d*x)^(1/2)/(a+b*x^2) +--R +--R +--R 1 +--R (213) -------------------- +--R 2 +-------+ +--R (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 336 + +--S 337 of 512 +r0167:= b^(1/2)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)-b^(1/2)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + a^(1/2)/(-b)^(1/2)/(b*c+a^(1/2)*(-b)^(1/2)*d)^(1/2) +--R +--R +--R (214) +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R \|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - \|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 337 + +--S 338 of 512 +a0167:= integrate(t0167,x) +--R +--R +--R (215) +--R - +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 338 + +--S 339 of 512 +m0167:= a0167-r0167 +--R +--R +--R (216) +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (2a b c d + 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d 2 +--R ((2a b c d + 2a b c ) |- ----------------------------- + a d ) +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R - +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R - a d +--R * +--R +---------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(- 2a d - 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |--------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-------------------+ +--R +---+ +-+ | +---+ +-+ +--R \|- b \|a \|- d\|- b \|a + b c +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R +-------------------------------+ +--R | 2 +--R 2 2 2 3 | d +--R (- 2a b c d - 2a b c ) |- ----------------------------- +--R | 3 4 2 2 2 2 3 4 +--R \| 4a b d + 8a b c d + 4a b c +--R + +--R 2 +--R a d +--R * +--R +-------------------------------------------------------+ +--R | +-------------------------------+ +--R | | 2 +--R | 2 2 2 | d +--R |(2a d + 2a b c ) |- ----------------------------- - c +--R | | 3 4 2 2 2 2 3 4 +--R | \| 4a b d + 8a b c d + 4a b c +--R |------------------------------------------------------- +--R | 2 2 2 +--R \| a d + a b c +--R + +--R +-------+ +--R d\|d x + c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R - 2\|b \|d\|- b \|a + b c atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ | +---+ +-+ \|b \|d x + c +--R 2\|b \|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R +---+ +-+ | +---+ +-+ | +---+ +-+ +--R 2\|- b \|a \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 339 + +--S 340 of 512 +d0167:= D(m0167,x) +--R +--R +--R (217) 0 +--R Type: Expression(Integer) +--E 340 + +--S 341 of 512 +t0168:= (c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R +-------+ +--R (- d x - c)\|d x + c +--R (218) --------------------- +--R 2 +--R b x - a +--R Type: Expression(Integer) +--E 341 + +--S 342 of 512 +r0168:= -2*d*(c+d*x)^(1/2)/b+(2*b^(1/2)*c*d-(b*c^2+a*d^2)/a^(1/2))*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + b/(b*c-a^(1/2)*b^(1/2)*d)^(1/2)+(2*b^(1/2)*c*d+(b*c^2+a*d^2)/_ + a^(1/2))*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/b/(b*c+a^(1/2)*b^(1/2)*d)^(1/2) +--R +--R +--R (219) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b - a d - b c )\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ 2 2 | +-+ +-+ \|b \|d x + c +--R (2c d\|a \|b + a d + b c )\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 342 + +--S 343 of 512 +a0168:= integrate(t0168,x) +--R +--R +--R (220) +--R - +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R b |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-------+ +--R - 4d\|d x + c +--R / +--R 2b +--R Type: Union(Expression(Integer),...) +--E 343 + +--S 344 of 512 +m0168:= a0168-r0168 +--R +--R +--R (221) +--R - +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R - +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R +-+ | \| 4a b +--R b\|a |----------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R +-----------------+ +---------------+ +--R | +-+ +-+ | +-+ +-+ +--R \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- - a b d - 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +-----------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |- 2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |----------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R * +--R log +--R +--------------------------+ +--R | 2 6 2 4 2 4 2 +--R 4 |a d + 6a b c d + 9b c d 2 4 2 2 2 +--R (- 2a b c |-------------------------- + a b d + 3a b c d ) +--R | 5 +--R \| 4a b +--R * +--R +---------------------------------------------------+ +--R | +--------------------------+ +--R | | 2 6 2 4 2 4 2 +--R | 2 |a d + 6a b c d + 9b c d 2 3 +--R |2a b |-------------------------- + 3a c d + b c +--R | | 5 +--R | \| 4a b +--R |--------------------------------------------------- +--R | 2 +--R \| a b +--R + +--R 2 5 2 3 2 4 +-------+ +--R (a d + 2a b c d - 3b c d)\|d x + c +--R + +--R +---------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b + 2a d + 2b c )\|d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +--R +-+ +-+ 2 2 | +-+ +-+ +--R (- 4c d\|a \|b - 2a d - 2b c )\|- d\|a \|b + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R 2b\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 344 + +--S 345 of 512 +d0168:= D(m0168,x) +--R +--R +--R (222) 0 +--R Type: Expression(Integer) +--E 345 + +--S 346 of 512 +t0169:= 1/(c+d*x)^(3/2)/(a+b*x^2) +--R +--R +--R 1 +--R (223) ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x + a d x + a c)\|d x + c +--R Type: Expression(Integer) +--E 346 + +--S 347 of 512 +r0169:= -2*d/(b*c^2+a*d^2)/(c+d*x)^(1/2)+((-b)^(3/2)*c/a^(1/2)+b*d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2))/_ + b^(1/2)/(b*c-a^(1/2)*(-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2)-_ + ((-b)^(3/2)*c/a^(1/2)-b*d)*atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c+_ + a^(1/2)*(-b)^(1/2)*d)^(1/2))/b^(1/2)/(b*c+a^(1/2)*_ + (-b)^(1/2)*d)^(1/2)/(b*c^2+a*d^2) +--R +--R +--R (224) +--R +-----------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a - b c\|- b )\|d x + c \|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +--R +-+ +---+ +-------+ | +---+ +-+ +--R (b d\|a + b c\|- b )\|d x + c \|- d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R + +--R +-------------------+ +-----------------+ +--R +-+ +-+ | +---+ +-+ | +---+ +-+ +--R - 2d\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ +-------+ | +---+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|d x + c \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 347 + +--S 348 of 512 +a0169:= integrate(t0169,x) +--R +--R +--R (225) +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d + 2b c )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 348 + +--S 349 of 512 +m0169:= a0169-r0169 +--R +--R +--R (226) +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d + 4a b c d - 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (- a d - b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d - 6a b c d - 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-------------------+ +--R 2 2 +-+ +-+ | +---+ +-+ +--R (a d + b c )\|a \|b \|- d\|- b \|a + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R * +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d - 4a b c d + 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d + 6a b c d + 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R - a b d + 6a b c d - 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d + 24a b c d + 60a b c d + 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d + 24a b c d + 4a b c +--R + +--R 2 2 3 +--R 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d + 3a b c d + 3a b c d + a b c +--R + +--R 3 2 2 +-------+ +--R (a b d - 3b c d)\|d x + c +--R + +--R +-----------------+ +--R +-+ +---+ | +---+ +-+ +--R (- 2b d\|a + 2b c\|- b )\|d\|- b \|a + b c +--R * +--R +-+ +-------+ +--R \|b \|d x + c +--R atanh(----------------------) +--R +-------------------+ +--R | +---+ +-+ +--R \|- d\|- b \|a + b c +--R + +--R +-------------------+ +-+ +-------+ +--R +-+ +---+ | +---+ +-+ \|b \|d x + c +--R (- 2b d\|a - 2b c\|- b )\|- d\|- b \|a + b c atanh(--------------------) +--R +-----------------+ +--R | +---+ +-+ +--R \|d\|- b \|a + b c +--R / +--R +-------------------+ +-----------------+ +--R 2 2 +-+ +-+ | +---+ +-+ | +---+ +-+ +--R (2a d + 2b c )\|a \|b \|- d\|- b \|a + b c \|d\|- b \|a + b c +--R Type: Expression(Integer) +--E 349 + +--S 350 of 512 +d0169:= D(m0169,x) +--R +--R +--R (227) 0 +--R Type: Expression(Integer) +--E 350 + +--S 351 of 512 +t0170:= 1/(c+d*x)^(3/2)/(a-b*x^2) +--R +--R +--R 1 +--R (228) - ----------------------------------------- +--R 3 2 +-------+ +--R (b d x + b c x - a d x - a c)\|d x + c +--R Type: Expression(Integer) +--E 351 + +--S 352 of 512 +r0170:= 2*d/(b*c^2-a*d^2)/(c+d*x)^(1/2)-b^(1/2)*(b^(1/2)*c/a^(1/2)+d)*_ + atanh(b^(1/2)*(c+d*x)^(1/2)/(b*c-a^(1/2)*b^(1/2)*d)^(1/2))/_ + (b*c-a^(1/2)*b^(1/2)*d)^(1/2)/(b*c^2-a*d^2)+b^(1/2)*(b^(1/2)*c/_ + a^(1/2)-d)*atanh(b^(1/2)*(c+d*x)^(1/2)/_ + (b*c+a^(1/2)*b^(1/2)*d)^(1/2))/(b*c+a^(1/2)*b^(1/2)*d)^(1/2)/_ + (b*c^2-a*d^2) +--R +--R +--R (229) +--R +---------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b + b c)\|d x + c \|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ +-------+ | +-+ +-+ \|b \|d x + c +--R (d\|a \|b - b c)\|d x + c \|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R + +--R +-----------------+ +---------------+ +--R +-+ | +-+ +-+ | +-+ +-+ +--R - 2d\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ +-------+ | +-+ +-+ | +-+ +-+ +--R (a d - b c )\|a \|d x + c \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 352 + +--S 353 of 512 +a0170:= integrate(t0170,x) +--R +--R +--R (230) +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (a d - b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R 2 2 +-------+ +--R (- a d + b c )\|d x + c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R - 4d +--R / +--R 2 2 +-------+ +--R (2a d - 2b c )\|d x + c +--R Type: Union(Expression(Integer),...) +--E 353 + +--S 354 of 512 +m0170:= a0170-r0170 +--R +--R +--R (231) +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (2a d - 4a b c d + 4a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (a d - b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R 2a b c d + 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (- 2a d + 6a b c d - 6a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +-----------------+ +--R 2 2 +-+ | +-+ +-+ +--R (- a d + b c )\|a \|- d\|a \|b + b c +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R * +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R * +--R log +--R 5 8 4 2 6 2 3 6 2 4 8 +--R (- 2a d + 4a b c d - 4a b c d + 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 4 2 3 2 +--R - 2a b c d - 6a b c d +--R * +--R ROOT +--R 4 6 3 2 4 2 2 4 2 3 6 +--R (2a d - 6a b c d + 6a b c d - 2a b c ) +--R * +--R ROOT +--R 2 6 2 2 4 3 4 2 +--R a b d + 6a b c d + 9b c d +--R / +--R 7 12 6 2 10 5 2 4 8 4 3 6 6 +--R 4a d - 24a b c d + 60a b c d - 80a b c d +--R + +--R 3 4 8 4 2 5 10 2 6 12 +--R 60a b c d - 24a b c d + 4a b c +--R + +--R 2 2 3 +--R - 3a b c d - b c +--R / +--R 4 6 3 2 4 2 2 4 2 3 6 +--R a d - 3a b c d + 3a b c d - a b c +--R + +--R 3 2 2 +-------+ +--R (a b d + 3b c d)\|d x + c +--R + +--R +---------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b - 2b c)\|d\|a \|b + b c atanh(--------------------) +--R +-----------------+ +--R | +-+ +-+ +--R \|- d\|a \|b + b c +--R + +--R +-----------------+ +-+ +-------+ +--R +-+ +-+ | +-+ +-+ \|b \|d x + c +--R (- 2d\|a \|b + 2b c)\|- d\|a \|b + b c atanh(------------------) +--R +---------------+ +--R | +-+ +-+ +--R \|d\|a \|b + b c +--R / +--R +-----------------+ +---------------+ +--R 2 2 +-+ | +-+ +-+ | +-+ +-+ +--R (2a d - 2b c )\|a \|- d\|a \|b + b c \|d\|a \|b + b c +--R Type: Expression(Integer) +--E 354 + +--S 355 of 512 +d0170:= D(m0170,x) +--R +--R +--R (232) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 512 +t0171:= (d+e*x)^(1/2)/(a+b*x+c*x^2) +--R +--R +--R +-------+ +--R \|e x + d +--R (233) -------------- +--R 2 +--R c x + b x + a +--R Type: Expression(Integer) +--E 356 + +--S 357 of 512 +r0171:= 2^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atan(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/(-2*c*d+_ + (b+(b^2-4*a*c)^(1/2))*e)^(1/2))/c^(1/2)/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)-2^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atanh(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + c^(1/2)/(2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2) +--R +--R +--R (234) +--R +-----------+ +--R +-+ | 2 +-+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R +-+ | 2 +-+ | | 2 +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|e\|- 4a c + b - b e + 2c d +--R * +--R +-+ +-+ +-------+ +--R \|2 \|c \|e x + d +--R atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R \|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 357 + +--S 358 of 512 +a0171:= integrate(t0171,x) +--R +--R +--R (235) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 358 + +--S 359 of 512 +m0171:= a0171-r0171 +--R +--R +--R (236) +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (4a c - b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +-----------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(- 8a c + 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |----------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R - +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R +-----------+ | | 3 2 2 +--R | 2 +-+ | \| 4a c - b c +--R \|- 4a c + b \|c |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R +--------------+ +--R | 2 +--R 2 2 | e +--R (- 4a c + b c) |- ------------ +--R | 3 2 2 +--R \| 4a c - b c +--R * +--R +---------------------------------------------+ +--R | +--------------+ +--R | | 2 +--R | 2 2 | e +--R |(8a c - 2b c) |- ------------ + 2b e - 4c d +--R | | 3 2 2 +--R | \| 4a c - b c +--R |--------------------------------------------- +--R | 2 2 +--R \| 4a c - b c +--R + +--R +-------+ +--R 2e\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 ) +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 +-+ | | 2 +--R 2\|- 4a c + b \|c \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 359 + +--S 360 of 512 +d0171:= D(m0171,x) +--R +--R +--R (237) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 512 +t0172:= 1/(d+e*x)^(3/2)/(a+b*x+c*x^2) +--R +--R +--R 1 +--R (238) ------------------------------------------------------- +--R 3 2 +-------+ +--R (c e x + (b e + c d)x + (a e + b d)x + a d)\|e x + d +--R Type: Expression(Integer) +--E 361 + +--S 362 of 512 +r0172:= -2*e/(c*d^2-b*d*e+a*e^2)/(d+e*x)^(1/2)-2^(1/2)*c^(1/2)*_ + (e+(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*atan(2^(1/2)*c^(1/2)*_ + (d+e*x)^(1/2)/(-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (-2*c*d+(b+(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2)+_ + 2^(1/2)*c^(1/2)*(e-(2*c*d-b*e)/(b^2-4*a*c)^(1/2))*_ + atanh(2^(1/2)*c^(1/2)*(d+e*x)^(1/2)/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2))/_ + (2*c*d-(b-(b^2-4*a*c)^(1/2))*e)^(1/2)/(c*d^2-b*d*e+a*e^2) +--R +--R +--R (239) +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +-------+ +--R (- e\|2 \|- 4a c + b + (b e - 2c d)\|2 )\|c \|e x + d +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R + +--R - +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R | 2 | | 2 +--R 2e\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +-----------+ +--R 2 2 | 2 +-------+ +--R (a e - b d e + c d )\|- 4a c + b \|e x + d +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 362 + +--S 363 of 512 +a0172:= integrate(t0172,x) +--R +--R +--R (240) +--R 2 2 +-------+ +--R (- a e + b d e - c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (8a c - 6a b c + a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (- 16a b c + 16a b c - 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (16a c - 16a b c - 9a b c + 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (40a b c - 6a b c - b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (- 60a b c - 5a b c + 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (48a b c + 32a b c - 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (- 16a c - 48a b c + 13b c )d e + (32a b c - 8b c )d e +--R + +--R 6 2 5 8 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (4a b c - 5a b c + b )e + (- 8a c + 22a b c - 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (- 36a b c + 9b c )d e + (24a c - 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R 2 2 +-------+ +--R (a e - b d e + c d )\|e x + d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (- 8a c + 2a b )e + (24a b c - 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (- 24a c - 18a b c + 6b c)d e + (24a b c - 6b c )d e +--R + +--R 4 2 3 6 +--R (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 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15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R - 4e +--R / +--R 2 2 +-------+ +--R (2a e - 2b d e + 2c d )\|e x + d +--R Type: Union(Expression(Integer),...) +--E 363 + +--S 364 of 512 +m0172:= a0172-r0172 +--R +--R +--R (241) +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (- a e + b d e - 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9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R +----------------------------+ +----------------------------+ +--R | +-----------+ | +-----------+ +--R | | 2 | | 2 +--R \|e\|- 4a c + b - b e + 2c d \|e\|- 4a c + b + b e - 2c d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 8a c + 6a b c - a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (16a b c - 16a b c + 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 16a c + 16a b c + 9a b c - 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 40a b c + 6a b c + b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (60a b c + 5a b c - 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 48a b c - 32a b c + 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (16a c + 48a b c - 13b c )d e + (- 32a b c + 8b c )d e +--R + +--R 6 2 5 8 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 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6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (- 24a c - 18a b c + 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (48a b c - 4a b c - 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (- 24a c - 18a b c + 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (24a b c - 6b c )d e + (- 8a c + 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (a e - b d e + c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (24a c + 18a b c - 6b c)d e + (- 24a b c + 6b c )d e +--R + +--R 4 2 3 6 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 2 2 3 5 3 3 +--R (12a c + 9a b c - 3a b )d e + (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R * +--R log +--R 5 2 4 2 3 4 8 +--R (- 8a c + 6a b c - a b )e +--R + +--R 4 2 3 3 2 5 7 +--R (16a b c - 16a b c + 3a b )d e +--R + +--R 4 3 3 2 2 2 4 6 2 6 +--R (- 16a c + 16a b c + 9a b c - 3a b )d e +--R + +--R 2 3 2 5 7 3 5 +--R (- 40a b c + 6a b c + b )d e +--R + +--R 2 2 3 4 2 6 4 4 +--R (60a b c + 5a b c - 5b c)d e +--R + +--R 2 4 3 3 5 2 5 3 +--R (- 48a b c - 32a b c + 11b c )d e +--R + +--R 2 5 2 4 4 3 6 2 5 3 4 7 +--R (16a c + 48a b c - 13b c )d e + (- 32a b c + 8b c )d e +--R + +--R 6 2 5 8 +--R (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 2 3 5 +--R (- a c + 2a b c - b )e + (- 6a b c + 6b c)d e +--R + +--R 3 2 2 2 4 3 3 3 4 4 2 +--R (6a c - 15b c )d e + 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 6 6 +--R (80a c + 340a b c + 30a b c - 26a b c - b )d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 2 2 3 5 5 2 3 2 2 4 4 +--R (- 4a b c + 5a b c - b )e + (8a c - 22a b c + 5b c)d e +--R + +--R 3 3 2 2 3 4 2 3 3 2 +--R (36a b c - 9b c )d e + (- 24a c + 6b c )d e +--R * +--R ROOT +--R 4 3 2 6 3 2 3 5 +--R (8a c - 2a b )e + (- 24a b c + 6a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (24a c + 18a b c - 6a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 48a b c + 4a b c + 2b )d e +--R + +--R 2 3 2 2 4 4 2 +--R (24a c + 18a b c - 6b c)d e +--R + +--R 3 3 2 5 4 2 3 6 +--R (- 24a b c + 6b c )d e + (8a c - 2b c )d +--R * +--R ROOT +--R 2 2 2 4 6 +--R (- a c + 2a b c - b )e +--R + +--R 2 3 5 3 2 2 2 4 +--R (- 6a b c + 6b c)d e + (6a c - 15b c )d e +--R + +--R 3 3 3 4 4 2 +--R 18b c d e - 9c d e +--R / +--R 7 6 2 12 6 5 3 11 +--R (4a c - a b )e + (- 24a b c + 6a b )d e +--R + +--R 6 2 5 2 4 4 2 10 +--R (24a c + 54a b c - 15a b )d e +--R + +--R 5 2 4 3 3 5 3 9 +--R (- 120a b c - 50a b c + 20a b )d e +--R + +--R 5 3 4 2 2 2 6 4 8 +--R (60a c + 225a b c - 15a b )d e +--R + +--R 4 3 3 3 2 2 5 7 5 7 +--R (- 240a b c - 180a b c + 36a b c + 6a b )d e +--R + +--R 4 4 3 2 3 2 4 2 6 8 +--R (80a c + 340a b c + 30a b c - 26a b c - b ) +--R * +--R 6 6 +--R d e +--R + +--R 3 4 2 3 3 5 2 7 7 5 +--R (- 240a b c - 180a b c + 36a b c + 6b c)d e +--R + +--R 3 5 2 2 4 6 2 8 4 +--R (60a c + 225a b c - 15b c )d e +--R + +--R 2 5 3 4 5 3 9 3 +--R (- 120a b c - 50a b c + 20b c )d e +--R + +--R 2 6 2 5 4 4 10 2 +--R (24a c + 54a b c - 15b c )d e +--R + +--R 6 3 5 11 7 2 6 12 +--R (- 24a b c + 6b c )d e + (4a c - b c )d +--R + +--R 3 3 2 2 2 2 2 3 3 +--R (- 6a b c + 2b )e + (12a c - 6b c)d e + 6b c d e - 4c d +--R / +--R 4 3 2 6 3 2 3 5 +--R (4a c - a b )e + (- 12a b c + 3a b )d e +--R + +--R 3 2 2 2 4 2 4 +--R (12a c + 9a b c - 3a b )d e +--R + +--R 2 2 3 5 3 3 +--R (- 24a b c + 2a b c + b )d e +--R + +--R 2 3 2 2 4 4 2 3 3 2 5 +--R (12a c + 9a b c - 3b c)d e + (- 12a b c + 3b c )d e +--R + +--R 4 2 3 6 +--R (4a c - b c )d +--R + +--R 3 2 2 3 3 2 4 2 +-------+ +--R ((4a c - 4b c )e + 12b c d e - 12c d e)\|e x + d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (- 2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b + b e - 2c d atanh(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b - b e + 2c d +--R + +--R +-----------+ +--R +-+ | 2 +-+ +-+ +--R (2e\|2 \|- 4a c + b + (- 2b e + 4c d)\|2 )\|c +--R * +--R +----------------------------+ +--R | +-----------+ +-+ +-+ +-------+ +--R | | 2 \|2 \|c \|e x + d +--R \|e\|- 4a c + b - b e + 2c d atan(-------------------------------) +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R / +--R +----------------------------+ +--R +-----------+ | +-----------+ +--R 2 2 | 2 | | 2 +--R (2a e - 2b d e + 2c d )\|- 4a c + b \|e\|- 4a c + b - b e + 2c d +--R * +--R +----------------------------+ +--R | +-----------+ +--R | | 2 +--R \|e\|- 4a c + b + b e - 2c d +--R Type: Expression(Integer) +--E 364 + +--S 365 of 512 +d0172:= D(m0172,x) +--R +--R +--R (242) 0 +--R Type: Expression(Integer) +--E 365 + +--S 366 of 512 +t0173:= 1/(-2+x)/(2+x)^(1/2) +--R +--R +--R 1 +--R (243) --------------- +--R +-----+ +--R (x - 2)\|x + 2 +--R Type: Expression(Integer) +--E 366 + +--S 367 of 512 +r0173:= -atanh(1/2*(2+x)^(1/2)) +--R +--R +--R +-----+ +--R \|x + 2 +--R (244) - atanh(--------) +--R 2 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 512 +a0173:= integrate(t0173,x) +--R +--R +--R +-----+ +-----+ +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) +--R (245) --------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 368 + +--S 369 of 512 +m0173:= a0173-r0173 +--R +--R +--R +-----+ +--R +-----+ +-----+ \|x + 2 +--R - log(\|x + 2 + 2) + log(\|x + 2 - 2) + 2atanh(--------) +--R 2 +--R (246) ---------------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 512 +d0173:= D(m0173,x) +--R +--R +--R (247) 0 +--R Type: Expression(Integer) +--E 370 + +--S 371 of 512 +t0174:= 1/(1+x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (248) - ---------------- +--R +-----+ +--R \|x + 2 - x - 1 +--R Type: Expression(Integer) +--E 371 + +--S 372 of 512 +r0174:= 2/5*atanh(1/5*(1-2*(2+x)^(1/2))*5^(1/2))*5^(1/2)+log(-1-x+(2+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 2 - \|5 +--R 5log(\|x + 2 - x - 1) - 2\|5 atanh(--------------------) +--R 5 +--R (249) --------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 372 + +--S 373 of 512 +a0174:= integrate(t0174,x) +--R +--R +--R (250) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 2 + x + 1) +--R +-----+ +--R \|x + 2 - x - 1 +--R ---------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 373 + +--S 374 of 512 +m0174:= a0174-r0174 +--R +--R +--R (251) +--R +-+ +-----+ +--R - \|5 log(\|x + 2 - x - 1) +--R + +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 2 + (- 2x - 7)\|5 - 5 +--R log(-----------------------------------------) +--R +-----+ +--R \|x + 2 - x - 1 +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 2 - \|5 +--R \|5 log(- \|x + 2 + x + 1) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 512 +d0174:= D(m0174,x) +--R +--R +--R (252) 0 +--R Type: Expression(Integer) +--E 375 + +--S 376 of 512 +t0175:= 1/(x-(1+x)^(1/2)) +--R +--R +--R 1 +--R (253) - ------------ +--R +-----+ +--R \|x + 1 - x +--R Type: Expression(Integer) +--E 376 + +--S 377 of 512 +r0175:= 2/5*atanh(1/5*(1-2*(1+x)^(1/2))*5^(1/2))*5^(1/2)+log(-x+(1+x)^(1/2)) +--R +--R +--R +-+ +-----+ +-+ +--R +-----+ +-+ 2\|5 \|x + 1 - \|5 +--R 5log(\|x + 1 - x) - 2\|5 atanh(--------------------) +--R 5 +--R (254) ----------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 377 + +--S 378 of 512 +a0175:= integrate(t0175,x) +--R +--R +--R (255) +--R +-+ +-----+ +-+ +--R (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +-+ +-----+ +--R log(-----------------------------------------) + \|5 log(- \|x + 1 + x) +--R +-----+ +--R \|x + 1 - x +--R ------------------------------------------------------------------------ +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 378 + +--S 379 of 512 +m0175:= a0175-r0175 +--R +--R +--R (256) +--R +-+ +-----+ +-+ +--R +-+ +-----+ (2\|5 + 10)\|x + 1 + (- 2x - 5)\|5 - 5 +--R - \|5 log(\|x + 1 - x) + log(-----------------------------------------) +--R +-----+ +--R \|x + 1 - x +--R + +--R +-+ +-----+ +-+ +--R +-+ +-----+ 2\|5 \|x + 1 - \|5 +--R \|5 log(- \|x + 1 + x) + 2atanh(--------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 379 + +--S 380 of 512 +d0175:= D(m0175,x) +--R +--R +--R (257) 0 +--R Type: Expression(Integer) +--E 380 + +--S 381 of 512 +t0176:= 1/(x-(2+x)^(1/2)) +--R +--R +--R 1 +--R (258) - ------------ +--R +-----+ +--R \|x + 2 - x +--R Type: Expression(Integer) +--E 381 + +--S 382 of 512 +r0176:= 4/3*log(2-(2+x)^(1/2))+2/3*log(1+(2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(- \|x + 2 + 2) +--R (259) ----------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 382 + +--S 383 of 512 +a0176:= integrate(t0176,x) +--R +--R +--R +-----+ +-----+ +--R 2log(\|x + 2 + 1) + 4log(\|x + 2 - 2) +--R (260) --------------------------------------- +--R 3 +--R Type: Union(Expression(Integer),...) +--E 383 + +--S 384 of 512 +m0176:= a0176-r0176 +--R +--R +--R +-----+ +-----+ +--R 4log(\|x + 2 - 2) - 4log(- \|x + 2 + 2) +--R (261) ----------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 384 + +--S 385 of 512 +d0176:= D(m0176,x) +--R +--R +--R (262) 0 +--R Type: Expression(Integer) +--E 385 + +--S 386 of 512 +t0177:= 1/(x-(1-x)^(1/2)) +--R +--R +--R 1 +--R (263) - -------------- +--R +-------+ +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 386 + +--S 387 of 512 +r0177:= 2/5*atanh(1/5*(1+2*(1-x)^(1/2))*5^(1/2))*5^(1/2)+log(x-(1-x)^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +--R +-------+ +-+ 2\|5 \|- x + 1 + \|5 +--R 5log(- \|- x + 1 + x) + 2\|5 atanh(----------------------) +--R 5 +--R (264) ----------------------------------------------------------- +--R 5 +--R Type: Expression(Integer) +--E 387 + +--S 388 of 512 +a0177:= integrate(t0177,x) +--R +--R +--R (265) +--R +-+ +-------+ +-+ +--R +-+ +-------+ (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R \|5 log(\|- x + 1 - x) + log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R -------------------------------------------------------------------------- +--R +-+ +--R \|5 +--R Type: Union(Expression(Integer),...) +--E 388 + +--S 389 of 512 +m0177:= a0177-r0177 +--R +--R +--R (266) +--R +-+ +-------+ +--R \|5 log(\|- x + 1 - x) +--R + +--R +-+ +-------+ +-+ +--R (2\|5 + 10)\|- x + 1 + (- 2x + 5)\|5 + 5 +--R log(-------------------------------------------) +--R +-------+ +--R \|- x + 1 - x +--R + +--R +-+ +-------+ +-+ +--R +-+ +-------+ 2\|5 \|- x + 1 + \|5 +--R - \|5 log(- \|- x + 1 + x) - 2atanh(----------------------) +--R 5 +--R / +--R +-+ +--R \|5 +--R Type: Expression(Integer) +--E 389 + +--S 390 of 512 +d0177:= D(m0177,x) +--R +--R +--R (267) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 512 +t0178:= 1/(4+(4-x)^(1/2)-x) +--R +--R +--R 1 +--R (268) ------------------ +--R +-------+ +--R \|- x + 4 - x + 4 +--R Type: Expression(Integer) +--E 391 + +--S 392 of 512 +r0178:= -2*log(1+(4-x)^(1/2)) +--R +--R +--R +-------+ +--R (269) - 2log(\|- x + 4 + 1) +--R Type: Expression(Integer) +--E 392 + +--S 393 of 512 +a0178:= integrate(t0178,x) +--R +--R +--R +-------+ +--R (270) - 2log(\|- x + 4 + 1) +--R Type: Union(Expression(Integer),...) +--E 393 + +--S 394 of 512 +m0178:= a0178-r0178 +--R +--R +--R (271) 0 +--R Type: Expression(Integer) +--E 394 + +--S 395 of 512 +d0178:= D(m0178,x) +--R +--R +--R (272) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 512 +t0179:= ((1-x)^(1/2)+(1+x)^(1/2))*(1-x)^(1/2) +--R +--R +--R +-------+ +-----+ +--R (273) \|- x + 1 \|x + 1 - x + 1 +--R Type: Expression(Integer) +--E 396 + +--S 397 of 512 +r0179:= x-1/2*x^2+1/2*x*(1-x^2)^(1/2)+1/2*asin(x) +--R +--R +--R +--------+ +--R | 2 2 +--R x\|- x + 1 + asin(x) - x + 2x +--R (274) -------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 512 +--a0179:= integrate(t0179,x) +--E 398 + +--S 399 of 512 +--m0179:= a0179-r0179 +--E 399 + +--S 400 of 512 +--d0179:= D(m0179,x) +--E 400 + +--S 401 of 512 +t0180:= ((1-x)^(1/2)+(1+x)^(1/2))^2 +--R +--R +--R +-------+ +-----+ +--R (275) 2\|- x + 1 \|x + 1 + 2 +--R Type: Expression(Integer) +--E 401 + +--S 402 of 512 +r0180:= 2*x+x*(1-x^2)^(1/2)+asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (276) x\|- x + 1 + asin(x) + 2x +--R Type: Expression(Integer) +--E 402 + +--S 403 of 512 +--a0180:= integrate(t0180,x) +--E 403 + +--S 404 of 512 +--m0180:= a0180-r0180 +--E 404 + +--S 405 of 512 +--d0180:= D(m0180,x) +--E 405 + +--S 406 of 512 +t0181:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-------+ +-----+ +--R (277) - 2\|- x + 1 \|x + 1 - 2 +--R Type: Expression(Integer) +--E 406 + +--S 407 of 512 +r0181:= -2*x-x*(1-x^2)^(1/2)-asin(x) +--R +--R +--R +--------+ +--R | 2 +--R (278) - x\|- x + 1 - asin(x) - 2x +--R Type: Expression(Integer) +--E 407 + +--S 408 of 512 +--a0181:= integrate(t0181,x) +--E 408 + +--S 409 of 512 +--m0181:= a0181-r0181 +--E 409 + +--S 410 of 512 +--d0181:= D(m0181,x) +--E 410 + +--S 411 of 512 +t0182:= ((1-x)^(1/2)+(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ +--R 2\|- x + 1 \|x + 1 + 2 +--R (279) ----------------------- +--R x +--R Type: Expression(Integer) +--E 411 + +--S 412 of 512 +r0182:= 2*(1-x^2)^(1/2)-2*atanh((1-x^2)^(1/2))+2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (280) - 2atanh(\|- x + 1 ) + 2\|- x + 1 + 2log(x) +--R Type: Expression(Integer) +--E 412 + + +-- +-------+ +-----+ +-- - \|- x + 1 \|x + 1 - 1 +-------+ +-----+ +-- (281) - 2log(------------------------) + 2\|- x + 1 \|x + 1 +-- 2 +-- x +-- Type: Union(Expression(Integer),...) + +--S 413 of 512 ok to fail due to sign changes (see above) +a0182:= integrate(t0182,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (281) - 2log(----------------------) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 413 + +--S 414 of 512 ok to fail due to sign changes (see above) +m0182:= a0182-r0182 +--R +--R +--R (282) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - 2log(----------------------) + 2atanh(\|- x + 1 ) + 2\|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - 2\|- x + 1 - 2log(x) +--R Type: Expression(Integer) +--E 414 + +--S 415 of 512 +d0182:= D(m0182,x) +--R +--R +--R (283) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 + 2x - 2)\|- x + 1 \|x + 1 + (- 2x + 2)\|- x + 1 + 2x - 2 +--R ----------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression(Integer) +--E 415 + +--S 416 of 512 +t0183:= (-(1-x)^(1/2)-(1+x)^(1/2))*((1-x)^(1/2)+(1+x)^(1/2))/x +--R +--R +--R +-------+ +-----+ +--R - 2\|- x + 1 \|x + 1 - 2 +--R (284) ------------------------- +--R x +--R Type: Expression(Integer) +--E 416 + +--S 417 of 512 +r0183:= -2*(1-x^2)^(1/2)+2*atanh((1-x^2)^(1/2))-2*log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (285) 2atanh(\|- x + 1 ) - 2\|- x + 1 - 2log(x) +--R Type: Expression(Integer) +--E 417 + +--S 418 of 512 +a0183:= integrate(t0183,x) +--R +--R +--R +-------+ +-----+ +-------+ +-----+ +--R (286) - 2log(\|- x + 1 \|x + 1 - 1) - 2\|- x + 1 \|x + 1 +--R Type: Union(Expression(Integer),...) +--E 418 + +--S 419 of 512 +m0183:= a0183-r0183 +--R +--R +--R (287) +--R +--------+ +--R +-------+ +-----+ | 2 +-------+ +-----+ +--R - 2log(\|- x + 1 \|x + 1 - 1) - 2atanh(\|- x + 1 ) - 2\|- x + 1 \|x + 1 +--R + +--R +--------+ +--R | 2 +--R 2\|- x + 1 + 2log(x) +--R Type: Expression(Integer) +--E 419 + +--S 420 of 512 +d0183:= D(m0183,x) +--R +--R +--R (288) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (2\|- x + 1 - 2x + 2)\|- x + 1 \|x + 1 + (2x - 2)\|- x + 1 + 2x - 2 +--R --------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 - x\|- x + 1 +--R Type: Expression(Integer) +--E 420 + +--S 421 of 512 +t0184:= ((1-x)^(1/2)+(1+x)^(1/2))/(-(1-x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-------+ +--R \|x + 1 + \|- x + 1 +--R (289) --------------------- +--R +-----+ +-------+ +--R \|x + 1 - \|- x + 1 +--R Type: Expression(Integer) +--E 421 + +--S 422 of 512 +r0184:= (1-x^2)^(1/2)-atanh((1-x^2)^(1/2))+log(x) +--R +--R +--R +--------+ +--------+ +--R | 2 | 2 +--R (290) - atanh(\|- x + 1 ) + \|- x + 1 + log(x) +--R Type: Expression(Integer) +--E 422 + + + +-- +-------+ +-----+ +-- - \|- x + 1 \|x + 1 - 1 +-------+ +-----+ +-- (291) - log(------------------------) + \|- x + 1 \|x + 1 +-- 2 +-- x +-- Type: Union(Expression(Integer),...) + +--S 423 of 512 ok to fail. seems there are 2 answers (see above) +a0184:= integrate(t0184,x) +--R +--R +--R +-------+ +-----+ +--R \|- x + 1 \|x + 1 + 1 +-------+ +-----+ +--R (291) - log(----------------------) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R Type: Union(Expression(Integer),...) +--E 423 + +--S 424 of 512 ok to fail. due to 2 answers (see above) +m0184:= a0184-r0184 +--R +--R +--R (292) +--R +-------+ +-----+ +--------+ +--R \|- x + 1 \|x + 1 + 1 | 2 +-------+ +-----+ +--R - log(----------------------) + atanh(\|- x + 1 ) + \|- x + 1 \|x + 1 +--R 2 +--R x +--R + +--R +--------+ +--R | 2 +--R - \|- x + 1 - log(x) +--R Type: Expression(Integer) +--E 424 + +--S 425 of 512 +d0184:= D(m0184,x) +--R +--R +--R (293) +--R +--------+ +--------+ +--R | 2 2 +-------+ +-----+ 2 | 2 2 +--R (\|- x + 1 + x - 1)\|- x + 1 \|x + 1 + (- x + 1)\|- x + 1 + x - 1 +--R ------------------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +-------+ +-----+ | 2 +--R x\|- x + 1 \|- x + 1 \|x + 1 + x\|- x + 1 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 512 +t0185:= (-(-1+x)^(1/2)+(1+x)^(1/2))/((-1+x)^(1/2)+(1+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R \|x + 1 - \|x - 1 +--R (294) ------------------- +--R +-----+ +-----+ +--R \|x + 1 + \|x - 1 +--R Type: Expression(Integer) +--E 426 + +--S 427 of 512 +r0185:= 1/2*x^2-1/2*(-1+x)^(1/2)*x*(1+x)^(1/2)+1/2*acosh(x) +--R +--R +--R +-----+ +-----+ 2 +--R - x\|x - 1 \|x + 1 + acosh(x) + x +--R (295) ----------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 427 + + + +-- +-----+ +-----+ +-----+ +-----+ 2 +-- - log(- \|x - 1 \|x + 1 + x) - x\|x - 1 \|x + 1 + x +-- (296) ------------------------------------------------------ +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 428 of 512 ok to fail. seems there are 2 answers (see above) +a0185:= integrate(t0185,x) +--R +--R +--R +-----+ +-----+ +-----+ +-----+ 2 +--R - log(\|x - 1 \|x + 1 - x) - x\|x - 1 \|x + 1 + x +--R (296) ---------------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 428 + +--S 429 of 512 ok to fail. due to 2 answers (see above) +m0185:= a0185-r0185 +--R +--R +--R +-----+ +-----+ +--R - log(\|x - 1 \|x + 1 - x) - acosh(x) +--R (297) -------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 429 + +--S 430 of 512 +d0185:= D(m0185,x) +--R +--R +--R +------+ +--R | 2 +-----+ +-----+ +--R \|x - 1 - \|x - 1 \|x + 1 +--R (298) ---------------------------- +--R +------+ +--R +-----+ +-----+ | 2 +--R 2\|x - 1 \|x + 1 \|x - 1 +--R Type: Expression(Integer) +--E 430 + +--S 431 of 512 +t0186:= (2*(3-x)^(1/2)+3/(1+x)^(1/2))^2/x +--R +--R +--R +-------+ +-----+ 2 +--R 12\|- x + 3 \|x + 1 - 4x + 8x + 21 +--R (299) ------------------------------------ +--R 2 +--R x + x +--R Type: Expression(Integer) +--E 431 + +--S 432 of 512 +r0186:= -4*x-12*asin(-1/2+1/2*x)-24*3^(1/2)*_ + atanh(1/3*(3-x)^(1/2)*3^(1/2)/(1+x)^(1/2))+21*log(x)-9*log(1+x) +--R +--R +--R (300) +--R +-+ +-------+ +--R +-+ \|3 \|- x + 3 x - 1 +--R - 24\|3 atanh(--------------) - 9log(x + 1) + 21log(x) - 12asin(-----) - 4x +--R +-----+ 2 +--R 3\|x + 1 +--R Type: Expression(Integer) +--E 432 + +--S 433 of 512 +--a0186:= integrate(t0186,x) +--E 433 + +--S 434 of 512 +--m0186:= a0186-r0186 +--E 434 + +--S 435 of 512 +--d0186:= D(m0186,x) +-- >> Error detected within library code: +-- integrate: +-- implementation incomplete (residue poly has multiple non-linear factors) +--E 435 + +--S 436 of 512 +t0187:= (1-x)^(1/2)/(1+x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (301) ---------- +--R +-+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 436 + +--S 437 of 512 +r0187:= -2*(1-x)^(1/2)+(1-x)^(1/2)*x^(1/2)-asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (302) - asin(\|x ) + \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression(Integer) +--E 437 + +--S 438 of 512 +--a0187:= integrate(t0187,x) +--E 438 + +--S 439 of 512 +--m0187:= a0187-r0187 +--E 439 + +--S 440 of 512 +--d0187:= D(m0187,x) +--E 440 + +--S 441 of 512 +t0188:= (1-x)^(1/2)/(1-x^(1/2)) +--R +--R +--R +-------+ +--R \|- x + 1 +--R (303) - ---------- +--R +-+ +--R \|x - 1 +--R Type: Expression(Integer) +--E 441 + +--S 442 of 512 +r0188:= -2*(1-x)^(1/2)-(1-x)^(1/2)*x^(1/2)+asin(x^(1/2)) +--R +--R +--R +-+ +-------+ +-+ +-------+ +--R (304) asin(\|x ) - \|- x + 1 \|x - 2\|- x + 1 +--R Type: Expression(Integer) +--E 442 + +--S 443 of 512 +--a0188:= integrate(t0188,x) +--E 443 + +--S 444 of 512 +--m0188:= a0188-r0188 +--E 444 + +--S 445 of 512 +--d0188:= D(m0188,x) +--E 445 + +--S 446 of 512 +t0189:= x/(1+x)/(2+x)^(1/2) +--R +--R +--R x +--R (305) --------------- +--R +-----+ +--R (x + 1)\|x + 2 +--R Type: Expression(Integer) +--E 446 + +--S 447 of 512 +r0189:= 2*(2+x)^(1/2)+2*atanh((2+x)^(1/2)) +--R +--R +--R +-----+ +-----+ +--R (306) 2atanh(\|x + 2 ) + 2\|x + 2 +--R Type: Expression(Integer) +--E 447 + +--S 448 of 512 +a0189:= integrate(t0189,x) +--R +--R +--R +-----+ +-----+ +-----+ +--R (307) log(\|x + 2 + 1) - log(\|x + 2 - 1) + 2\|x + 2 +--R Type: Union(Expression(Integer),...) +--E 448 + +--S 449 of 512 +m0189:= a0189-r0189 +--R +--R +--R +-----+ +-----+ +-----+ +--R (308) log(\|x + 2 + 1) - log(\|x + 2 - 1) - 2atanh(\|x + 2 ) +--R Type: Expression(Integer) +--E 449 + +--S 450 of 512 +d0189:= D(m0189,x) +--R +--R +--R (309) 0 +--R Type: Expression(Integer) +--E 450 + +--S 451 of 512 +t0190:= (1+x^2)^(1/2)/(-1+x^2) +--R +--R +--R +------+ +--R | 2 +--R \|x + 1 +--R (310) --------- +--R 2 +--R x - 1 +--R Type: Expression(Integer) +--E 451 + +--S 452 of 512 +r0190:= asinh(x)-2^(1/2)*atanh(2^(1/2)*x/(1+x^2)^(1/2)) +--R +--R +--R +-+ +--R +-+ x\|2 +--R (311) - \|2 atanh(---------) + asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R Type: Expression(Integer) +--E 452 + +--S 453 of 512 +a0190:= integrate(t0190,x) +--R +--R +--R (312) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R / +--R 2 +--R Type: Union(Expression(Integer),...) +--E 453 + +--S 454 of 512 +m0190:= a0190-r0190 +--R +--R +--R (313) +--R +------+ +--R | 2 +--R - 2log(\|x + 1 - x) +--R + +--R +------+ +--R +-+ 3 | 2 2 +-+ 4 2 +--R +-+ (2x\|2 + 2x - 2x)\|x + 1 + (- 2x + 2)\|2 - 2x + x - 3 +--R \|2 log(-------------------------------------------------------------) +--R +------+ +--R 3 | 2 4 2 +--R (2x - 2x)\|x + 1 - 2x + x + 1 +--R + +--R +-+ +--R +-+ x\|2 +--R 2\|2 atanh(---------) - 2asinh(x) +--R +------+ +--R | 2 +--R \|x + 1 +--R / +--R 2 +--R Type: Expression(Integer) +--E 454 + +--S 455 of 512 +d0190:= D(m0190,x) +--R +--R +--R (314) 0 +--R Type: Expression(Integer) +--E 455 + +--S 456 of 512 +t0191:= (1+x)^(1/2)*(1+x^3)/(1+x^2) +--R +--R +--R 3 +-----+ +--R (x + 1)\|x + 1 +--R (315) ---------------- +--R 2 +--R x + 1 +--R Type: Expression(Integer) +--E 456 + +--S 457 of 512 +r0191:= -2*(1+x)^(1/2)-2/3*(1+x)^(3/2)+2/5*(1+x)^(5/2)-_ + atan(((2+2*2^(1/2))^(1/2)-2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)+_ + atan(((2+2*2^(1/2))^(1/2)+2*(1+x)^(1/2))/_ + (-2+2*2^(1/2))^(1/2))/(2^(1/2)-1)^(1/2)-_ + 1/2*log(1+2^(1/2)+x-(2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/_ + (1+2^(1/2))^(1/2)+1/2*log(1+2^(1/2)+x+_ + (2+2*2^(1/2))^(1/2)*(1+x)^(1/2))/(1+2^(1/2))^(1/2) +--R +--R +--R (316) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R 15\|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - 15\|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R - 30\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +--------+ +--------+ +--R 2 +-----+ | +-+ | +-+ +--R (12x + 4x - 68)\|x + 1 \|\|2 - 1 \|\|2 + 1 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 30\|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 457 + +--S 458 of 512 +a0191:= integrate(t0191,x) +--R +--R +--R (317) +--R - +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi +--R 15\|8 cos(---) +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 4+-+ %pi 8 8 +--R - 30\|8 sin(---)atan(---------------------------------------) +--R 8 +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R + +--R 2 +-----+ +--R (12x + 4x - 68)\|x + 1 +--R / +--R 30 +--R Type: Union(Expression(Integer),...) +--E 458 + +--S 459 of 512 +m0191:= a0191-r0191 +--R +--R +--R (318) +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R - \|\|2 - 1 log(\|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (2\|8 sin(---) - 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R \|8 cos(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R log +--R 4+-+ %pi 4+-+ %pi +-----+ 4+-+2 %pi 2 +--R (- 2\|8 sin(---) + 2\|8 cos(---))\|x + 1 + \|8 sin(---) +--R 8 8 8 +--R + +--R 4+-+2 %pi 2 +--R \|8 cos(---) + 2x + 2 +--R 8 +--R + +--R +--------+ +---------+ +--R | +-+ +-----+ | +-+ +-+ +--R \|\|2 - 1 log(- \|x + 1 \|2\|2 + 2 + \|2 + x + 1) +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 + 2\|x + 1 +--R - 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R +---------+ +--R +--------+ | +-+ +-----+ +--R | +-+ \|2\|2 + 2 - 2\|x + 1 +--R 2\|\|2 + 1 atan(------------------------) +--R +---------+ +--R | +-+ +--R \|2\|2 - 2 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 - \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R + +--R - +--R +--------+ +--------+ +--R 4+-+ %pi | +-+ | +-+ +--R 2\|8 sin(---)\|\|2 - 1 \|\|2 + 1 +--R 8 +--R * +--R 4+-+ %pi 4+-+ %pi +--R \|8 sin(---) + \|8 cos(---) +--R 8 8 +--R atan(---------------------------------------) +--R +-----+ 4+-+ %pi 4+-+ %pi +--R 2\|x + 1 + \|8 sin(---) - \|8 cos(---) +--R 8 8 +--R / +--R +--------+ +--------+ +--R | +-+ | +-+ +--R 2\|\|2 - 1 \|\|2 + 1 +--R Type: Expression(Integer) +--E 459 + +--S 460 of 512 +d0191:= D(m0191,x) +--R +--R +--R (319) +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((176x + 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((- 160x - 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((160x + 480x + 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((124x + 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((- 136x - 408x - 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (552x + 2208x + 2760x + 1104)\|2 - 552x - 2760x - 3864x +--R + +--R - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((- 80x - 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((96x + 288x + 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 368x - 1472x - 1840x - 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (136x + 680x + 1224x + 952x + 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((40x + 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((- 52x - 156x - 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (224x + 896x + 1120x + 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 60x - 300x - 540x - 420x - 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (150x + 900x + 2100x + 2400x + 1350x + 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((- 16x - 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((16x + 48x + 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((- 80x - 320x - 400x - 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (28x + 140x + 252x + 196x + 56)\|2 - 28x - 168x - 336x +--R + +--R - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 36x - 216x - 504x - 576x - 324x - 72)\|2 + 36x +--R + +--R 4 3 2 +--R 252x + 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 +--R (10x + 70x + 200x + 300x + 250x + 110x + 20)\|2 - 10x +--R + +--R 5 4 3 2 +--R - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((4x + 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((- 4x - 12x - 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((12x + 48x + 60x + 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (- 4x - 20x - 36x - 28x - 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 3 +--R (9x + 54x + 126x + 144x + 81x + 18)\|2 - 9x - 63x - 162x +--R + +--R 2 +--R - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (- x - 7x - 20x - 30x - 25x - 11x - 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 6 +--R (2x + 16x + 54x + 100x + 110x + 72x + 26x + 4)\|2 - 2x - 18x +--R + +--R 5 4 3 2 +--R - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 + 1 \|2\|2 + 2 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)sin(---) +--R 8 +--R + +--R +-+ %pi %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---)sin(---) +--R 8 8 +--R + +--R +-+ %pi 2 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 3 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 4 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 2 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 5 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 3 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 6 +--R ((- 176x - 352)\|2 - 176x - 528)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 4 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R (4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x +--R + +--R 12 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 7 +--R ((160x + 320)\|2 + 160x + 480)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 5 +--R ((- 160x - 480x - 320)\|2 - 160x - 640x - 480)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 8 +--R ((- 124x - 248)\|2 - 124x - 372)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 6 +--R ((136x + 408x + 272)\|2 + 136x + 544x + 408)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 552x - 2208x - 2760x - 1104)\|2 - 552x - 2760x +--R + +--R - 3864x - 1656 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 9 +--R ((80x + 160)\|2 + 80x + 240)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 7 +--R ((- 96x - 288x - 192)\|2 - 96x - 384x - 288)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (368x + 1472x + 1840x + 736)\|2 + 368x + 1840x + 2576x +--R + +--R 1104 +--R * +--R %pi 5 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 136x - 680x - 1224x - 952x - 272)\|2 - 136x - 816x +--R + +--R 2 +--R - 1632x - 1360x - 408 +--R * +--R 4+-+2 %pi 3 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi +--R cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 10 +--R ((- 40x - 80)\|2 - 40x - 120)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 8 +--R ((52x + 156x + 104)\|2 + 52x + 208x + 156)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R (- 224x - 896x - 1120x - 448)\|2 - 224x - 1120x - 1568x +--R + +--R - 672 +--R * +--R %pi 6 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (60x + 300x + 540x + 420x + 120)\|2 + 60x + 360x +--R + +--R 2 +--R 720x + 600x + 180 +--R * +--R 4+-+2 %pi 4 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 +--R (- 150x - 900x - 2100x - 2400x - 1350x - 300)\|2 - 150x +--R + +--R 4 3 2 +--R - 1050x - 2700x - 3300x - 1950x - 450 +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x +--R + +--R 4 3 2 +--R 25x + 40x + 35x + 16x + 3 +--R * +--R 4+-+2 +--R \|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R +-+ %pi 11 +--R ((16x + 32)\|2 + 16x + 48)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 9 +--R ((- 16x - 48x - 32)\|2 - 16x - 64x - 48)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 +--R ((80x + 320x + 400x + 160)\|2 + 80x + 400x + 560x + 240) +--R * +--R %pi 7 +--R cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 +--R (- 28x - 140x - 252x - 196x - 56)\|2 - 28x - 168x +--R + +--R 2 +--R - 336x - 280x - 84 +--R * +--R 4+-+2 %pi 5 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (36x + 216x + 504x + 576x + 324x + 72)\|2 + 36x + 252x +--R + +--R 3 2 +--R 648x + 792x + 468x + 108 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ +--R (- 10x - 70x - 200x - 300x - 250x - 110x - 20)\|2 +--R + +--R 6 5 4 3 2 +--R - 10x - 80x - 250x - 400x - 350x - 160x - 30 +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R +-+ %pi 12 +--R ((- 4x - 8)\|2 - 4x - 12)cos(---) +--R 8 +--R + +--R 2 +-+ 2 4+-+2 %pi 10 +--R ((4x + 12x + 8)\|2 + 4x + 16x + 12)\|8 cos(---) +--R 8 +--R + +--R 3 2 +-+ 3 2 %pi 8 +--R ((- 12x - 48x - 60x - 24)\|2 - 12x - 60x - 84x - 36)cos(---) +--R 8 +--R + +--R 4 3 2 +-+ 4 3 2 +--R ((4x + 20x + 36x + 28x + 8)\|2 + 4x + 24x + 48x + 40x + 12) +--R * +--R 4+-+2 %pi 6 +--R \|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 +-+ 5 4 +--R (- 9x - 54x - 126x - 144x - 81x - 18)\|2 - 9x - 63x +--R + +--R 3 2 +--R - 162x - 198x - 117x - 27 +--R * +--R %pi 4 +--R cos(---) +--R 8 +--R + +--R 6 5 4 3 2 +-+ 6 5 4 +--R (x + 7x + 20x + 30x + 25x + 11x + 2)\|2 + x + 8x + 25x +--R + +--R 3 2 +--R 40x + 35x + 16x + 3 +--R * +--R 4+-+2 %pi 2 +--R \|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +-+ 7 +--R (- 2x - 16x - 54x - 100x - 110x - 72x - 26x - 4)\|2 - 2x +--R + +--R 6 5 4 3 2 +--R - 18x - 66x - 130x - 150x - 102x - 38x - 6 +--R * +--R +--------+ +---------+ +--R +-----+ | +-+ | +-+ +--R \|x + 1 \|\|2 - 1 \|2\|2 - 2 +--R + +--R 2 %pi 12 2 %pi %pi 11 +--R (8x + 8)sin(---) + (- 32x - 32)cos(---)sin(---) +--R 8 8 8 +--R + +--R 2 %pi 2 3 2 4+-+2 %pi 10 +--R ((80x + 80)cos(---) + (- 6x - 6x - 6x - 6)\|8 )sin(---) +--R 8 8 +--R + +--R 2 %pi 3 3 2 4+-+2 %pi +--R ((- 160x - 160)cos(---) + (20x + 20x + 20x + 20)\|8 cos(---)) +--R 8 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 2 %pi 4 3 2 4+-+2 %pi 2 +--R (248x + 248)cos(---) + (- 74x - 74x - 74x - 74)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 +--R 4x + 8x + 8x + 8x + 4 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 2 %pi 5 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 3 +--R (144x + 144x + 144x + 144)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi +--R (- 64x - 128x - 128x - 128x - 64)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 2 %pi 6 +--R (352x + 352)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 4 +--R (- 212x - 212x - 212x - 212)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 2 +--R (224x + 448x + 448x + 448x + 224)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 +--R (x + 3x + 4x + 4x + 3x + 1)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 2 %pi 7 +--R (- 320x - 320)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 5 +--R (264x + 264x + 264x + 264)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 3 +--R (- 352x - 704x - 704x - 704x - 352)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi +--R (14x + 42x + 56x + 56x + 42x + 14)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 2 %pi 8 +--R (248x + 248)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 6 +--R (- 236x - 236x - 236x - 236)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 4 +--R (728x + 1456x + 1456x + 1456x + 728)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 2 +--R (- 11x - 33x - 44x - 44x - 33x - 11)\|8 cos(---) +--R 8 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 2 %pi 9 +--R (- 160x - 160)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 7 +--R (176x + 176x + 176x + 176)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 5 +--R (- 576x - 1152x - 1152x - 1152x - 576)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 3 +--R (140x + 420x + 560x + 560x + 420x + 140)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi +--R (32x + 128x + 224x + 256x + 224x + 128x + 32)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 2 %pi 10 +--R (80x + 80)cos(---) +--R 8 +--R + +--R 3 2 4+-+2 %pi 8 +--R (- 102x - 102x - 102x - 102)\|8 cos(---) +--R 8 +--R + +--R 4 3 2 %pi 6 +--R (416x + 832x + 832x + 832x + 416)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 4 +--R (- 93x - 279x - 372x - 372x - 279x - 93)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 2 +--R (112x + 448x + 784x + 896x + 784x + 448x + 112)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 +--R (2x + 10x + 22x + 30x + 30x + 22x + 10x + 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 2 %pi 11 3 2 4+-+2 %pi 9 +--R (- 32x - 32)cos(---) + (36x + 36x + 36x + 36)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 7 +--R (- 160x - 320x - 320x - 320x - 160)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 5 +--R (54x + 162x + 216x + 216x + 162x + 54)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 3 +--R (- 64x - 256x - 448x - 512x - 448x - 256x - 64)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi +--R (4x + 20x + 44x + 60x + 60x + 44x + 20x + 4)\|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 2 %pi 12 3 2 4+-+2 %pi 10 +--R (8x + 8)cos(---) + (- 10x - 10x - 10x - 10)\|8 cos(---) +--R 8 8 +--R + +--R 4 3 2 %pi 8 +--R (36x + 72x + 72x + 72x + 36)cos(---) +--R 8 +--R + +--R 5 4 3 2 4+-+2 %pi 6 +--R (- 9x - 27x - 36x - 36x - 27x - 9)\|8 cos(---) +--R 8 +--R + +--R 6 5 4 3 2 %pi 4 +--R (16x + 64x + 112x + 128x + 112x + 64x + 16)cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 10x - 22x - 30x - 30x - 22x - 10x - 2)\|8 cos(---) +--R 8 +--R * +--R +-----+ +--R \|x + 1 +--R / +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)sin(---) +--R 8 +--R + +--R 3 2 %pi %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---)sin(---) +--R 8 8 +--R + +--R 3 2 %pi 2 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 +--R (- 8x - 16x - 16x - 16x - 8)\|8 +--R * +--R %pi 10 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 3 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R * +--R %pi 9 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 4 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 2 5 4 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) + 24x + 72x +--R 8 +--R + +--R 3 2 +--R 96x + 96x + 72x + 24 +--R * +--R %pi 8 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 5 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 3 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R * +--R %pi 7 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 6 +--R (352x + 352x + 352x + 352)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 4 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 2 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 +--R * +--R %pi 6 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 7 +--R (- 320x - 320x - 320x - 320)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 5 +--R (320x + 640x + 640x + 640x + 320)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 3 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R * +--R %pi 5 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 8 +--R (248x + 248x + 248x + 248)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 6 +--R (- 272x - 544x - 544x - 544x - 272)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 4 +--R (1104x + 3312x + 4416x + 4416x + 3312x + 1104)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 2 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R 18x + 90x + 198x + 270x + 270x + 198x + 90x + 18 +--R * +--R %pi 4 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 9 +--R (- 160x - 160x - 160x - 160)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 7 +--R (192x + 384x + 384x + 384x + 192)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 5 +--R (- 736x - 2208x - 2944x - 2944x - 2208x - 736)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 +--R (272x + 1088x + 1904x + 2176x + 1904x + 1088x + 272)\|8 +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72)cos(---) +--R 8 +--R * +--R %pi 3 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 10 +--R (80x + 80x + 80x + 80)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 8 +--R (- 104x - 208x - 208x - 208x - 104)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 6 +--R (448x + 1344x + 1792x + 1792x + 1344x + 448)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 4 +--R (- 120x - 480x - 840x - 960x - 840x - 480x - 120)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (300x + 1500x + 3300x + 4500x + 4500x + 3300x + 1500x + 300) +--R * +--R %pi 2 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 +--R * +--R %pi 2 +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 11 +--R (- 32x - 32x - 32x - 32)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 9 +--R (32x + 64x + 64x + 64x + 32)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 7 +--R (- 160x - 480x - 640x - 640x - 480x - 160)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 5 +--R (56x + 224x + 392x + 448x + 392x + 224x + 56)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 +--R (- 72x - 360x - 792x - 1080x - 1080x - 792x - 360x - 72) +--R * +--R %pi 3 +--R cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 +--R (20x + 120x + 320x + 520x + 600x + 520x + 320x + 120x + 20) +--R * +--R 4+-+2 %pi +--R \|8 cos(---) +--R 8 +--R * +--R %pi +--R sin(---) +--R 8 +--R + +--R 3 2 %pi 12 +--R (8x + 8x + 8x + 8)cos(---) +--R 8 +--R + +--R 4 3 2 4+-+2 %pi 10 +--R (- 8x - 16x - 16x - 16x - 8)\|8 cos(---) +--R 8 +--R + +--R 5 4 3 2 %pi 8 +--R (24x + 72x + 96x + 96x + 72x + 24)cos(---) +--R 8 +--R + +--R 6 5 4 3 2 4+-+2 %pi 6 +--R (- 8x - 32x - 56x - 64x - 56x - 32x - 8)\|8 cos(---) +--R 8 +--R + +--R 7 6 5 4 3 2 %pi 4 +--R (18x + 90x + 198x + 270x + 270x + 198x + 90x + 18)cos(---) +--R 8 +--R + +--R 8 7 6 5 4 3 2 4+-+2 %pi 2 +--R (- 2x - 12x - 32x - 52x - 60x - 52x - 32x - 12x - 2)\|8 cos(---) +--R 8 +--R + +--R 9 8 7 6 5 4 3 2 +--R 4x + 28x + 88x + 168x + 224x + 224x + 168x + 88x + 28x + 4 +--R Type: Expression(Integer) +--E 460 + +--S 461 of 512 +t0192:= (-1+x)^(1/3)/(1+x)^(1/3) +--R +--R +--R 3+-----+ +--R \|x - 1 +--R (320) -------- +--R 3+-----+ +--R \|x + 1 +--R Type: Expression(Integer) +--E 461 + +--S 462 of 512 +r0192:= (-1+x)^(1/3)*(1+x)^(2/3)-2/3*_ + atan(1/3*(1+2*(-1+x)^(1/3)/(1+x)^(1/3))*3^(1/2))*3^(1/2)+_ + 2/3*log(1-(-1+x)^(1/3)/(1+x)^(1/3))-_ + 1/3*log(1+(-1+x)^(2/3)/(1+x)^(2/3)+(-1+x)^(1/3)/(1+x)^(1/3)) +--R +--R +--R (321) +--R 3+-----+2 3+-----+3+-----+ 3+-----+2 +--R \|x + 1 + \|x - 1 \|x + 1 + \|x - 1 +--R - log(----------------------------------------) +--R 3+-----+2 +--R \|x + 1 +--R + +--R 3+-----+ 3+-----+ +-+3+-----+ +-+3+-----+ +--R \|x + 1 - \|x - 1 +-+ \|3 \|x + 1 + 2\|3 \|x - 1 +--R 2log(-------------------) - 2\|3 atan(----------------------------) +--R 3+-----+ 3+-----+ +--R \|x + 1 3\|x + 1 +--R + +--R 3+-----+3+-----+2 +--R 3\|x - 1 \|x + 1 +--R / +--R 3 +--R Type: Expression(Integer) +--E 462 + +--S 463 of 512 +--a0192:= integrate(t0192,x) +--E 463 + +--S 464 of 512 +--m0192:= a0192-r0192 +--E 464 + +--S 465 of 512 +--d0192:= D(m0192,x) +--E 465 + +--S 466 of 512 +t0193:= x^(1/2)/((2-x)^(1/2)-x^(1/2)) +--R +--R +--R +-+ +--R \|x +--R (322) - ----------------- +--R +-+ +-------+ +--R \|x - \|- x + 2 +--R Type: Expression(Integer) +--E 466 + +--S 467 of 512 +r0193:= -1/2*x-1/2*(-(-2+x)*x)^(1/2)+atanh((2-x)^(1/2)/x^(1/2))-1/2*log(1-x) +--R +--R +--R +-------+ +---------+ +--R \|- x + 2 | 2 +--R 2atanh(----------) - \|- x + 2x - log(- x + 1) - x +--R +-+ +--R \|x +--R (323) ---------------------------------------------------- +--R 2 +--R Type: Expression(Integer) +--E 467 + + +-- +-------+ +-+ +-- - \|- x + 2 \|x - 1 +-------+ +-+ +-- log(--------------------) - \|- x + 2 \|x - x +-- 2 +-- x - 2x + 1 +-- (324) ---------------------------------------------- +-- 2 +-- Type: Union(Expression(Integer),...) + +--S 468 of 512 ok to fail. seems there are 2 answers (see above) +a0193:= integrate(t0193,x) +--R +--R +--R +-------+ +-+ +--R \|- x + 2 \|x + 1 +-------+ +-+ +--R log(------------------) - \|- x + 2 \|x - x +--R 2 +--R x - 2x + 1 +--R (324) -------------------------------------------- +--R 2 +--R Type: Union(Expression(Integer),...) +--E 468 + +--S 469 of 512 ok to fail. due to 2 answers (see above) +m0193:= a0193-r0193 +--R +--R +--R (325) +--R +-------+ +-+ +-------+ +--R \|- x + 2 \|x + 1 \|- x + 2 +-------+ +-+ +--R log(------------------) - 2atanh(----------) - \|- x + 2 \|x +--R 2 +-+ +--R x - 2x + 1 \|x +--R + +--R +---------+ +--R | 2 +--R \|- x + 2x + log(- x + 1) +--R / +--R 2 +--R Type: Expression(Integer) +--E 469 + +--S 470 of 512 +d0193:= D(m0193,x) +--R +--R +--R +---------+ +--R +-------+ +-+ | 2 +--R (- x + 1)\|- x + 2 \|x + (x - 1)\|- x + 2x +--R (326) --------------------------------------------- +--R +---------+ +--R | 2 +-------+ +-+ +--R 2\|- x + 2x \|- x + 2 \|x +--R Type: Expression(Integer) +--E 470 + +--S 471 of 512 +t0194:= 1/(9+b*x^2)^(1/2) +--R +--R +--R 1 +--R (327) ----------- +--R +--------+ +--R | 2 +--R \|b x + 9 +--R Type: Expression(Integer) +--E 471 + +--S 472 of 512 +r0194:= asinh(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(-----) +--R 3 +--R (328) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 472 + +--S 473 of 512 +a0194:= integrate(t0194,x) +--R +--R +--R (329) +--R +--------+ +--R +-+ | 2 2 +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x +--R log(--------------------------------------------------) +--R +--------+ +--R | 2 +--R \|b x + 9 - 3 +--R [-------------------------------------------------------, +--R +-+ +--R \|b +--R +--------+ +--R +---+ | 2 +---+ +--R \|- b \|b x + 9 - 3\|- b +--R 2atan(---------------------------) +--R b x +--R ----------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 473 + +--S 474 of 512 +m0194a:= a0194.1-r0194 +--R +--R +--R (330) +--R +--------+ +--R +-+ | 2 2 +-+ +-+ +--R (3\|b - b x)\|b x + 9 + (- b x - 9)\|b + 3b x x\|b +--R log(--------------------------------------------------) - asinh(-----) +--R +--------+ 3 +--R | 2 +--R \|b x + 9 - 3 +--R ---------------------------------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 474 + +--S 475 of 512 +d0194a:= D(m0194a,x) +--R +--R +--R (331) 0 +--R Type: Expression(Integer) +--E 475 + +--S 476 of 512 +m0194b:= a0194.2-r0194 +--R +--R +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R +-+ \|- b \|b x + 9 - 3\|- b +---+ x\|b +--R 2\|b atan(---------------------------) - \|- b asinh(-----) +--R b x 3 +--R (332) ----------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 476 + +--S 477 of 512 +d0194b:= D(m0194a,x) +--R +--R +--R (333) 0 +--R Type: Expression(Integer) +--E 477 + +--S 478 of 512 +t0195:= 1/(9-b*x^2)^(1/2) +--R +--R +--R 1 +--R (334) ------------- +--R +----------+ +--R | 2 +--R \|- b x + 9 +--R Type: Expression(Integer) +--E 478 + +--S 479 of 512 +r0195:= asin(1/3*b^(1/2)*x)/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(-----) +--R 3 +--R (335) ----------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 479 + +--S 480 of 512 +a0195:= integrate(t0195,x) +--R +--R +--R (336) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R [----------------------------------------------------------------, +--R +---+ +--R \|- b +--R +----------+ +--R | 2 +-+ +--R (\|- b x + 9 - 3)\|b +--R 2atan(-----------------------) +--R b x +--R - ------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 480 + +--S 481 of 512 +m0195a:= a0195.1-r0195 +--R +--R +--R (337) +--R +----------+ +----------+ +--R | 2 2 +---+ | 2 +--R +-+ (3\|- b x + 9 + b x - 9)\|- b + b x\|- b x + 9 - 3b x +--R \|b log(-----------------------------------------------------------) +--R +----------+ +--R | 2 +--R \|- b x + 9 - 3 +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(-----) +--R 3 +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 481 + +--S 482 of 512 +d0195a:= D(m0195a,x) +--R +--R +--R (338) 0 +--R Type: Expression(Integer) +--E 482 + +--S 483 of 512 +m0195b:= a0195.2-r0195 +--R +--R +--R +----------+ +--R | 2 +-+ +-+ +--R (\|- b x + 9 - 3)\|b x\|b +--R - 2atan(-----------------------) - asin(-----) +--R b x 3 +--R (339) ---------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 483 + +--S 484 of 512 +d0195b:= D(m0195b,x) +--R +--R +--R (340) 0 +--R Type: Expression(Integer) +--E 484 + +--S 485 of 512 +t0196:= 1/(%pi+b*x^2)^(1/2) +--R +--R +--R 1 +--R (341) ------------- +--R +----------+ +--R | 2 +--R \|b x + %pi +--R Type: Expression(Integer) +--E 485 + +--S 486 of 512 +r0196:= asinh(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asinh(------) +--R +---+ +--R \|%pi +--R (342) ------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 486 + +--S 487 of 512 +a0196:= integrate(t0196,x) +--R +--R +--R (343) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R [---------------------------------------------------------------------, +--R +-+ +--R \|b +--R +----------+ +--R +---+ | 2 +---+ +---+ +--R \|- b \|b x + %pi - \|- b \|%pi +--R 2atan(----------------------------------) +--R b x +--R -----------------------------------------] +--R +---+ +--R \|- b +--R Type: Union(List(Expression(Integer)),...) +--E 487 + +--S 488 of 512 +m0196a:= a0196.1-r0196 +--R +--R +--R (344) +--R +----------+ +--R +-+ +---+ | 2 +---+ 2 +-+ +--R (\|b \|%pi - b x)\|b x + %pi + b x\|%pi + (- b x - %pi)\|b +--R log(----------------------------------------------------------------) +--R +----------+ +--R +---+ | 2 +--R \|%pi \|b x + %pi - %pi +--R + +--R +-+ +--R x\|b +--R - asinh(------) +--R +---+ +--R \|%pi +--R / +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 488 + +--S 489 of 512 +d0196a:= D(m0196a,x) +--R +--R +--R (345) +--R +----------+ +--R | 2 +--R 2 2 +-+ +---+ 2 3 2 |b x + %pi +--R ((3b %pi x + 4%pi )\|b \|%pi - b %pi x - 4b %pi x) |---------- +--R \| %pi +--R + +--R 2 4 2 2 +-+ +---+ 2 3 2 +--R (b x + 5b %pi x + 4%pi )\|b \|%pi - 3b %pi x - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R \|b x + %pi +--R + +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R + +--R 3 5 2 3 2 +---+ 2 4 2 2 3 +-+ +--R (b x + 5b %pi x + 4b %pi x)\|%pi + (- 3b %pi x - 7b %pi x - 4%pi )\|b +--R / +--R 2 3 2 +---+ 2 4 2 2 3 +-+ +--R ((3b %pi x + 4b %pi x)\|%pi + (- b %pi x - 5b %pi x - 4%pi )\|b ) +--R * +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R |---------- \|b x + %pi +--R \| %pi +--R + +--R 2 4 2 2 3 +-+ +---+ 3 5 2 2 3 +--R (3b %pi x + 7b %pi x + 4%pi )\|b \|%pi - b %pi x - 5b %pi x +--R + +--R 3 +--R - 4b %pi x +--R * +--R +----------+ +--R | 2 +--R |b x + %pi +--R |---------- +--R \| %pi +--R Type: Expression(Integer) +--E 489 + +--S 490 of 512 +m0196b:= a0196.2-r0196 +--R +--R +--R +----------+ +--R +---+ | 2 +---+ +---+ +-+ +--R +-+ \|- b \|b x + %pi - \|- b \|%pi +---+ x\|b +--R 2\|b atan(----------------------------------) - \|- b asinh(------) +--R b x +---+ +--R \|%pi +--R (346) ------------------------------------------------------------------- +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 490 + +--S 491 of 512 +d0196b:= D(m0196b,x) +--R +--R +--R +----------+ +--R +----------+ | 2 +--R +---+ | 2 |b x + %pi +--R - \|%pi \|b x + %pi + %pi |---------- +--R \| %pi +--R (347) ---------------------------------------- +--R +----------+ +--R | 2 +----------+ +--R |b x + %pi | 2 +--R %pi |---------- \|b x + %pi +--R \| %pi +--R Type: Expression(Integer) +--E 491 + +--S 492 of 512 +t0197:= 1/(%pi-b*x^2)^(1/2) +--R +--R +--R 1 +--R (348) --------------- +--R +------------+ +--R | 2 +--R \|- b x + %pi +--R Type: Expression(Integer) +--E 492 + +--S 493 of 512 +r0197:= asin(b^(1/2)*x/%pi^(1/2))/b^(1/2) +--R +--R +--R +-+ +--R x\|b +--R asin(------) +--R +---+ +--R \|%pi +--R (349) ------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 493 + +--S 494 of 512 +a0197:= integrate(t0197,x) +--R +--R +--R (350) +--R [ +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R / +--R +---+ +--R \|- b +--R , +--R +------------+ +--R +-+ +---+ | 2 +-+ +--R \|b \|%pi - \|- b x + %pi \|b +--R 2atan(--------------------------------) +--R b x +--R ---------------------------------------] +--R +-+ +--R \|b +--R Type: Union(List(Expression(Integer)),...) +--E 494 + +--S 495 of 512 +m0197a:= a0197.1-r0197 +--R +--R +--R (351) +--R +-+ +--R \|b +--R * +--R log +--R +------------+ +--R | 2 +---+ +---+ 2 +---+ +--R (\|- b x + %pi \|- b - b x)\|%pi + (b x - %pi)\|- b +--R + +--R +------------+ +--R | 2 +--R b x\|- b x + %pi +--R / +--R +------------+ +--R | 2 +---+ +--R \|- b x + %pi \|%pi - %pi +--R + +--R +-+ +--R +---+ x\|b +--R - \|- b asin(------) +--R +---+ +--R \|%pi +--R / +--R +---+ +-+ +--R \|- b \|b +--R Type: Expression(Integer) +--E 495 + +--S 496 of 512 +d0197a:= D(m0197a,x) +--R +--R +--R (352) +--R +------------+ +--R +------------+ | 2 +--R 2 2 | 2 |- b x + %pi +--R (- 3b %pi x + 4%pi )\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 4 2 2 | 2 +--R (b x - 5b %pi x + 4%pi )\|- b x + %pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R | 2 +--R 2 3 2 |- b x + %pi 3 5 2 3 2 +--R (3b %pi x - 4b %pi x) |------------ - b x + 5b %pi x - 4b %pi x +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi 2 4 +--R (- b %pi x + 5b %pi x - 4%pi ) |------------ - 3b %pi x +--R \| %pi +--R + +--R 2 2 3 +--R 7b %pi x - 4%pi +--R * +--R +---+ +--R \|- b +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (- b %pi x + 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R + +--R +------------+ +--R 2 3 2 | 2 +--R (- 3b %pi x + 4b %pi x)\|- b x + %pi +--R / +--R +------------+ +--R | 2 +--R 2 4 2 2 3 |- b x + %pi +---+ +--R (3b %pi x - 7b %pi x + 4%pi ) |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 3 2 | 2 |- b x + %pi +--R (3b %pi x - 4b %pi x)\|- b x + %pi |------------ +--R \| %pi +--R * +--R +---+ +--R \|%pi +--R + +--R +------------+ +--R +------------+ | 2 +--R 2 4 2 2 3 | 2 |- b x + %pi +---+ +--R (- b %pi x + 5b %pi x - 4%pi )\|- b x + %pi |------------ \|- b +--R \| %pi +--R + +--R +------------+ +--R | 2 +--R 3 5 2 2 3 3 |- b x + %pi +--R (b %pi x - 5b %pi x + 4b %pi x) |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 496 + +--S 497 of 512 +m0197b:= a0197.2-r0197 +--R +--R +--R +------------+ +--R +-+ +---+ | 2 +-+ +-+ +--R \|b \|%pi - \|- b x + %pi \|b x\|b +--R 2atan(--------------------------------) - asin(------) +--R b x +---+ +--R \|%pi +--R (353) ------------------------------------------------------ +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 497 + +--S 498 of 512 +d0197b:= D(m0197b,x) +--R +--R +--R +------------+ +--R +------------+ | 2 +--R | 2 +---+ |- b x + %pi +--R - \|- b x + %pi \|%pi + %pi |------------ +--R \| %pi +--R (354) -------------------------------------------- +--R +------------+ +--R +------------+ | 2 +--R | 2 |- b x + %pi +--R %pi\|- b x + %pi |------------ +--R \| %pi +--R Type: Expression(Integer) +--E 498 + +--S 499 of 512 +t0198:= 1/(a+b*x)/(c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (355) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x + c +--R Type: Expression(Integer) +--E 499 + +--S 500 of 512 +r0198:= atanh((b^2*c+a^2*d)^(1/2)*(c+d*x^2)^(1/2)/_ + (-b*c+a*d*x))/(b^2*c+a^2*d)^(1/2) +--R +--R +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R atanh(-----------------------) +--R a d x - b c +--R (356) ------------------------------ +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression(Integer) +--E 500 + +--S 501 of 512 +a0198:= integrate(t0198,x) +--R +--R +--R (357) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R 2atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R -----------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d - b c +--R Type: Union(List(Expression(Integer)),...) +--E 501 + +--S 502 of 512 +m0198a:= a0198.1-r0198 +--R +--R +--R (358) +--R log +--R +---------+ +--------+ +--R 2 +-+ | 2 2 3 2 | 2 +--R ((a b x + a )\|c \|a d + b c + (- a d - a b c)x)\|d x + c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d - b c)x - a b c x - a c)\|a d + b c +--R + +--R 2 3 2 3 2 +-+ +--R ((a b d + b c)x + (a d + a b c)x)\|c +--R / +--R +--------+ +--R +-+ | 2 +--R (b x + a)\|c \|d x + c - b c x - a c +--R + +--R +---------+ +--------+ +--R | 2 2 | 2 +--R \|a d + b c \|d x + c +--R - atanh(-----------------------) +--R a d x - b c +--R / +--R +---------+ +--R | 2 2 +--R \|a d + b c +--R Type: Expression(Integer) +--E 502 + +--S 503 of 512 +d0198a:= D(m0198a,x) +--R +--R +--R (359) 0 +--R Type: Expression(Integer) +--E 503 + +--S 504 of 512 +m0198b:= a0198.2-r0198 +--R +--R +--R (360) +--R +---------+ +--------+ +--R +-----------+ | 2 2 | 2 +--R | 2 2 \|a d + b c \|d x + c +--R - \|- a d - b c atanh(-----------------------) +--R a d x - b c +--R + +--R +---------+ +--R | 2 2 +--R 2\|a d + b c +--R * +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +-+ +--R a\|- a d - b c \|d x + c + (- b x - a)\|- a d - b c \|c +--R atan(----------------------------------------------------------) +--R 2 2 +--R (a d + b c)x +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d - b c \|a d + b c +--R Type: Expression(Integer) +--E 504 + +--S 505 of 512 +d0198b:= D(m0198b,x) +--R +--R +--R (361) 0 +--R Type: Expression(Integer) +--E 505 + +--S 506 of 512 +t0199:= 1/(a+b*x)/(-c+d*x^2)^(1/2) +--R +--R +--R 1 +--R (362) -------------------- +--R +--------+ +--R | 2 +--R (b x + a)\|d x - c +--R Type: Expression(Integer) +--E 506 + +--S 507 of 512 +r0199:= atan((b^2*c-a^2*d)^(1/2)*(-c+d*x^2)^(1/2)/(b*c+a*d*x))/(b^2*c-a^2*d)^(1/2) +--R +--R +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R atan(-------------------------) +--R a d x + b c +--R (363) ------------------------------- +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression(Integer) +--E 507 + +--S 508 of 512 +a0199:= integrate(t0199,x) +--R +--R +--R (364) +--R [ +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R / +--R +---------+ +--R | 2 2 +--R \|a d - b c +--R , +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R -------------------------------------------------------------------] +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Union(List(Expression(Integer)),...) +--E 508 + +--S 509 of 512 +m0199a:= a0199.1-r0199 +--R +--R +--R (365) +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R * +--R log +--R +---------+ +--------+ +--R 2 +---+ | 2 2 3 2 | 2 +--R ((a b x + a )\|- c \|a d - b c + (- a d + a b c)x)\|d x - c +--R + +--R +---------+ +--R 2 2 2 2 | 2 2 +--R ((- a d + b c)x + a b c x + a c)\|a d - b c +--R + +--R 2 3 2 3 2 +---+ +--R ((a b d - b c)x + (a d - a b c)x)\|- c +--R / +--R +--------+ +--R +---+ | 2 +--R (b x + a)\|- c \|d x - c + b c x + a c +--R + +--R +-----------+ +--------+ +--R +---------+ | 2 2 | 2 +--R | 2 2 \|- a d + b c \|d x - c +--R - \|a d - b c atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +---------+ +--R | 2 2 | 2 2 +--R \|- a d + b c \|a d - b c +--R Type: Expression(Integer) +--E 509 + +--S 510 of 512 +d0199a:= D(m0199a,x) +--R +--R +--R (366) 0 +--R Type: Expression(Integer) +--E 510 + +--S 511 of 512 +m0199b:= a0199.2-r0199 +--R +--R +--R (367) +--R +-----------+ +--------+ +-----------+ +--R | 2 2 | 2 | 2 2 +---+ +--R a\|- a d + b c \|d x - c + (- b x - a)\|- a d + b c \|- c +--R 2atan(------------------------------------------------------------) +--R 2 2 +--R (a d - b c)x +--R + +--R +-----------+ +--------+ +--R | 2 2 | 2 +--R \|- a d + b c \|d x - c +--R - atan(-------------------------) +--R a d x + b c +--R / +--R +-----------+ +--R | 2 2 +--R \|- a d + b c +--R Type: Expression(Integer) +--E 511 + +--S 512 of 512 +d0199b:= D(m0199b,x) +--R +--R +--R (368) 0 +--R Type: Expression(Integer) +--E 512 + +)spool +\end{chunk} +\eject +\begin{thebibliography}{99} +\bibitem{1} +Rich, Albert D. ``Rule-based Mathematics'' \verb|www.apmaths.uwo.ca/~arich| +\end{thebibliography} +\end{document} diff --git a/src/axiom-website/CATS/richalgebraic100-199.input.pdf b/src/axiom-website/CATS/richalgebraic100-199.input.pdf new file mode 100644 index 0000000..4070994 Binary files /dev/null and b/src/axiom-website/CATS/richalgebraic100-199.input.pdf differ diff --git a/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet b/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet new file mode 100644 index 0000000..fc6e6ee --- /dev/null +++ b/src/axiom-website/CATS/richalgebraic200-299.input.pamphlet @@ -0,0 +1,10314 @@ +\documentclass{article} +\usepackage{axiom} +\setlength{\textwidth}{400pt} +\begin{document} +\title{\$SPAD/src/input richalgebraic200-299.input} +\author{Albert Rich and Timothy Daly} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\begin{chunk}{*} +)set break resume +)sys rm -f richalgebraic200-299.output +)spool richalgebraic200-299.output +)set message test on +)set message auto off +)clear all + +--S 1 of 554 +t0200:= x^2/(1-a^2-2*a*b*x-b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (1) --------------------------- +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R Type: Expression(Integer) +--E 1 + +--S 2 of 554 +r0200:= 1/2*(3*a*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)-_ + x*(1-a^2-2*a*b*x-b^2*x^2)^(1/2)*b+asin(a+b*x)+2*a^2*asin(a+b*x))/b^3 +--R +--R +--R +------------------------+ +--R | 2 2 2 2 +--R (- b x + 3a)\|- b x - 2a b x - a + 1 + (2a + 1)asin(b x + a) +--R (2) ---------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 2 + +--S 3 of 554 +a0200:= integrate(t0200,x) +--R +--R +--R (3) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R +--------+ +--R 4 4 3 3 3 2 2 4 2 | 2 +--R (2a b x - 2b x + (- 6a - 3a)b x + (- 4a + 2a + 2)b x)\|- a + 1 +--R + +--R 2 3 3 3 2 2 4 2 +--R ((- 2a + 1)b x + (2a + a)b x + (4a - 2a - 2)b x) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Union(Expression(Integer),...) +--E 3 + +--S 4 of 554 +m0200:= a0200-r0200 +--R +--R +--R (4) +--R +------------------------+ +--------+ +--R 3 4 2 | 2 2 2 | 2 +--R ((8a + 4a)b x + 8a - 4a - 4)\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R (8a - 2)b x + (16a - 8a - 8a)b x + 8a - 12a + 4 +--R * +--R +--------+ +------------------------+ +--R | 2 | 2 2 2 +--R \|- a + 1 - \|- b x - 2a b x - a + 1 +--R atan(-----------------------------------------) +--R b x +--R + +--R 3 4 2 +--R ((- 4a - 2a)b x - 4a + 2a + 2)asin(b x + a) +--R * +--R +------------------------+ +--R | 2 2 2 +--R \|- b x - 2a b x - a + 1 +--R + +--R 3 2 2 4 2 5 3 +--R (6a - 3a)b x + (12a - 12a )b x + 6a - 12a + 6a +--R * +--R +--------+ +--R | 2 +--R \|- a + 1 +--R + +--R +------------------------+ +--R 4 2 5 3 | 2 2 2 +--R ((- 6a + 6a )b x - 6a + 12a - 6a)\|- b x - 2a b x - a + 1 +--R + +--R 4 2 2 5 3 6 4 +--R ((- 4a + 1)b x + (- 8a + 4a + 4a)b x - 4a + 6a - 2)asin(b x + a) +--R / +--R +------------------------+ +--------+ +--R 4 2 3 | 2 2 2 | 2 +--R (4a b x + (4a - 4)b )\|- b x - 2a b x - a + 1 \|- a + 1 +--R + +--R 2 5 2 3 4 4 2 3 +--R (4a - 2)b x + (8a - 8a)b x + (4a - 8a + 4)b +--R Type: Expression(Integer) +--E 4 + +--S 5 of 554 +d0200:= D(m0200,x) +--R +--R +--R (5) 0 +--R Type: Expression(Integer) +--E 5 + +--S 6 of 554 +t0201:= x^2/(1+a^2+2*a*b*x+b^2*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (6) ------------------------- +--R +----------------------+ +--R | 2 2 2 +--R \|b x + 2a b x + a + 1 +--R Type: Expression(Integer) +--E 6 + +--S 7 of 554 +r0201:= -1/2*(3*a*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)-_ + x*(1+a^2+2*a*b*x+b^2*x^2)^(1/2)*b+asinh(a+b*x)-2*a^2*asinh(a+b*x))/b^3 +--R +--R +--R +----------------------+ +--R | 2 2 2 2 +--R (b x - 3a)\|b x + 2a b x + a + 1 + (2a - 1)asinh(b x + a) +--R (7) ------------------------------------------------------------- +--R 3 +--R 2b +--R Type: Expression(Integer) +--E 7 + +--S 8 of 554 +a0201:= integrate(t0201,x) +--R +--R +--R (8) +--R +----------------------+ +--R 2 3 | 2 2 2 +--R ((- 16a + 8)b x - 16a + 8a)\|b x + 2a b x + a + 1 +--R + +--R 2 2 2 3 4 +--R (16a - 8)b x + (32a - 16a)b x + 16a - 4 +--R * +--R +----------------------+ +--R | 2 2 2 +--R log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R +----------------------+ +--R 3 3 2 2 2 3 | 2 2 2 +--R (- 8b x + 8a b x + (26a - 4)b x + 10a + 12a)\|b x + 2a b x + a + 1 +--R + +--R 4 4 2 2 2 3 4 2 +--R 8b x + (- 34a + 8)b x + (- 36a - 16a)b x - 10a - 17a +--R / +--R +----------------------+ +--R 4 3 | 2 2 2 5 2 4 +--R (16b x + 16a b )\|b x + 2a b x + a + 1 - 16b x - 32a b x +--R + +--R 2 3 +--R (- 16a - 8)b +--R Type: Union(Expression(Integer),...) +--E 8 + +--S 9 of 554 +m0201:= a0201-r0201 +--R +--R +--R (9) +--R +----------------------+ +--R 2 | 2 2 2 +--R (- 8a + 4)log(\|b x + 2a b x + a + 1 - b x - a) +--R + +--R 2 2 +--R (- 8a + 4)asinh(b x + a) - 7a +--R / +--R 3 +--R 8b +--R Type: Expression(Integer) +--E 9 + +--S 10 of 554 +d0201:= D(m0201,x) +--R +--R +--R (10) 0 +--R Type: Expression(Integer) +--E 10 + +--S 11 of 554 +t0202:= 1/(x-(1-x^2)^(1/2)) +--R +--R +--R 1 +--R (11) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 11 + +--S 12 of 554 +r0202:= -1/2*asin(x)-1/2*atanh(x/(1-x^2)^(1/2))+1/4*log(1-2*x^2) +--R +--R +--R x 2 +--R - 2atanh(-----------) + log(- 2x + 1) - 2asin(x) +--R +--------+ +--R | 2 +--R \|- x + 1 +--R (12) ------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 12 + +--S 13 of 554 +a0202:= integrate(t0202,x) +--R +--R +--R (13) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--------+ +--R | 2 2 | 2 +--R (- x - 1)\|- x + 1 - x + x + 1 \|- x + 1 - 1 +--R log(---------------------------------) + 4atan(---------------) +--R 2 x +--R x +--R + +--R 2 +--R log(2x - 1) +--R / +--R 4 +--R Type: Union(Expression(Integer),...) +--E 13 + +--S 14 of 554 +m0202:= a0202-r0202 +--R +--R +--R (14) +--R +--------+ +--R | 2 2 +--R (x - 1)\|- x + 1 - x - x + 1 +--R - log(-------------------------------) +--R 2 +--R x +--R + +--R +--------+ +--R | 2 2 +--R (- x - 1)\|- x + 1 - x + x + 1 x +--R log(---------------------------------) + 2atanh(-----------) +--R 2 +--------+ +--R x | 2 +--R \|- x + 1 +--R + +--R +--------+ +--R | 2 +--R \|- x + 1 - 1 2 2 +--R 4atan(---------------) + log(2x - 1) - log(- 2x + 1) + 2asin(x) +--R x +--R / +--R 4 +--R Type: Expression(Integer) +--E 14 + +--S 15 of 554 +d0202:= D(m0202,x) +--R +--R +--R (15) 0 +--R Type: Expression(Integer) +--E 15 + +--S 16 of 554 +t0203:= x/(x-(1-x^2)^(1/2)) +--R +--R +--R x +--R (16) - --------------- +--R +--------+ +--R | 2 +--R \|- x + 1 - x +--R Type: Expression(Integer) +--E 16 + +--S 17 of 554 +r0203:= 1/2*x+1/2*(1-x^2)^(1/2)-1/4*atanh(x*2^(1/2))*2^(1/2)-_ + 1/4*atanh(2^(1/2)*(1-x^2)^(1/2))*2^(1/2) +--R +--R +--R +--------+ +--------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R - \|2 atanh(\|2 \|- x + 1 ) + 2\|- x + 1 - \|2 atanh(x\|2 ) + 2x +--R (17) ------------------------------------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 17 + +--S 18 of 554 +a0203:= integrate(t0203,x) +--R +--R +--R (18) +--R +--------+ +--R | 2 +--R (\|- x + 1 - 1) +--R * +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R 2 +-+ +--------+ 2 +-+ +--R (2x + 1)\|2 - 4x +-+ | 2 (2x + 1)\|2 - 4x +--R (log(------------------) + 2x\|2 )\|- x + 1 - log(------------------) +--R 2 2 +--R 2x - 1 2x - 1 +--R + +--R 2 +-+ +--R (- 2x - 2x)\|2 +--R / +--R +--------+ +--R +-+ | 2 +-+ +--R 4\|2 \|- x + 1 - 4\|2 +--R Type: Union(Expression(Integer),...) +--E 18 + +--S 19 of 554 +m0203:= a0203-r0203 +--R +--R +--R (19) +--R +--------+ +--R 2 +-+ 2 | 2 4 2 +-+ 4 2 +--R ((4x - 2)\|2 - 4x )\|- x + 1 + (6x - 5x + 2)\|2 - 8x + 4x +--R log(------------------------------------------------------------------) +--R +--------+ +--R 2 | 2 4 2 +--R (4x - 2)\|- x + 1 + 2x - 5x + 2 +--R + +--R +--------+ 2 +-+ +--R +-+ | 2 (2x + 1)\|2 - 4x +-+ +-+ +--R 2atanh(\|2 \|- x + 1 ) + log(------------------) + 2atanh(x\|2 ) + 2\|2 +--R 2 +--R 2x - 1 +--R / +--R +-+ +--R 4\|2 +--R Type: Expression(Integer) +--E 19 + +--S 20 of 554 +d0203:= D(m0203,x) +--R +--R +--R (20) 0 +--R Type: Expression(Integer) +--E 20 + +--S 21 of 554 +t0204:= 1/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 1 +--R (21) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 21 + +--S 22 of 554 +r0204:= 1/2*EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)*_ + 2^(1/2)/(-d)^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 22 + +--S 23 of 554 +a0204:= integrate(t0204,x) +--R +--R +--R x +--R ++ 1 +--R (22) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 23 + +--S 24 of 554 +m0204:= a0204-r0204 +--R +--R +--R x +--R ++ 1 +--R (23) | ---------------------- d%T - r0204 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression(Integer) +--E 24 + +--S 25 of 554 +d0204:= D(m0204,x) +--R +--R +--R 1 +--R (24) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 25 + +--S 26 of 554 +t0205:= x/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R x +--R (25) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 26 + +--S 27 of 554 +r0205:= atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + 2 +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (26) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 27 + +--S 28 of 554 +--a0205:= integrate(t0205,x) +--E 28 + +--S 29 of 554 +--m0205:= a0205-r0205 +--E 29 + +--S 30 of 554 +--d0205:= D(m0205,x) +--E 30 + +--S 31 of 554 +t0206:= x^2/(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R 2 +--R x +--R (27) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 31 + +--S 32 of 554 +r0206:= 2^(1/2)*(EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)-_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d))/b/(-d)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 32 + +--S 33 of 554 +a0206:= integrate(t0206,x) +--R +--R +--R x 2 +--R ++ %T +--R (28) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 33 + +--S 34 of 554 +m0206:= a0206-r0206 +--R +--R +--R x 2 +--R ++ %T +--R (29) | ---------------------- d%T - r0206 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|%T b + 2 \|%T d + 3 +--R Type: Expression(Integer) +--E 34 + +--S 35 of 554 +d0206:= D(m0206,x) +--R +--R +--R 2 +--R x +--R (30) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + 2 \|d x + 3 +--R Type: Expression(Integer) +--E 35 + +--S 36 of 554 +t0207:= x/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R x +--R (31) ---------------------- +--R +--------+ +--------+ +--R | 2 | 2 +--R \|b x + a \|d x + c +--R Type: Expression(Integer) +--E 36 + +--S 37 of 554 +r0207:= atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(1/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--R \|d \|b x + a +--R atanh(---------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (32) ---------------------- +--R +-+ +-+ +--R \|b \|d +--R Type: Expression(Integer) +--E 37 + +--S 38 of 554 +--a0207:= integrate(t0207,x) +--E 38 + +--S 39 of 554 +--m0207:= a0207-r0207 +--E 39 + +--S 40 of 554 +--d0207:= D(m0207,x) +--E 40 + +--S 41 of 554 +t0208:= 1/(1-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (33) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 41 + +--S 42 of 554 +r0208:= 1/2*EllipticF(asin(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 42 + +--S 43 of 554 +a0208:= integrate(t0208,x) +--R +--R +--R x +--R ++ 1 +--R (34) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 43 + +--S 44 of 554 +m0208:= a0208-r0208 +--R +--R +--R x +--R ++ 1 +--R (35) | ----------------------- d%T - r0208 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 44 + +--S 45 of 554 +d0208:= D(m0208,x) +--R +--R +--R 1 +--R (36) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 45 + +--S 46 of 554 +t0209:= 1/(1-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (37) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression(Integer) +--E 46 + +--S 47 of 554 +r0209:= 1/2*EllipticF(asin(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 47 + +--S 48 of 554 +a0209:= integrate(t0209,x) +--R +--R +--R x +--R ++ 1 +--R (38) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 48 + +--S 49 of 554 +m0209:= a0209-r0209 +--R +--R +--R x +--R ++ 1 +--R (39) | ------------------------- d%T - r0209 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 1 +--R Type: Expression(Integer) +--E 49 + +--S 50 of 554 +d0209:= D(m0209,x) +--R +--R +--R 1 +--R (40) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 1 +--R Type: Expression(Integer) +--E 50 + +--S 51 of 554 +t0210:= 1/(4-x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (41) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression(Integer) +--E 51 + +--S 52 of 554 +r0210:= 1/2*EllipticF(asin(1/2*x),6)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 52 + +--S 53 of 554 +a0210:= integrate(t0210,x) +--R +--R +--R x +--R ++ 1 +--R (42) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 53 + +--S 54 of 554 +m0210:= a0210-r0210 +--R +--R +--R x +--R ++ 1 +--R (43) | ----------------------- d%T - r0210 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 4 \|3%T + 2 +--R Type: Expression(Integer) +--E 54 + +--S 55 of 554 +d0210:= D(m0210,x) +--R +--R +--R 1 +--R (44) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 4 \|3x + 2 +--R Type: Expression(Integer) +--E 55 + +--S 56 of 554 +t0211:= 1/(4-x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (45) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression(Integer) +--E 56 + +--S 57 of 554 +r0211:= 1/2*EllipticF(asin(1/2*x),6)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 57 + +--S 58 of 554 +a0211:= integrate(t0211,x) +--R +--R +--R x +--R ++ 1 +--R (46) | ------------------------- d%T +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Union(Expression(Integer),...) +--E 58 + +--S 59 of 554 +m0211:= a0211-r0211 +--R +--R +--R x +--R ++ 1 +--R (47) | ------------------------- d%T - r0211 +--R ++ +----------+ +---------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|- %T + 4 +--R Type: Expression(Integer) +--E 59 + +--S 60 of 554 +d0211:= D(m0211,x) +--R +--R +--R 1 +--R (48) ----------------------- +--R +---------+ +--------+ +--R | 2 | 2 +--R \|- 3x + 2 \|- x + 4 +--R Type: Expression(Integer) +--E 60 + +--S 61 of 554 +t0212:= 1/(1-4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (49) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 61 + +--S 62 of 554 +r0212:= 1/4*EllipticF(asin(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 62 + +--S 63 of 554 +a0212:= integrate(t0212,x) +--R +--R +--R x +--R ++ 1 +--R (50) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 63 + +--S 64 of 554 +m0212:= a0212-r0212 +--R +--R +--R x +--R ++ 1 +--R (51) | ------------------------ d%T - r0212 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 64 + +--S 65 of 554 +d0212:= D(m0212,x) +--R +--R +--R 1 +--R (52) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 4x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 65 + +--S 66 of 554 +t0213:= 1/(1-4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (53) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression(Integer) +--E 66 + +--S 67 of 554 +r0213:= 1/4*EllipticF(asin(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 67 + +--S 68 of 554 +a0213:= integrate(t0213,x) +--R +--R +--R x +--R ++ 1 +--R (54) | -------------------------- d%T +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 68 + +--S 69 of 554 +m0213:= a0213-r0213 +--R +--R +--R x +--R ++ 1 +--R (55) | -------------------------- d%T - r0213 +--R ++ +----------+ +----------+ +--R | 2 | 2 +--R \|- 4%T + 1 \|- 3%T + 2 +--R Type: Expression(Integer) +--E 69 + +--S 70 of 554 +d0213:= D(m0213,x) +--R +--R +--R 1 +--R (56) ------------------------ +--R +---------+ +---------+ +--R | 2 | 2 +--R \|- 4x + 1 \|- 3x + 2 +--R Type: Expression(Integer) +--E 70 + +--S 71 of 554 +t0214:= 1/(1+x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (57) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 71 + +--S 72 of 554 +r0214:= -1/2*%i*EllipticF(%i*asinh(x),3/2)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 72 + +--S 73 of 554 +a0214:= integrate(t0214,x) +--R +--R +--R x +--R ++ 1 +--R (58) | --------------------- d%T +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Union(Expression(Integer),...) +--E 73 + +--S 74 of 554 +m0214:= a0214-r0214 +--R +--R +--R x +--R ++ 1 +--R (59) | --------------------- d%T - r0214 +--R ++ +-------+ +--------+ +--R | 2 | 2 +--R \|%T + 1 \|3%T + 2 +--R Type: Expression(Integer) +--E 74 + +--S 75 of 554 +d0214:= D(m0214,x) +--R +--R +--R 1 +--R (60) ------------------- +--R +------+ +-------+ +--R | 2 | 2 +--R \|x + 1 \|3x + 2 +--R Type: Expression(Integer) +--E 75 + +--S 76 of 554 +t0215:= 1/(1+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (61) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression(Integer) +--E 76 + +--S 77 of 554 +r0215:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),2/3)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 77 + +--S 78 of 554 +a0215:= integrate(t0215,x) +--R +--R +--R x +--R ++ 1 +--R (62) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 78 + +--S 79 of 554 +m0215:= a0215-r0215 +--R +--R +--R x +--R ++ 1 +--R (63) | ----------------------- d%T - r0215 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 1 +--R Type: Expression(Integer) +--E 79 + +--S 80 of 554 +d0215:= D(m0215,x) +--R +--R +--R 1 +--R (64) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 1 +--R Type: Expression(Integer) +--E 80 + +--S 81 of 554 +t0216:= 1/(4+x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (65) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression(Integer) +--E 81 + +--S 82 of 554 +r0216:= 1/6*EllipticF(asin(1/2*6^(1/2)*x),1/6)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 82 + +--S 83 of 554 +a0216:= integrate(t0216,x) +--R +--R +--R x +--R ++ 1 +--R (66) | ----------------------- d%T +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Union(Expression(Integer),...) +--E 83 + +--S 84 of 554 +m0216:= a0216-r0216 +--R +--R +--R x +--R ++ 1 +--R (67) | ----------------------- d%T - r0216 +--R ++ +----------+ +-------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|%T + 4 +--R Type: Expression(Integer) +--E 84 + +--S 85 of 554 +d0216:= D(m0216,x) +--R +--R +--R 1 +--R (68) --------------------- +--R +---------+ +------+ +--R | 2 | 2 +--R \|- 3x + 2 \|x + 4 +--R Type: Expression(Integer) +--E 85 + +--S 86 of 554 +t0217:= 1/(1+4*x^2)^(1/2)/(2+3*x^2)^(1/2) +--R +--R +--R 1 +--R (69) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 86 + +--S 87 of 554 +r0217:= -1/4*%i*EllipticF(%i*asinh(2*x),3/8)*2^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 87 + +--S 88 of 554 +a0217:= integrate(t0217,x) +--R +--R +--R x +--R ++ 1 +--R (70) | ---------------------- d%T +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Union(Expression(Integer),...) +--E 88 + +--S 89 of 554 +m0217:= a0217-r0217 +--R +--R +--R x +--R ++ 1 +--R (71) | ---------------------- d%T - r0217 +--R ++ +--------+ +--------+ +--R | 2 | 2 +--R \|3%T + 2 \|4%T + 1 +--R Type: Expression(Integer) +--E 89 + +--S 90 of 554 +d0217:= D(m0217,x) +--R +--R +--R 1 +--R (72) -------------------- +--R +-------+ +-------+ +--R | 2 | 2 +--R \|3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 90 + +--S 91 of 554 +t0218:= 1/(1+4*x^2)^(1/2)/(2-3*x^2)^(1/2) +--R +--R +--R 1 +--R (73) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 91 + +--S 92 of 554 +r0218:= 1/3*EllipticF(asin(1/2*6^(1/2)*x),8/3)*3^(1/2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R Fraction(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 92 + +--S 93 of 554 +a0218:= integrate(t0218,x) +--R +--R +--R x +--R ++ 1 +--R (74) | ------------------------ d%T +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Union(Expression(Integer),...) +--E 93 + +--S 94 of 554 +m0218:= a0218-r0218 +--R +--R +--R x +--R ++ 1 +--R (75) | ------------------------ d%T - r0218 +--R ++ +----------+ +--------+ +--R | 2 | 2 +--R \|- 3%T + 2 \|4%T + 1 +--R Type: Expression(Integer) +--E 94 + +--S 95 of 554 +d0218:= D(m0218,x) +--R +--R +--R 1 +--R (76) ---------------------- +--R +---------+ +-------+ +--R | 2 | 2 +--R \|- 3x + 2 \|4x + 1 +--R Type: Expression(Integer) +--E 95 + +--S 96 of 554 +t0219:= 1/(1-x^2)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (77) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 96 + +--S 97 of 554 +r0219:= -EllipticF(acos(x),2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Integer) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 97 + +--S 98 of 554 +a0219:= integrate(t0219,x) +--R +--R +--R x +--R ++ 1 +--R (78) | ----------------------- d%T +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Union(Expression(Integer),...) +--E 98 + +--S 99 of 554 +m0219:= a0219-r0219 +--R +--R +--R x +--R ++ 1 +--R (79) | ----------------------- d%T - r0219 +--R ++ +---------+ +--------+ +--R | 2 | 2 +--R \|- %T + 1 \|2%T - 1 +--R Type: Expression(Integer) +--E 99 + +--S 100 of 554 +d0219:= D(m0219,x) +--R +--R +--R 1 +--R (80) --------------------- +--R +--------+ +-------+ +--R | 2 | 2 +--R \|- x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 100 + +--S 101 of 554 +t0220:= 1/(-1+x)^(1/2)/(1+x)^(1/2)/(-1+2*x^2)^(1/2) +--R +--R +--R 1 +--R (81) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 101 + +--S 102 of 554 +r0220:= -%i*EllipticF(%i*acosh(x),2) +--R +--R There are no library operations named EllipticF +--R Use HyperDoc Browse or issue +--R )what op EllipticF +--R to learn if there is any operation containing " EllipticF " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticF with argument type(s) +--R Expression(Complex(Integer)) +--R PositiveInteger +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 102 + +--S 103 of 554 +a0220:= integrate(t0220,x) +--R +--R +--R x +--R ++ 1 +--R (82) | ----------------------------- d%T +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Union(Expression(Integer),...) +--E 103 + +--S 104 of 554 +m0220:= a0220-r0220 +--R +--R +--R x +--R ++ 1 +--R (83) | ----------------------------- d%T - r0220 +--R ++ +--------+ +--R +------+ +------+ | 2 +--R \|%T - 1 \|%T + 1 \|2%T - 1 +--R Type: Expression(Integer) +--E 104 + +--S 105 of 554 +d0220:= D(m0220,x) +--R +--R +--R 1 +--R (84) -------------------------- +--R +-------+ +--R +-----+ +-----+ | 2 +--R \|x - 1 \|x + 1 \|2x - 1 +--R Type: Expression(Integer) +--E 105 + +--S 106 of 554 +t0221:= (2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (85) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 106 + +--S 107 of 554 +r0221:= 2^(1/2)*EllipticE(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 107 + +--S 108 of 554 +a0221:= integrate(t0221,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (86) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 108 + +--S 109 of 554 +m0221:= a0221-r0221 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + 2 +--R (87) | ----------- d%T - r0221 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression(Integer) +--E 109 + +--S 110 of 554 +d0221:= D(m0221,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + 2 +--R (88) ----------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 110 + +--S 111 of 554 +t0222:= x*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + 2 +--R (89) ------------ +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 111 + +--S 112 of 554 +r0222:= 1/2*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-1/2*(3*b-2*d)*_ + atanh(d^(1/2)*(2+b*x^2)^(1/2)/b^(1/2)/(3+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + 2 +-+ +-+ | 2 | 2 +--R (2d - 3b)atanh(---------------) + \|b \|d \|b x + 2 \|d x + 3 +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + 3 +--R (90) ---------------------------------------------------------------- +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression(Integer) +--E 112 + +--S 113 of 554 +--a0222:= integrate(t0222,x) +--E 113 + +--S 114 of 554 +--m0222:= a0222-r0222 +--E 114 + +--S 115 of 554 +--d0222:= D(m0222,x) +--E 115 + +--S 116 of 554 +t0223:= x^2*(2+b*x^2)^(1/2)/(3+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (91) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 116 + +--S 117 of 554 +r0223:= 1/3*x*(2+b*x^2)^(1/2)*(3+d*x^2)^(1/2)/d-_ + 2/3*(3*b-d)*EllipticE(asin(1/2*(-b)^(1/2)*x*2^(1/2)),2/3*d/b)*_ + 3^(1/2)/(-b)^(1/2)/d^2+2^(1/2)*(3*b-2*d)*_ + EllipticF(asin(1/3*(-d)^(1/2)*x*3^(1/2)),3/2*b/d)/(-d)^(5/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Fraction(Integer))) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 117 + +--S 118 of 554 +a0223:= integrate(t0223,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (92) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Union(Expression(Integer),...) +--E 118 + +--S 119 of 554 +m0223:= a0223-r0223 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + 2 +--R (93) | -------------- d%T - r0223 +--R ++ +--------+ +--R | 2 +--R \|%T d + 3 +--R Type: Expression(Integer) +--E 119 + +--S 120 of 554 +d0223:= D(m0223,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + 2 +--R (94) ------------- +--R +--------+ +--R | 2 +--R \|d x + 3 +--R Type: Expression(Integer) +--E 120 + +--S 121 of 554 +t0224:= (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (95) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 121 + +--S 122 of 554 +r0224:= c^(1/2)*(a+b*x^2)^(1/2)*((c+d*x^2)/c)^(1/2)*_ + EllipticE(asin((-d)^(1/2)*x/c^(1/2)),b*c/a/d)/(-d)^(1/2)/_ + ((a+b*x^2)/a)^(1/2)/(c+d*x^2)^(1/2) +--R +--R There are no library operations named EllipticE +--R Use HyperDoc Browse or issue +--R )what op EllipticE +--R to learn if there is any operation containing " EllipticE " in +--R its name. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named +--R EllipticE with argument type(s) +--R Expression(Integer) +--R Fraction(Polynomial(Integer)) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 122 + +--S 123 of 554 +a0224:= integrate(t0224,x) +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (96) | ----------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression(Integer),...) +--E 123 + +--S 124 of 554 +m0224:= a0224-r0224 +--R +--R +--R +--------+ +--R x | 2 +--R ++ \|%T b + a +--R (97) | ----------- d%T - r0224 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression(Integer) +--E 124 + +--S 125 of 554 +d0224:= D(m0224,x) +--R +--R +--R +--------+ +--R | 2 +--R \|b x + a +--R (98) ----------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 125 + +--S 126 of 554 +t0225:= x*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R x\|b x + a +--R (99) ------------ +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 126 + +--S 127 of 554 +r0225:= 1/2*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d-1/2*(b*c-a*d)*_ + atanh(d^(1/2)*(a+b*x^2)^(1/2)/b^(1/2)/(c+d*x^2)^(1/2))/b^(1/2)/d^(3/2) +--R +--R +--R +--------+ +--R +-+ | 2 +--------+ +--------+ +--R \|d \|b x + a +-+ +-+ | 2 | 2 +--R (a d - b c)atanh(---------------) + \|b \|d \|b x + a \|d x + c +--R +--------+ +--R +-+ | 2 +--R \|b \|d x + c +--R (100) ------------------------------------------------------------------ +--R +-+ +-+ +--R 2d\|b \|d +--R Type: Expression(Integer) +--E 127 + +--S 128 of 554 +--a0225:= integrate(t0225,x) +--E 128 + +--S 129 of 554 +--m0225:= a0225-r0225 +--E 129 + +--S 130 of 554 +--d0225:= D(m0225,x) +--E 130 + +--S 131 of 554 +t0226:= x^2*(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (101) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 131 + +--S 132 of 554 +r0226:= 1/3*x*(a+b*x^2)^(1/2)*(c+d*x^2)^(1/2)/d+1/3*%i*c*(2*b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticE(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/d^2/_ + (a+b*x^2)^(1/2)/(c+d*x^2)^(1/2)-2/3*%i*c*(b*c-a*d)*_ + (1+b*x^2/a)^(1/2)*(1+d*x^2/c)^(1/2)*_ + EllipticF(%i*asinh((b/a)^(1/2)*x),a*d/b/c)/(b/a)^(1/2)/_ + d^2/(a+b*x^2)^(1/2)/(c+d*x^2)^(1/2) +--R +--R There are 37 exposed and 23 unexposed library operations named * +--R having 2 argument(s) but none was determined to be applicable. +--R Use HyperDoc Browse, or issue +--R )display op * +--R to learn more about the available operations. Perhaps +--R package-calling the operation or using coercions on the arguments +--R will allow you to apply the operation. +--R +--RDaly Bug +--R Cannot find a definition or applicable library operation named * +--R with argument type(s) +--R Polynomial(Complex(Fraction(Integer))) +--R Expression(Integer) +--R +--R Perhaps you should use "@" to indicate the required return type, +--R or "$" to specify which version of the function you need. +--E 132 + +--S 133 of 554 +a0226:= integrate(t0226,x) +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (102) | -------------- d%T +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Union(Expression(Integer),...) +--E 133 + +--S 134 of 554 +m0226:= a0226-r0226 +--R +--R +--R +--------+ +--R x 2 | 2 +--R ++ %T \|%T b + a +--R (103) | -------------- d%T - r0226 +--R ++ +--------+ +--R | 2 +--R \|%T d + c +--R Type: Expression(Integer) +--E 134 + +--S 135 of 554 +d0226:= D(m0226,x) +--R +--R +--R +--------+ +--R 2 | 2 +--R x \|b x + a +--R (104) ------------- +--R +--------+ +--R | 2 +--R \|d x + c +--R Type: Expression(Integer) +--E 135 + +--S 136 of 554 +t0227:= (x-(-4+x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +------+ +--R | | 2 +--R (105) \|- \|x - 4 + x +--R Type: Expression(Integer) +--E 136 + +--S 137 of 554 +r0227:= 2/3*(x-(-4+x^2)^(1/2))^(1/2)*(2*x+(-4+x^2)^(1/2)) +--R +--R +--R +---------------+ +--R +------+ | +------+ +--R | 2 | | 2 +--R (2\|x - 4 + 4x)\|- \|x - 4 + x +--R (106) ----------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 137 + +--S 138 of 554 +a0227:= integrate(t0227,x) +--R +--R +--R +------+ +--R | 2 2 +--R - 2x\|x - 4 + 2x + 8 +--R (107) ----------------------- +--R +---------------+ +--R | +------+ +--R | | 2 +--R 3\|- \|x - 4 + x +--R Type: Union(Expression(Integer),...) +--E 138 + +--S 139 of 554 +m0227:= a0227-r0227 +--R +--R +--R (108) 0 +--R Type: Expression(Integer) +--E 139 + +--S 140 of 554 +d0227:= D(m0227,x) +--R +--R +--R (109) 0 +--R Type: Expression(Integer) +--E 140 + +--S 141 of 554 +t0228:= (1+(1-x^2)^(1/2))^(1/2) +--R +--R +--R +---------------+ +--R | +--------+ +--R | | 2 +--R (110) \|\|- x + 1 + 1 +--R Type: Expression(Integer) +--E 141 + +--S 142 of 554 +r0228:= 2/3*(1+x^2-(1-x^2)^(1/2))*(1+(1-x^2)^(1/2))^(1/2)/x +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (111) -------------------------------------------- +--R 3x +--R Type: Expression(Integer) +--E 142 + +--S 143 of 554 +a0228:= integrate(t0228,x) +--R +--R +--R +---------------+ +--R +--------+ | +--------+ +--R | 2 2 | | 2 +--R (- 2\|- x + 1 + 2x + 2)\|\|- x + 1 + 1 +--R (112) -------------------------------------------- +--R 3x +--R Type: Union(Expression(Integer),...) +--E 143 + +--S 144 of 554 +m0228:= a0228-r0228 +--R +--R +--R (113) 0 +--R Type: Expression(Integer) +--E 144 + +--S 145 of 554 +d0228:= D(m0228,x) +--R +--R +--R (114) 0 +--R Type: Expression(Integer) +--E 145 + +--S 146 of 554 +t0229:= (-1+4*x^2)^(1/2)/(x+(-1+4*x^2)^(1/2)) +--R +--R +--R +-------+ +--R | 2 +--R \|4x - 1 +--R (115) -------------- +--R +-------+ +--R | 2 +--R \|4x - 1 + x +--R Type: Expression(Integer) +--E 146 + +--S 147 of 554 +r0229:= 4/3*x-1/3*(-1+4*x^2)^(1/2)-1/9*atanh(3^(1/2)*x)*3^(1/2)+_ + 1/9*atanh(3^(1/2)*(-1+4*x^2)^(1/2))*3^(1/2) +--R +--R +--R +-------+ +-------+ +--R +-+ +-+ | 2 | 2 +-+ +-+ +--R \|3 atanh(\|3 \|4x - 1 ) - 3\|4x - 1 - \|3 atanh(x\|3 ) + 12x +--R (116) ---------------------------------------------------------------- +--R 9 +--R Type: Expression(Integer) +--E 147 + +--S 148 of 554 +a0229:= integrate(t0229,x) +--R +--R +--R (117) +--R +-------+ +--R | 2 +--R (\|4x - 1 - 2x) +--R * +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R 2 +-+ +-------+ +--R (3x + 1)\|3 - 6x +-+ | 2 +--R (log(------------------) + 12x\|3 )\|4x - 1 +--R 2 +--R 3x - 1 +--R + +--R 2 +-+ +--R (3x + 1)\|3 - 6x 2 +-+ +--R - 2x log(------------------) + (- 24x + 2)\|3 +--R 2 +--R 3x - 1 +--R / +--R +-------+ +--R +-+ | 2 +-+ +--R 6\|3 \|4x - 1 - 12x\|3 +--R Type: Union(Expression(Integer),...) +--E 148 + +--S 149 of 554 +m0229:= a0229-r0229 +--R +--R +--R (118) +--R log +--R +-------+ +--R 3 +-+ 2 | 2 4 2 +-+ +--R ((24x - 4x)\|3 - 24x + 3)\|4x - 1 + (- 48x + 14x - 1)\|3 +--R + +--R 3 +--R 48x - 12x +--R / +--R +-------+ +--R 3 | 2 4 2 +--R (12x - 4x)\|4x - 1 - 24x + 11x - 1 +--R + +--R +-------+ 2 +-+ +--R +-+ | 2 (3x + 1)\|3 - 6x +-+ +--R - 2atanh(\|3 \|4x - 1 ) + log(------------------) + 2atanh(x\|3 ) +--R 2 +--R 3x - 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 149 + +--S 150 of 554 +d0229:= D(m0229,x) +--R +--R +--R (119) 0 +--R Type: Expression(Integer) +--E 150 + +--S 151 of 554 +t0230:= (-1+x+x^2)/(1+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (120) ------------- +--R +------+ +--R | 2 +--R \|x + 1 + 1 +--R Type: Expression(Integer) +--E 151 + +--S 152 of 554 +r0230:= -1/x-x+(1+1/x+1/2*x)*(1+x^2)^(1/2)-1/2*asinh(x)-log(1+(1+x^2)^(1/2)) +--R +--R +--R (121) +--R +------+ +------+ +--R | 2 2 | 2 2 +--R - 2x log(\|x + 1 + 1) + (x + 2x + 2)\|x + 1 - x asinh(x) - 2x - 2 +--R ----------------------------------------------------------------------- +--R 2x +--R Type: Expression(Integer) +--E 152 + +--S 153 of 554 +a0230:= integrate(t0230,x) +--R +--R +--R (122) +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((- 8x - 2x)\|x + 1 + 8x + 6x )log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((4x + x)\|x + 1 - 4x - 3x )log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 3 | 2 4 2 | 2 +--R ((8x + 2x)\|x + 1 - 8x - 6x )log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 3 5 4 3 2 | 2 +--R ((- 8x - 2x)log(x) - 4x - 16x - 3x - 16x - 4x - 2)\|x + 1 +--R + +--R 4 2 6 5 4 3 2 +--R (8x + 6x )log(x) + 4x + 16x + 5x + 24x + 5x + 8x + 2 +--R / +--R +------+ +--R 3 | 2 4 2 +--R (8x + 2x)\|x + 1 - 8x - 6x +--R Type: Union(Expression(Integer),...) +--E 153 + +--S 154 of 554 +m0230:= a0230-r0230 +--R +--R +--R (123) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) + 2 +--R / +--R 2 +--R Type: Expression(Integer) +--E 154 + +--S 155 of 554 +d0230:= D(m0230,x) +--R +--R +--R (124) 0 +--R Type: Expression(Integer) +--E 155 + +--S 156 of 554 +t0231:= (-1+x+x^2)/(1+x+(1+x^2)^(1/2)) +--R +--R +--R 2 +--R x + x - 1 +--R (125) ----------------- +--R +------+ +--R | 2 +--R \|x + 1 + x + 1 +--R Type: Expression(Integer) +--E 156 + +--S 157 of 554 +r0231:= 1/2*x^2+1/6*x^3+1/12*(4-3*x-2*x^2)*(1+x^2)^(1/2)-_ + 1/4*asinh(x)-1/2*log(1+(1+x^2)^(1/2)) +--R +--R +--R (126) +--R +------+ +------+ +--R | 2 2 | 2 3 2 +--R - 6log(\|x + 1 + 1) + (- 2x - 3x + 4)\|x + 1 - 3asinh(x) + 2x + 6x +--R ------------------------------------------------------------------------- +--R 12 +--R Type: Expression(Integer) +--E 157 + +--S 158 of 554 +a0231:= integrate(t0231,x) +--R +--R +--R (127) +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((- 24x - 6)\|x + 1 + 24x + 18x)log(\|x + 1 - x + 1) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((12x + 3)\|x + 1 - 12x - 9x)log(\|x + 1 - x) +--R + +--R +------+ +------+ +--R 2 | 2 3 | 2 +--R ((24x + 6)\|x + 1 - 24x - 18x)log(\|x + 1 - x - 1) +--R + +--R +------+ +--R 2 5 4 3 2 | 2 +--R ((- 24x - 6)log(x) + 16x + 36x - 8x + 15x - 12x)\|x + 1 +--R + +--R 3 6 5 3 2 +--R (24x + 18x)log(x) - 16x - 36x - 33x + 18x - 3x + 4 +--R / +--R +------+ +--R 2 | 2 3 +--R (48x + 12)\|x + 1 - 48x - 36x +--R Type: Union(Expression(Integer),...) +--E 158 + +--S 159 of 554 +m0231:= a0231-r0231 +--R +--R +--R (128) +--R +------+ +------+ +------+ +--R | 2 | 2 | 2 +--R 2log(\|x + 1 + 1) - 2log(\|x + 1 - x + 1) + log(\|x + 1 - x) +--R + +--R +------+ +--R | 2 +--R 2log(\|x + 1 - x - 1) - 2log(x) + asinh(x) +--R / +--R 4 +--R Type: Expression(Integer) +--E 159 + +--S 160 of 554 +d0231:= D(m0231,x) +--R +--R +--R (129) 0 +--R Type: Expression(Integer) +--E 160 + +--S 161 of 554 +t0232:= x/(1-x^3)^(2/3) +--R +--R +--R x +--R (130) ------------ +--R +--------+2 +--R 3| 3 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 161 + +--S 162 of 554 +r0232:= -1/3*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*3^(1/2)+_ + 1/6*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-1/3*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (131) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R +-+ \|3 \|- x + 1 - 2x\|3 +--R - 2\|3 atan(------------------------) +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 6 +--R Type: Expression(Integer) +--E 162 + +--S 163 of 554 +a0232:= integrate(t0232,x) +--R +--R +--R (132) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 +--R - 6atan(------------------------) +--R 3x +--R / +--R +-+ +--R 6\|3 +--R Type: Union(Expression(Integer),...) +--E 163 + +--S 164 of 554 +m0232:= a0232-r0232 +--R +--R +--R (133) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 6\|3 +--R Type: Expression(Integer) +--E 164 + +--S 165 of 554 +d0232:= D(m0232,x) +--R +--R +--R (134) 0 +--R Type: Expression(Integer) +--E 165 + +--S 166 of 554 +t0233:= x*(1-x^3)^(1/3) +--R +--R +--R +--------+ +--R 3| 3 +--R (135) x\|- x + 1 +--R Type: Expression(Integer) +--E 166 + +--S 167 of 554 +r0233:= 1/3*x^2*(1-x^3)^(1/3)-1/9*atan(1/3*(1-2*x/(1-x^3)^(1/3))*3^(1/2))*_ + 3^(1/2)+1/18*log(1+x^2/(1-x^3)^(2/3)-x/(1-x^3)^(1/3))-_ + 1/9*log(1+x/(1-x^3)^(1/3)) +--R +--R +--R (136) +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R \|- x + 1 + x \|- x + 1 - x\|- x + 1 + x +--R - 2log(---------------) + log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R +-+ \|3 \|- x + 1 - 2x\|3 2 3| 3 +--R - 2\|3 atan(------------------------) + 6x \|- x + 1 +--R +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R 18 +--R Type: Expression(Integer) +--E 167 + +--S 168 of 554 +a0233:= integrate(t0233,x) +--R +--R +--R (137) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--R +-+3| 3 +-+ +--------+ +--R 2\|3 \|- x + 1 - x\|3 2 +-+3| 3 +--R - 6atan(------------------------) + 6x \|3 \|- x + 1 +--R 3x +--R / +--R +-+ +--R 18\|3 +--R Type: Union(Expression(Integer),...) +--E 168 + +--S 169 of 554 +m0233:= a0233-r0233 +--R +--R +--R (138) +--R +--------+2 +--------+ +--------+ +--R 3| 3 3| 3 2 3| 3 +--R +-+ \|- x + 1 - x\|- x + 1 + x +-+ \|- x + 1 + x +--R \|3 log(--------------------------------) - 2\|3 log(---------------) +--R 2 x +--R x +--R + +--R +--------+ +--------+2 +--------+ +--R 3| 3 3| 3 3| 3 2 +--R +-+ \|- x + 1 + x +-+ \|- x + 1 - x\|- x + 1 + x +--R 2\|3 log(---------------) - \|3 log(--------------------------------) +--R +--------+ +--------+2 +--R 3| 3 3| 3 +--R \|- x + 1 \|- x + 1 +--R + +--R +--------+ +--------+ +--R +-+3| 3 +-+ +-+3| 3 +-+ +--R 2\|3 \|- x + 1 - x\|3 \|3 \|- x + 1 - 2x\|3 +--R - 6atan(------------------------) + 6atan(------------------------) +--R 3x +--------+ +--R 3| 3 +--R 3\|- x + 1 +--R / +--R +-+ +--R 18\|3 +--R Type: Expression(Integer) +--E 169 + +--S 170 of 554 +d0233:= D(m0233,x) +--R +--R +--R (139) 0 +--R Type: Expression(Integer) +--E 170 + +--S 171 of 554 +t0234:= (a+b*x^4)^(3/2) +--R +--R +--R +--------+ +--R 4 | 4 +--R (140) (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 171 + +--S 172 of 554 +r0234:= 2/7*a*x*(a+b*x^4)^(1/2)+1/7*x*(a+b*x^4)^(3/2)+4/7*a^(9/4)*_ + ((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (141) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b 2 9 5 2 4+---+ +--R 4a \|a |-------- atanh(asin(-------) + (b x + 4a b x + 3a x)\|- b +--R \| a 4+-+ +--R \|a +--R ---------------------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression(Integer) +--E 172 + +--S 173 of 554 +a0234:= integrate(t0234,x) +--R +--R +--R x +--------+ +--R ++ 4 | 4 +--R (142) | (%T b + a)\|%T b + a d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 173 + +--S 174 of 554 +m0234:= a0234-r0234 +--R +--R +--R (143) +--R +--------+ +--R | 4 4+---+ +--R 2 4+-+ |b x + a x\|- b +--R - 4a \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ 4 | 4 +--R 7\|- b \|b x + a | (%T b + a)\|%T b + a d%T +--R ++ +--R + +--R 2 9 5 2 4+---+ +--R (- b x - 4a b x - 3a x)\|- b +--R / +--R +--------+ +--R 4+---+ | 4 +--R 7\|- b \|b x + a +--R Type: Expression(Integer) +--E 174 + +--S 175 of 554 +d0234:= D(m0234,x) +--R +--R +--R (144) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R 2 |b x + a x\|- b 2 |b x + a |\|a - x \|- b +--R (4a |-------- asin(-------) - 4a |-------- ) |----------------- +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 4 2 +--R 4a b x + 4a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (7 |-------- \|b x + a asin(-------) - 7 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 175 + +--S 176 of 554 +t0235:= (a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (145) \|b x + a +--R Type: Expression(Integer) +--E 176 + +--S 177 of 554 +r0235:= 1/3*x*(a+b*x^4)^(1/2)+2/3*a^(5/4)*((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b 5 4+---+ +--R 2a\|a |-------- atanh(asin(-------)) + (b x + a x)\|- b +--R \| a 4+-+ +--R \|a +--R (146) ---------------------------------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression(Integer) +--E 177 + +--S 178 of 554 +a0235:= integrate(t0235,x) +--R +--R +--R x +--------+ +--R ++ | 4 +--R (147) | \|%T b + a d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 178 + +--S 179 of 554 +m0235:= a0235-r0235 +--R +--R +--R (148) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - 2a\|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--------+ +--R 4+---+ | 4 ++ | 4 5 4+---+ +--R 3\|- b \|b x + a | \|%T b + a d%T + (- b x - a x)\|- b +--R ++ +--R / +--R +--------+ +--R 4+---+ | 4 +--R 3\|- b \|b x + a +--R Type: Expression(Integer) +--E 179 + +--S 180 of 554 +d0235:= D(m0235,x) +--R +--R +--R (149) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (2a |-------- asin(-------) - 2a |-------- ) |----------------- + 2b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 2a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (3 |-------- \|b x + a asin(-------) - 3 |-------- \|b x + a) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 180 + +--S 181 of 554 +t0236:= 1/(a+b*x^4)^(1/2) +--R +--R +--R 1 +--R (150) ----------- +--R +--------+ +--R | 4 +--R \|b x + a +--R Type: Expression(Integer) +--E 181 + +--S 182 of 554 +r0236:= a^(1/4)*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + (-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R (151) ----------------------------------- +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression(Integer) +--E 182 + +--S 183 of 554 +a0236:= integrate(t0236,x) +--R +--R +--R x +--R ++ 1 +--R (152) | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R Type: Union(Expression(Integer),...) +--E 183 + +--S 184 of 554 +m0236:= a0236-r0236 +--R +--R +--R (153) +--R +--------+ +--R | 4 4+---+ +--R 4+-+ |b x + a x\|- b +--R - \|a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+ | 4 ++ 1 +--R \|- b \|b x + a | ----------- d%T +--R ++ +--------+ +--R | 4 +--R \|%T b + a +--R / +--R +--------+ +--R 4+---+ | 4 +--R \|- b \|b x + a +--R Type: Expression(Integer) +--E 184 + +--S 185 of 554 +d0236:= D(m0236,x) +--R +--R +--R (154) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R |b x + a | 4 x\|- b |b x + a | 4 +--R (a |-------- \|b x + a asin(-------) - a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 185 + +--S 186 of 554 +t0237:= 1/(a+b*x^4)^(3/2) +--R +--R +--R 1 +--R (155) --------------------- +--R +--------+ +--R 4 | 4 +--R (b x + a)\|b x + a +--R Type: Expression(Integer) +--E 186 + +--S 187 of 554 +r0237:= 1/2*(x*a^(3/4)*(-b)^(1/4)+((a+b*x^4)/a)^(1/2)*_ + atanh(asin((-b)^(1/4)*x/a^(1/4)))*a)/a^(7/4)/(a+b*x^4)^(1/2)/(-b)^(1/4) +--R +--R +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b 4+---+4+-+3 +--R a |-------- atanh(asin(-------)) + x\|- b \|a +--R \| a 4+-+ +--R \|a +--R (156) ----------------------------------------------- +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 187 + +--S 188 of 554 +a0237:= integrate(t0237,x) +--R +--R +--R x +--R ++ 1 +--R (157) | --------------------- d%T +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R Type: Union(Expression(Integer),...) +--E 188 + +--S 189 of 554 +m0237:= a0237-r0237 +--R +--R +--R (158) +--R +--------+ +--R | 4 4+---+ +--R |b x + a x\|- b +--R - a |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ x +--R 4+---+4+-+3 | 4 ++ 1 4+---+4+-+3 +--R 2a\|- b \|a \|b x + a | --------------------- d%T - x\|- b \|a +--R ++ +--------+ +--R 4 | 4 +--R (%T b + a)\|%T b + a +--R / +--R +--------+ +--R 4+---+4+-+3 | 4 +--R 2a\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 189 + +--S 190 of 554 +d0237:= D(m0237,x) +--R +--R +--R (159) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (a |-------- asin(-------) - a |-------- ) |----------------- + b x + a +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 2 |b x + a | 4 x\|- b 2 |b x + a | 4 +--R (2a |-------- \|b x + a asin(-------) - 2a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 190 + +--S 191 of 554 +t0238:= 1/(a+b*x^4)^(5/2) +--R +--R +--R 1 +--R (160) -------------------------------- +--R +--------+ +--R 2 8 4 2 | 4 +--R (b x + 2a b x + a )\|b x + a +--R Type: Expression(Integer) +--E 191 + +--S 192 of 554 +r0238:= 1/6*x/a/(a+b*x^4)^(3/2)+5/12*x/a^2/(a+b*x^4)^(1/2)+_ + 5/12*((a+b*x^4)/a)^(1/2)*atanh(asin((-b)^(1/4)*x/a^(1/4)))/_ + a^(7/4)/(-b)^(1/4)/(a+b*x^4)^(1/2) +--R +--R +--R (161) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b 5 4+---+4+-+3 +--R (5a b x + 5a ) |-------- atanh(asin(-------)) + (5b x + 7a x)\|- b \|a +--R \| a 4+-+ +--R \|a +--R -------------------------------------------------------------------------- +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 192 + +--S 193 of 554 +a0238:= integrate(t0238,x) +--R +--R +--R x +--R ++ 1 +--R (162) | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R Type: Union(Expression(Integer),...) +--E 193 + +--S 194 of 554 +m0238:= a0238-r0238 +--R +--R +--R (163) +--R +--------+ +--R | 4 4+---+ +--R 4 2 |b x + a x\|- b +--R (- 5a b x - 5a ) |-------- atanh(asin(-------)) +--R \| a 4+-+ +--R \|a +--R + +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R * +--R x +--R ++ 1 +--R | --------------------------------- d%T +--R ++ +--------+ +--R 8 2 4 2 | 4 +--R (%T b + 2%T a b + a )\|%T b + a +--R + +--R 5 4+---+4+-+3 +--R (- 5b x - 7a x)\|- b \|a +--R / +--R +--------+ +--R 2 4 3 4+---+4+-+3 | 4 +--R (12a b x + 12a )\|- b \|a \|b x + a +--R Type: Expression(Integer) +--E 194 + +--S 195 of 554 +d0238:= D(m0238,x) +--R +--R +--R (164) +--R +--------+ +--------+ +-----------------+ +--R | 4 4+---+ 2 | 4 |4+-+2 2 4+---+2 +--R |b x + a x\|- b |b x + a |\|a - x \|- b 4 +--R (5a |-------- asin(-------) - 5a |-------- ) |----------------- + 5b x +--R \| a 4+-+ \| a | 4+-+2 +--R \|a \| \|a +--R + +--R 5a +--R / +--R +--------+ +--------+ +--R | 4 +--------+ 4+---+ 2 | 4 +--------+ +--R 3 |b x + a | 4 x\|- b 3 |b x + a | 4 +--R (12a |-------- \|b x + a asin(-------) - 12a |-------- \|b x + a ) +--R \| a 4+-+ \| a +--R \|a +--R * +--R +-----------------+ +--R |4+-+2 2 4+---+2 +--R |\|a - x \|- b +--R |----------------- +--R | 4+-+2 +--R \| \|a +--R Type: Expression(Integer) +--E 195 + +--S 196 of 554 +t0239:= (1+x^4)^(3/2) +--R +--R +--R +------+ +--R 4 | 4 +--R (165) (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 196 + +--S 197 of 554 +r0239:= 2/7*x*(1+x^4)^(1/2)+1/7*x*(1+x^4)^(3/2)-4/7*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x 5 +-+ | 4 +--R (- 4\|- 1 + 4)atanh(asin(-----------)) + (x + 3x)\|2 \|x + 1 +--R +-+ +--R \|2 +--R (166) ---------------------------------------------------------------- +--R +-+ +--R 7\|2 +--R Type: Expression(Integer) +--E 197 + +--S 198 of 554 +a0239:= integrate(t0239,x) +--R +--R +--R x +-------+ +--R ++ 4 | 4 +--R (167) | (%T + 1)\|%T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 198 + +--S 199 of 554 +m0239:= a0239-r0239 +--R +--R +--R (168) +--R x +-------+ +---+ +--R +-+ ++ 4 | 4 +---+ x\|- 1 + x +--R 7\|2 | (%T + 1)\|%T + 1 d%T + (4\|- 1 - 4)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R 5 +-+ | 4 +--R (- x - 3x)\|2 \|x + 1 +--R / +--R +-+ +--R 7\|2 +--R Type: Expression(Integer) +--E 199 + +--S 200 of 554 +d0239:= D(m0239,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 4\|x + 1 + (4asin(-----------) - 4)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (169) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (7asin(-----------) - 7)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 200 + +--S 201 of 554 +t0240:= (1+x^4)^(1/2) +--R +--R +--R +------+ +--R | 4 +--R (170) \|x + 1 +--R Type: Expression(Integer) +--E 201 + +--S 202 of 554 +r0240:= 1/3*x*(1+x^4)^(1/2)-2/3*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +------+ +--R +---+ x\|- 1 + x +-+ | 4 +--R (- 2\|- 1 + 2)atanh(asin(-----------)) + x\|2 \|x + 1 +--R +-+ +--R \|2 +--R (171) -------------------------------------------------------- +--R +-+ +--R 3\|2 +--R Type: Expression(Integer) +--E 202 + +--S 203 of 554 +a0240:= integrate(t0240,x) +--R +--R +--R x +-------+ +--R ++ | 4 +--R (172) | \|%T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 203 + +--S 204 of 554 +m0240:= a0240-r0240 +--R +--R +--R (173) +--R x +-------+ +---+ +--R +-+ ++ | 4 +---+ x\|- 1 + x +--R 3\|2 | \|%T + 1 d%T + (2\|- 1 - 2)atanh(asin(-----------)) +--R ++ +-+ +--R \|2 +--R + +--R +------+ +--R +-+ | 4 +--R - x\|2 \|x + 1 +--R / +--R +-+ +--R 3\|2 +--R Type: Expression(Integer) +--E 204 + +--S 205 of 554 +d0240:= D(m0240,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 2\|x + 1 + (2asin(-----------) - 2)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (174) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (3asin(-----------) - 3)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 205 + +--S 206 of 554 +t0241:= 1/(1+x^4)^(1/2) +--R +--R +--R 1 +--R (175) --------- +--R +------+ +--R | 4 +--R \|x + 1 +--R Type: Expression(Integer) +--E 206 + +--S 207 of 554 +r0241:= -(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +---+ +--R +---+ x\|- 1 + x +--R (- \|- 1 + 1)atanh(asin(-----------)) +--R +-+ +--R \|2 +--R (176) -------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 207 + +--S 208 of 554 +a0241:= integrate(t0241,x) +--R +--R +--R x +--R ++ 1 +--R (177) | ---------- d%T +--R ++ +-------+ +--R | 4 +--R \|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 208 + +--S 209 of 554 +m0241:= a0241-r0241 +--R +--R +--R x +---+ +--R +-+ ++ 1 +---+ x\|- 1 + x +--R \|2 | ---------- d%T + (\|- 1 - 1)atanh(asin(-----------)) +--R ++ +-------+ +-+ +--R | 4 \|2 +--R \|%T + 1 +--R (178) --------------------------------------------------------------- +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 209 + +--S 210 of 554 +d0241:= D(m0241,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (179) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (asin(-----------) - 1)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 210 + +--S 211 of 554 +t0242:= 1/(1+x^4)^(3/2) +--R +--R +--R 1 +--R (180) ----------------- +--R +------+ +--R 4 | 4 +--R (x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 211 + +--S 212 of 554 +r0242:= 1/2*x/(1+x^4)^(1/2)-1/2*(-1)^(3/4)*atanh(asin((-1)^(1/4)*x)) +--R +--R +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (- \|- 1 + 1)\|x + 1 atanh(asin(-----------)) + x\|2 +--R +-+ +--R \|2 +--R (181) ------------------------------------------------------- +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression(Integer) +--E 212 + +--S 213 of 554 +a0242:= integrate(t0242,x) +--R +--R +--R x +--R ++ 1 +--R (182) | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 213 + +--S 214 of 554 +m0242:= a0242-r0242 +--R +--R +--R (183) +--R +------+ x +--R +-+ | 4 ++ 1 +--R 2\|2 \|x + 1 | ------------------- d%T +--R ++ +-------+ +--R 4 | 4 +--R (%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R +---+ | 4 x\|- 1 + x +-+ +--R (\|- 1 - 1)\|x + 1 atanh(asin(-----------)) - x\|2 +--R +-+ +--R \|2 +--R / +--R +------+ +--R +-+ | 4 +--R 2\|2 \|x + 1 +--R Type: Expression(Integer) +--E 214 + +--S 215 of 554 +d0242:= D(m0242,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R \|x + 1 + (asin(-----------) - 1)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (184) ----------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (2asin(-----------) - 2)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 215 + +--S 216 of 554 +t0243:= 1/(1+x^4)^(5/2) +--R +--R +--R 1 +--R (185) ----------------------- +--R +------+ +--R 8 4 | 4 +--R (x + 2x + 1)\|x + 1 +--R Type: Expression(Integer) +--E 216 + +--S 217 of 554 +r0243:= 1/6*x/(1+x^4)^(3/2)+5/12*x/(1+x^4)^(1/2)-5/12*(-1)^(3/4)*_ + atanh(asin((-1)^(1/4)*x)) +--R +--R +--R (186) +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((- 5x - 5)\|- 1 + 5x + 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (5x + 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression(Integer) +--E 217 + +--S 218 of 554 +a0243:= integrate(t0243,x) +--R +--R +--R x +--R ++ 1 +--R (187) | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R Type: Union(Expression(Integer),...) +--E 218 + +--S 219 of 554 +m0243:= a0243-r0243 +--R +--R +--R (188) +--R +------+ x +--R 4 +-+ | 4 ++ 1 +--R (12x + 12)\|2 \|x + 1 | -------------------------- d%T +--R ++ +-------+ +--R 8 4 | 4 +--R (%T + 2%T + 1)\|%T + 1 +--R + +--R +------+ +---+ +--R 4 +---+ 4 | 4 x\|- 1 + x +--R ((5x + 5)\|- 1 - 5x - 5)\|x + 1 atanh(asin(-----------)) +--R +-+ +--R \|2 +--R + +--R 5 +-+ +--R (- 5x - 7x)\|2 +--R / +--R +------+ +--R 4 +-+ | 4 +--R (12x + 12)\|2 \|x + 1 +--R Type: Expression(Integer) +--E 219 + +--S 220 of 554 +d0243:= D(m0243,x) +--R +--R +--R +------+ +---+ 2 +--------------+ +--R | 4 x\|- 1 + x | 2 +---+ +--R 5\|x + 1 + (5asin(-----------) - 5)\|- x \|- 1 + 1 +--R +-+ +--R \|2 +--R (189) ------------------------------------------------------- +--R +---+ 2 +--------------+ +------+ +--R x\|- 1 + x | 2 +---+ | 4 +--R (12asin(-----------) - 12)\|- x \|- 1 + 1 \|x + 1 +--R +-+ +--R \|2 +--R Type: Expression(Integer) +--E 220 + +--S 221 of 554 +t0244:= (1-x^4)^(1/2) +--R +--R +--R +--------+ +--R | 4 +--R (190) \|- x + 1 +--R Type: Expression(Integer) +--E 221 + +--S 222 of 554 +r0244:= 1/3*x*(1-x^4)^(1/2)+2/3*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R 2atanh(asin(x)) + x\|- x + 1 +--R (191) ------------------------------ +--R 3 +--R Type: Expression(Integer) +--E 222 + +--S 223 of 554 +a0244:= integrate(t0244,x) +--R +--R +--R x +---------+ +--R ++ | 4 +--R (192) | \|- %T + 1 d%T +--R ++ +--R Type: Union(Expression(Integer),...) +--E 223 + +--S 224 of 554 +m0244:= a0244-r0244 +--R +--R +--R x +---------+ +--------+ +--R ++ | 4 | 4 +--R 3 | \|- %T + 1 d%T - 2atanh(asin(x)) - x\|- x + 1 +--R ++ +--R (193) ------------------------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 224 + +--S 225 of 554 +d0244:= D(m0244,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (2asin(x) - 2)\|- x + 1 + 2\|- x + 1 +--R (194) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (3asin(x) - 3)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 225 + +--S 226 of 554 +t0245:= 1/(1-x^4)^(1/2) +--R +--R +--R 1 +--R (195) ----------- +--R +--------+ +--R | 4 +--R \|- x + 1 +--R Type: Expression(Integer) +--E 226 + +--S 227 of 554 +r0245:= atanh(asin(x)) +--R +--R +--R (196) atanh(asin(x)) +--R Type: Expression(Integer) +--E 227 + +--S 228 of 554 +a0245:= integrate(t0245,x) +--R +--R +--R x +--R ++ 1 +--R (197) | ------------ d%T +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 228 + +--S 229 of 554 +m0245:= a0245-r0245 +--R +--R +--R x +--R ++ 1 +--R (198) | ------------ d%T - atanh(asin(x)) +--R ++ +---------+ +--R | 4 +--R \|- %T + 1 +--R Type: Expression(Integer) +--E 229 + +--S 230 of 554 +d0245:= D(m0245,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (199) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (asin(x) - 1)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 230 + +--S 231 of 554 +t0246:= 1/(1-x^4)^(3/2) +--R +--R +--R 1 +--R (200) - ------------------- +--R +--------+ +--R 4 | 4 +--R (x - 1)\|- x + 1 +--R Type: Expression(Integer) +--E 231 + +--S 232 of 554 +r0246:= 1/2*x/(1-x^4)^(1/2)+1/2*atanh(asin(x)) +--R +--R +--R +--------+ +--R | 4 +--R \|- x + 1 atanh(asin(x)) + x +--R (201) ----------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 232 + +--S 233 of 554 +a0246:= integrate(t0246,x) +--R +--R +--R x +--R ++ 1 +--R (202) | - --------------------- d%T +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 233 + +--S 234 of 554 +m0246:= a0246-r0246 +--R +--R +--R (203) +--R +--------+ x +--------+ +--R | 4 ++ 1 | 4 +--R 2\|- x + 1 | - --------------------- d%T - \|- x + 1 atanh(asin(x)) - x +--R ++ +---------+ +--R 4 | 4 +--R (%T - 1)\|- %T + 1 +--R ----------------------------------------------------------------------------- +--R +--------+ +--R | 4 +--R 2\|- x + 1 +--R Type: Expression(Integer) +--E 234 + +--S 235 of 554 +d0246:= D(m0246,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (asin(x) - 1)\|- x + 1 + \|- x + 1 +--R (204) --------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (2asin(x) - 2)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 235 + +--S 236 of 554 +t0247:= 1/(1-x^4)^(5/2) +--R +--R +--R 1 +--R (205) ------------------------- +--R +--------+ +--R 8 4 | 4 +--R (x - 2x + 1)\|- x + 1 +--R Type: Expression(Integer) +--E 236 + +--S 237 of 554 +r0247:= 1/6*x/(1-x^4)^(3/2)+5/12*x/(1-x^4)^(1/2)+5/12*atanh(asin(x)) +--R +--R +--R +--------+ +--R 4 | 4 5 +--R (5x - 5)\|- x + 1 atanh(asin(x)) + 5x - 7x +--R (206) --------------------------------------------- +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression(Integer) +--E 237 + +--S 238 of 554 +a0247:= integrate(t0247,x) +--R +--R +--R x +--R ++ 1 +--R (207) | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R Type: Union(Expression(Integer),...) +--E 238 + +--S 239 of 554 +m0247:= a0247-r0247 +--R +--R +--R (208) +--R +--------+ x +--R 4 | 4 ++ 1 +--R (12x - 12)\|- x + 1 | ---------------------------- d%T +--R ++ +---------+ +--R 8 4 | 4 +--R (%T - 2%T + 1)\|- %T + 1 +--R + +--R +--------+ +--R 4 | 4 5 +--R (- 5x + 5)\|- x + 1 atanh(asin(x)) - 5x + 7x +--R / +--R +--------+ +--R 4 | 4 +--R (12x - 12)\|- x + 1 +--R Type: Expression(Integer) +--E 239 + +--S 240 of 554 +d0247:= D(m0247,x) +--R +--R +--R +--------+ +--------+ +--R 2 | 2 | 4 +--R (5asin(x) - 5)\|- x + 1 + 5\|- x + 1 +--R (209) ----------------------------------------- +--R +--------+ +--------+ +--R 2 | 4 | 2 +--R (12asin(x) - 12)\|- x + 1 \|- x + 1 +--R Type: Expression(Integer) +--E 240 + +--S 241 of 554 +t0248:= 1/x/(1+x^6)^(1/2) +--R +--R +--R 1 +--R (210) ---------- +--R +------+ +--R | 6 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 241 + +--S 242 of 554 +r0248:= -1/3*atanh((1+x^6)^(1/2)) +--R +--R +--R +------+ +--R | 6 +--R atanh(\|x + 1 ) +--R (211) - ---------------- +--R 3 +--R Type: Expression(Integer) +--E 242 + +--S 243 of 554 +a0248:= integrate(t0248,x) +--R +--R +--R +------+ +------+ +--R | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (212) ----------------------------------------- +--R 6 +--R Type: Union(Expression(Integer),...) +--E 243 + +--S 244 of 554 +m0248:= a0248-r0248 +--R +--R +--R +------+ +------+ +------+ +--R | 6 | 6 | 6 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (213) ------------------------------------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 244 + +--S 245 of 554 +d0248:= D(m0248,x) +--R +--R +--R (214) 0 +--R Type: Expression(Integer) +--E 245 + +--S 246 of 554 +t0249:= 1/x/(-25+x^6)^(1/2) +--R +--R +--R 1 +--R (215) ----------- +--R +-------+ +--R | 6 +--R x\|x - 25 +--R Type: Expression(Integer) +--E 246 + +--S 247 of 554 +r0249:= 1/15*atan(1/5*(-25+x^6)^(1/2)) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (216) ---------------- +--R 15 +--R Type: Expression(Integer) +--E 247 + +--S 248 of 554 +a0249:= integrate(t0249,x) +--R +--R +--R +-------+ +--R | 6 +--R \|x - 25 +--R atan(----------) +--R 5 +--R (217) ---------------- +--R 15 +--R Type: Union(Expression(Integer),...) +--E 248 + +--S 249 of 554 +m0249:= a0249-r0249 +--R +--R +--R (218) 0 +--R Type: Expression(Integer) +--E 249 + +--S 250 of 554 +d0249:= D(m0249,x) +--R +--R +--R (219) 0 +--R Type: Expression(Integer) +--E 250 + +--S 251 of 554 +t0250:= x^8*(-1+4*x^6)^(1/2) +--R +--R +--R +-------+ +--R 8 | 6 +--R (220) x \|4x - 1 +--R Type: Expression(Integer) +--E 251 + +--S 252 of 554 +r0250:= -1/96*x^3*(-1+4*x^6)^(1/2)+1/12*x^9*(-1+4*x^6)^(1/2)-_ + 1/192*atanh(1/2*(-1+4*x^6)^(1/2)/x^3) +--R +--R +--R +-------+ +--R | 6 +-------+ +--R \|4x - 1 9 3 | 6 +--R - atanh(----------) + (16x - 2x )\|4x - 1 +--R 3 +--R 2x +--R (221) -------------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 252 + +--S 253 of 554 +a0250:= integrate(t0250,x) +--R +--R +--R (222) +--R +-------+ +-------+ +--R 9 3 | 6 12 6 | 6 3 +--R ((64x - 8x )\|4x - 1 - 128x + 32x - 1)log(\|4x - 1 - 2x ) +--R + +--R +-------+ +--R 21 15 9 3 | 6 24 18 12 +--R (- 2048x + 768x - 80x + 2x )\|4x - 1 + 4096x - 2048x + 320x +--R + +--R 6 +--R - 16x +--R / +--R +-------+ +--R 9 3 | 6 12 6 +--R (12288x - 1536x )\|4x - 1 - 24576x + 6144x - 192 +--R Type: Union(Expression(Integer),...) +--E 253 + +--S 254 of 554 +m0250:= a0250-r0250 +--R +--R +--R +-------+ +--R +-------+ | 6 +--R | 6 3 \|4x - 1 +--R log(\|4x - 1 - 2x ) + atanh(----------) +--R 3 +--R 2x +--R (223) ----------------------------------------- +--R 192 +--R Type: Expression(Integer) +--E 254 + +--S 255 of 554 +d0250:= D(m0250,x) +--R +--R +--R (224) 0 +--R Type: Expression(Integer) +--E 255 + +--S 256 of 554 +t0251:= x^2*(-2+x^6)^(1/2) +--R +--R +--R +------+ +--R 2 | 6 +--R (225) x \|x - 2 +--R Type: Expression(Integer) +--E 256 + +--S 257 of 554 +r0251:= 1/6*x^3*(-2+x^6)^(1/2)-1/3*atanh((-2+x^6)^(1/2)/x^3) +--R +--R +--R +------+ +--R | 6 +------+ +--R \|x - 2 3 | 6 +--R - 2atanh(---------) + x \|x - 2 +--R 3 +--R x +--R (226) --------------------------------- +--R 6 +--R Type: Expression(Integer) +--E 257 + +--S 258 of 554 +a0251:= integrate(t0251,x) +--R +--R +--R (227) +--R +------+ +------+ +------+ +--R 3 | 6 6 | 6 3 9 3 | 6 12 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 6 +--R - 2x +--R / +--R +------+ +--R 3 | 6 6 +--R 6x \|x - 2 - 6x + 6 +--R Type: Union(Expression(Integer),...) +--E 258 + +--S 259 of 554 +m0251:= a0251-r0251 +--R +--R +--R +------+ +--R +------+ | 6 +--R | 6 3 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 3 +--R x +--R (228) -------------------------------------- +--R 3 +--R Type: Expression(Integer) +--E 259 + +--S 260 of 554 +d0251:= D(m0251,x) +--R +--R +--R (229) 0 +--R Type: Expression(Integer) +--E 260 + +--S 261 of 554 +t0252:= 1/x/(1+x^8)^(1/2) +--R +--R +--R 1 +--R (230) ---------- +--R +------+ +--R | 8 +--R x\|x + 1 +--R Type: Expression(Integer) +--E 261 + +--S 262 of 554 +r0252:= -1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +--R | 8 +--R atanh(\|x + 1 ) +--R (231) - ---------------- +--R 4 +--R Type: Expression(Integer) +--E 262 + +--S 263 of 554 +a0252:= integrate(t0252,x) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) +--R (232) ----------------------------------------- +--R 8 +--R Type: Union(Expression(Integer),...) +--E 263 + +--S 264 of 554 +m0252:= a0252-r0252 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (233) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 264 + +--S 265 of 554 +d0252:= D(m0252,x) +--R +--R +--R (234) 0 +--R Type: Expression(Integer) +--E 265 + +--S 266 of 554 +t0253:= x^3*(-2+x^8)^(1/2) +--R +--R +--R +------+ +--R 3 | 8 +--R (235) x \|x - 2 +--R Type: Expression(Integer) +--E 266 + +--S 267 of 554 +r0253:= 1/8*x^4*(-2+x^8)^(1/2)-1/4*atanh((-2+x^8)^(1/2)/x^4) +--R +--R +--R +------+ +--R | 8 +------+ +--R \|x - 2 4 | 8 +--R - 2atanh(---------) + x \|x - 2 +--R 4 +--R x +--R (236) --------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 267 + +--S 268 of 554 +a0253:= integrate(t0253,x) +--R +--R +--R (237) +--R +------+ +------+ +------+ +--R 4 | 8 8 | 8 4 12 4 | 8 16 +--R (2x \|x - 2 - 2x + 2)log(\|x - 2 - x ) + (- x + x )\|x - 2 + x +--R + +--R 8 +--R - 2x +--R / +--R +------+ +--R 4 | 8 8 +--R 8x \|x - 2 - 8x + 8 +--R Type: Union(Expression(Integer),...) +--E 268 + +--S 269 of 554 +m0253:= a0253-r0253 +--R +--R +--R +------+ +--R +------+ | 8 +--R | 8 4 \|x - 2 +--R log(\|x - 2 - x ) + atanh(---------) +--R 4 +--R x +--R (238) -------------------------------------- +--R 4 +--R Type: Expression(Integer) +--E 269 + +--S 270 of 554 +d0253:= D(m0253,x) +--R +--R +--R (239) 0 +--R Type: Expression(Integer) +--E 270 + +--S 271 of 554 +t0254:= (1+x^8)^(1/2)*(1+2*x^8)/(x+2*x^9+x^17) +--R +--R +--R +------+ +--R 8 | 8 +--R (2x + 1)\|x + 1 +--R (240) ------------------ +--R 17 9 +--R x + 2x + x +--R Type: Expression(Integer) +--E 271 + +--S 272 of 554 +r0254:= -1/4/(1+x^8)^(1/2)-1/4*atanh((1+x^8)^(1/2)) +--R +--R +--R +------+ +------+ +--R | 8 | 8 +--R - \|x + 1 atanh(\|x + 1 ) - 1 +--R (241) ------------------------------- +--R +------+ +--R | 8 +--R 4\|x + 1 +--R Type: Expression(Integer) +--E 272 + +--S 273 of 554 +a0254:= integrate(t0254,x) +--R +--R +--R +------+ +------+ +------+ +------+ +--R | 8 | 8 | 8 | 8 +--R - \|x + 1 log(\|x + 1 + 1) + \|x + 1 log(\|x + 1 - 1) - 2 +--R (242) --------------------------------------------------------------- +--R +------+ +--R | 8 +--R 8\|x + 1 +--R Type: Union(Expression(Integer),...) +--E 273 + +--S 274 of 554 +m0254:= a0254-r0254 +--R +--R +--R +------+ +------+ +------+ +--R | 8 | 8 | 8 +--R - log(\|x + 1 + 1) + log(\|x + 1 - 1) + 2atanh(\|x + 1 ) +--R (243) ------------------------------------------------------------- +--R 8 +--R Type: Expression(Integer) +--E 274 + +--S 275 of 554 +d0254:= D(m0254,x) +--R +--R +--R (244) 0 +--R Type: Expression(Integer) +--E 275 + +--S 276 of 554 +t0255:= x^4/(-2+x^10)^(1/2) +--R +--R +--R 4 +--R x +--R (245) ---------- +--R +-------+ +--R | 10 +--R \|x - 2 +--R Type: Expression(Integer) +--E 276 + +--S 277 of 554 +r0255:= 1/5*atanh((-2+x^10)^(1/2)/x^5) +--R +--R +--R +-------+ +--R | 10 +--R \|x - 2 +--R atanh(----------) +--R 5 +--R x +--R (246) ----------------- +--R 5 +--R Type: Expression(Integer) +--E 277 + +--S 278 of 554 +a0255:= integrate(t0255,x) +--R +--R +--R +-------+ +--R | 10 5 +--R log(\|x - 2 - x ) +--R (247) - -------------------- +--R 5 +--R Type: Union(Expression(Integer),...) +--E 278 + +--S 279 of 554 +m0255:= a0255-r0255 +--R +--R +--R +-------+ +--R +-------+ | 10 +--R | 10 5 \|x - 2 +--R - log(\|x - 2 - x ) - atanh(----------) +--R 5 +--R x +--R (248) ------------------------------------------ +--R 5 +--R Type: Expression(Integer) +--E 279 + +--S 280 of 554 +d0255:= D(m0255,x) +--R +--R +--R (249) 0 +--R Type: Expression(Integer) +--E 280 + +--S 281 of 554 +t0256:= x^31*(1+x^16)^(1/2)/(1-x^16) +--R +--R +--R +-------+ +--R 31 | 16 +--R x \|x + 1 +--R (250) - ------------- +--R 16 +--R x - 1 +--R Type: Expression(Integer) +--E 281 + +--S 282 of 554 +r0256:= -1/8*(1+x^16)^(1/2)-1/24*(1+x^16)^(3/2)+1/8*_ + atanh(1/2*(1+x^16)^(1/2)*2^(1/2))*2^(1/2) +--R +--R +--R +-------+ +--R +-+ | 16 +-------+ +--R +-+ \|2 \|x + 1 16 | 16 +--R 3\|2 atanh(--------------) + (- x - 4)\|x + 1 +--R 2 +--R (251) -------------------------------------------------- +--R 24 +--R Type: Expression(Integer) +--E 282 + +--S 283 of 554 +a0256:= integrate(t0256,x) +--R +--R +--R +-------+ +--R | 16 16 +-+ +-------+ +--R 4\|x + 1 + (x + 3)\|2 16 +-+ | 16 +--R 3log(---------------------------) + (- x - 4)\|2 \|x + 1 +--R 16 +--R x - 1 +--R (252) ------------------------------------------------------------- +--R +-+ +--R 24\|2 +--R Type: Union(Expression(Integer),...) +--E 283 + +--S 284 of 554 +m0256:= a0256-r0256 +--R +--R +--R +-------+ +-------+ +--R | 16 16 +-+ +-+ | 16 +--R 4\|x + 1 + (x + 3)\|2 \|2 \|x + 1 +--R log(---------------------------) - 2atanh(--------------) +--R 16 2 +--R x - 1 +--R (253) --------------------------------------------------------- +--R +-+ +--R 8\|2 +--R Type: Expression(Integer) +--E 284 + +--S 285 of 554 +d0256:= D(m0256,x) +--R +--R +--R (254) 0 +--R Type: Expression(Integer) +--E 285 + +--S 286 of 554 +t0257:= x^3*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 3 |a x + b +--R (255) x |------- +--R \| x +--R Type: Expression(Integer) +--E 286 + +--S 287 of 554 +r0257:= 5/64*b^3*(a+b/x)^(1/2)*x/a^3-5/96*b^2*(a+b/x)^(1/2)*x^2/a^2+_ + 1/24*b*(a+b/x)^(1/2)*x^3/a+1/4*(a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (256) +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 4 \| x 3 4 2 3 2 2 3 +-+ |a x + b +--R - 15b atanh(----------) + (48a x + 8a b x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------------- +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 287 + +--S 288 of 554 +a0257:= integrate(t0257,x) +--R +--R +--R (257) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x + 16a b x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x + 8a b x - 10a b x + 15b x)\|- a |------- +--R \| x +--R / +--R 3 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 288 + +--S 289 of 554 +m0257a:= a0257.1-r0257 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (258) ----------------------------------------------------------------- +--R 3 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 289 + +--S 290 of 554 +d0257a:= D(m0257a,x) +--R +--R +--R (259) 0 +--R Type: Expression(Integer) +--E 290 + +--S 291 of 554 +m0257b:= a0257.2-r0257 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (260) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 291 + +--S 292 of 554 +d0257b:= D(m0257b,x) +--R +--R +--R (261) 0 +--R Type: Expression(Integer) +--E 292 + +--S 293 of 554 +t0258:= x^2*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R 2 |a x + b +--R (262) x |------- +--R \| x +--R Type: Expression(Integer) +--E 293 + +--S 294 of 554 +r0258:= -1/8*b^2*(a+b/x)^(1/2)*x/a^2+1/12*b*(a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(a+b/x)^(1/2)+1/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R 3b atanh(----------) + (8a x + 2a b x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (263) ------------------------------------------------------------- +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 294 + +--S 295 of 554 +a0258:= integrate(t0258,x) +--R +--R +--R (264) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 3b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x + 4a b x - 6b x)\|a |------- +--R \| x +--R / +--R 2 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R 3b atan(----------------) + (8a x + 2a b x - 3b x)\|- a |------- +--R a \| x +--R --------------------------------------------------------------------] +--R 2 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 295 + +--S 296 of 554 +m0258a:= a0258.1-r0258 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (265) ------------------------------------------------------------- +--R 2 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 296 + +--S 297 of 554 +d0258a:= D(m0258a,x) +--R +--R +--R (266) 0 +--R Type: Expression(Integer) +--E 297 + +--S 298 of 554 +m0258b:= a0258.2-r0258 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R - b \|- a atanh(----------) + b \|a atan(----------------) +--R +-+ a +--R \|a +--R (267) ---------------------------------------------------------- +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 298 + +--S 299 of 554 +d0258b:= D(m0258b,x) +--R +--R +--R (268) 0 +--R Type: Expression(Integer) +--E 299 + +--S 300 of 554 +t0259:= x*(a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (269) x |------- +--R \| x +--R Type: Expression(Integer) +--E 300 + +--S 301 of 554 +r0259:= 1/4*b*(a+b/x)^(1/2)*x/a+1/2*x^2*(a+b/x)^(1/2)-_ + 1/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R - b atanh(----------) + (2a x + b x)\|a |------- +--R +-+ \| x +--R \|a +--R (270) --------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 301 + +--S 302 of 554 +a0259:= integrate(t0259,x) +--R +--R +--R (271) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + (4a x + 2b x)\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------------------, +--R +-+ +--R 8a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R - b atan(----------------) + (2a x + b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R +---+ +--R 4a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 302 + +--S 303 of 554 +m0259a:= a0259.1-r0259 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (272) --------------------------------------------------------------- +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 303 + +--S 304 of 554 +d0259a:= D(m0259a,x) +--R +--R +--R (273) 0 +--R Type: Expression(Integer) +--E 304 + +--S 305 of 554 +m0259b:= a0259.2-r0259 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R b \|- a atanh(----------) - b \|a atan(----------------) +--R +-+ a +--R \|a +--R (274) -------------------------------------------------------- +--R +---+ +-+ +--R 4a\|- a \|a +--R Type: Expression(Integer) +--E 305 + +--S 306 of 554 +d0259b:= D(m0259b,x) +--R +--R +--R (275) 0 +--R Type: Expression(Integer) +--E 306 + +--S 307 of 554 +t0260:= (a+b/x)^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R (276) |------- +--R \| x +--R Type: Expression(Integer) +--E 307 + +--S 308 of 554 +r0260:= x*(a+b/x)^(1/2)+b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (277) ------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 308 + +--S 309 of 554 +a0260:= integrate(t0260,x) +--R +--R +--R (278) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [---------------------------------------------------------, +--R +-+ +--R 2\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R b atan(----------------) + x\|- a |------- +--R a \| x +--R --------------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 309 + +--S 310 of 554 +m0260a:= a0260.1-r0260 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(2a x |------- + (2a x + b)\|a ) - 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (279) ------------------------------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 310 + +--S 311 of 554 +d0260a:= D(m0260a,x) +--R +--R +--R (280) 0 +--R Type: Expression(Integer) +--E 311 + +--S 312 of 554 +m0260b:= a0260.2-r0260 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - b\|- a atanh(----------) + b\|a atan(----------------) +--R +-+ a +--R \|a +--R (281) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 312 + +--S 313 of 554 +d0260b:= D(m0260b,x) +--R +--R +--R (282) 0 +--R Type: Expression(Integer) +--E 313 + +--S 314 of 554 +t0261:= (a+b/x)^(1/2)/x +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R (283) ---------- +--R x +--R Type: Expression(Integer) +--E 314 + +--S 315 of 554 +r0261:= -2*(a+b/x)^(1/2)+2*a^(1/2)*atanh((a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +-+ \| x |a x + b +--R (284) 2\|a atanh(----------) - 2 |------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 315 + +--S 316 of 554 +a0261:= integrate(t0261,x) +--R +--R +--R (285) +--R +-------+ +-------+ +--R +-+ +-+ |a x + b |a x + b +--R [\|a log(2x\|a |------- + 2a x + b) - 2 |-------, +--R \| x \| x +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R +---+ \| x |a x + b +--R 2\|- a atan(----------) - 2 |-------] +--R +---+ \| x +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 316 + +--S 317 of 554 +m0261a:= a0261.1-r0261 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R +-+ +-+ |a x + b +-+ \| x +--R (286) \|a log(2x\|a |------- + 2a x + b) - 2\|a atanh(----------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 317 + +--S 318 of 554 +d0261a:= D(m0261a,x) +--R +--R +--R (287) 0 +--R Type: Expression(Integer) +--E 318 + +--S 319 of 554 +m0261b:= a0261.2-r0261 +--R +--R +--R +-------+ +-------+ +--R |a x + b |a x + b +--R |------- |------- +--R +-+ \| x +---+ \| x +--R (288) - 2\|a atanh(----------) + 2\|- a atan(----------) +--R +-+ +---+ +--R \|a \|- a +--R Type: Expression(Integer) +--E 319 + +--S 320 of 554 +d0261b:= D(m0261b,x) +--R +--R +--R (289) 0 +--R Type: Expression(Integer) +--E 320 + +--S 321 of 554 +t0262:= x^3*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 3 |- a x + b +--R (290) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 321 + +--S 322 of 554 +r0262:= -5/64*b^3*(-a+b/x)^(1/2)*x/a^3-5/96*b^2*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/24*b*(-a+b/x)^(1/2)*x^3/a+1/4*(-a+b/x)^(1/2)*x^4-_ + 5/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (291) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 15b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 322 + +--S 323 of 554 +a0262:= integrate(t0262,x) +--R +--R +--R (292) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (96a x - 16a b x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 15b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (48a x - 8a b x - 10a b x - 15b x) |--------- \|a +--R \| x +--R / +--R 3 +-+ +--R 192a \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 323 + +--S 324 of 554 +m0262a:= a0262.1-r0262 +--R +--R +--R (293) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression(Integer) +--E 324 + +--S 325 of 554 +d0262a:= D(m0262a,x) +--R +--R +--R (294) 0 +--R Type: Expression(Integer) +--E 325 + +--S 326 of 554 +m0262b:= a0262.2-r0262 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (295) --------------------------------------------------- +--R 3 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 326 + +--S 327 of 554 +d0262b:= D(m0262b,x) +--R +--R +--R (296) 0 +--R Type: Expression(Integer) +--E 327 + +--S 328 of 554 +t0263:= x^2*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R 2 |- a x + b +--R (297) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 328 + +--S 329 of 554 +r0263:= -1/8*b^2*(-a+b/x)^(1/2)*x/a^2-1/12*b*(-a+b/x)^(1/2)*x^2/a+_ + 1/3*x^3*(-a+b/x)^(1/2)-1/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (298) ------------------------------------------------------------------ +--R 2 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 329 + +--S 330 of 554 +a0263:= integrate(t0263,x) +--R +--R +--R (299) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (16a x - 4a b x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 3b atan(----------------) + (8a x - 2a b x - 3b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------------------] +--R 2 +-+ +--R 24a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 330 + +--S 331 of 554 +m0263a:= a0263.1-r0263 +--R +--R +--R (300) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression(Integer) +--E 331 + +--S 332 of 554 +d0263a:= D(m0263a,x) +--R +--R +--R (301) 0 +--R Type: Expression(Integer) +--E 332 + +--S 333 of 554 +m0263b:= a0263.2-r0263 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (302) ------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 333 + +--S 334 of 554 +d0263b:= D(m0263b,x) +--R +--R +--R (303) 0 +--R Type: Expression(Integer) +--E 334 + +--S 335 of 554 +t0264:= x*(-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (304) x |--------- +--R \| x +--R Type: Expression(Integer) +--E 335 + +--S 336 of 554 +r0264:= -1/4*b*(-a+b/x)^(1/2)*x/a+1/2*x^2*(-a+b/x)^(1/2)-_ + 1/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(------------) + (2a x - b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (305) ------------------------------------------------------ +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 336 + +--S 337 of 554 +a0264:= integrate(t0264,x) +--R +--R +--R (306) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (4a x - 2b x)\|- a |--------- +--R \| x +--R / +--R +---+ +--R 8a\|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - b atan(----------------) + (2a x - b x) |--------- \|a +--R a \| x +--R ----------------------------------------------------------] +--R +-+ +--R 4a\|a +--R Type: Union(List(Expression(Integer)),...) +--E 337 + +--S 338 of 554 +m0264a:= a0264.1-r0264 +--R +--R +--R (307) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 2b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 8a\|- a \|a +--R Type: Expression(Integer) +--E 338 + +--S 339 of 554 +d0264a:= D(m0264a,x) +--R +--R +--R (308) 0 +--R Type: Expression(Integer) +--E 339 + +--S 340 of 554 +m0264b:= a0264.2-r0264 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (309) ------------------------------------------------- +--R +-+ +--R 4a\|a +--R Type: Expression(Integer) +--E 340 + +--S 341 of 554 +d0264b:= D(m0264b,x) +--R +--R +--R (310) 0 +--R Type: Expression(Integer) +--E 341 + +--S 342 of 554 +t0265:= (-a+b/x)^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R (311) |--------- +--R \| x +--R Type: Expression(Integer) +--E 342 + +--S 343 of 554 +r0265:= x*(-a+b/x)^(1/2)-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) + x |--------- \|a +--R +-+ \| x +--R \|a +--R (312) ------------------------------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 343 + +--S 344 of 554 +a0265:= integrate(t0265,x) +--R +--R +--R (313) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) + x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 344 + +--S 345 of 554 +m0265a:= a0265.1-r0265 +--R +--R +--R (314) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2\|- a \|a +--R Type: Expression(Integer) +--E 345 + +--S 346 of 554 +d0265a:= D(m0265a,x) +--R +--R +--R (315) 0 +--R Type: Expression(Integer) +--E 346 + +--S 347 of 554 +m0265b:= a0265.2-r0265 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (316) ------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 347 + +--S 348 of 554 +d0265b:= D(m0265b,x) +--R +--R +--R (317) 0 +--R Type: Expression(Integer) +--E 348 + +--S 349 of 554 +t0266:= (-a+b/x)^(1/2)/x +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R (318) ------------ +--R x +--R Type: Expression(Integer) +--E 349 + +--S 350 of 554 +r0266:= -2*(-a+b/x)^(1/2)+2*a^(1/2)*atan((-a+b/x)^(1/2)/a^(1/2)) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R +-+ \| x |- a x + b +--R (319) 2\|a atan(------------) - 2 |--------- +--R +-+ \| x +--R \|a +--R Type: Expression(Integer) +--E 350 + +--S 351 of 554 +a0266:= integrate(t0266,x) +--R +--R +--R (320) +--R +---------+ +---------+ +--R +---+ +---+ |- a x + b |- a x + b +--R [\|- a log(2x\|- a |--------- - 2a x + b) - 2 |---------, +--R \| x \| x +--R +-+ +---------+ +--R +-+ \|a |- a x + b +--R - 2\|a atan(------------) - 2 |---------] +--R +---------+ \| x +--R |- a x + b +--R |--------- +--R \| x +--R Type: Union(List(Expression(Integer)),...) +--E 351 + +--S 352 of 554 +m0266a:= a0266.1-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +---+ +---+ |- a x + b +-+ \| x +--R (321) \|- a log(2x\|- a |--------- - 2a x + b) - 2\|a atan(------------) +--R \| x +-+ +--R \|a +--R Type: Expression(Integer) +--E 352 + +--S 353 of 554 +d0266a:= D(m0266a,x) +--R +--R +--R (322) 0 +--R Type: Expression(Integer) +--E 353 + +--S 354 of 554 +m0266b:= a0266.2-r0266 +--R +--R +--R +---------+ +--R |- a x + b +--R +-+ |--------- +--R +-+ \|a +-+ \| x +--R (323) - 2\|a atan(------------) - 2\|a atan(------------) +--R +---------+ +-+ +--R |- a x + b \|a +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 354 + +--S 355 of 554 +d0266b:= D(m0266b,x) +--R +--R +--R (324) 0 +--R Type: Expression(Integer) +--E 355 + +--S 356 of 554 +t0267:= x^3/(a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (325) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 356 + +--S 357 of 554 +r0267:= -35/64*b^3*(a+b/x)^(1/2)*x/a^4+35/96*b^2*(a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(a+b/x)^(1/2)*x^3/a^2+1/4*(a+b/x)^(1/2)*x^4/a+_ + 35/64*b^4*atanh((a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (326) +--R +-------+ +--R |a x + b +--R |------- +--R 4 \| x +--R 105b atanh(----------) +--R +-+ +--R \|a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 357 + +--S 358 of 554 +a0267:= integrate(t0267,x) +--R +--R +--R (327) +--R [ +--R +-------+ +--R 4 |a x + b +-+ +--R 105b log(2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +-+ |a x + b +--R (96a x - 112a b x + 140a b x - 210b x)\|a |------- +--R \| x +--R / +--R 4 +-+ +--R 384a \|a +--R , +--R +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +--R 4 \| x +--R 105b atan(----------------) +--R a +--R + +--R +-------+ +--R 3 4 2 3 2 2 3 +---+ |a x + b +--R (48a x - 56a b x + 70a b x - 105b x)\|- a |------- +--R \| x +--R / +--R 4 +---+ +--R 192a \|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 358 + +--S 359 of 554 +m0267a:= a0267.1-r0267 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 4 |a x + b +-+ 4 \| x +--R 35b log(2a x |------- + (2a x + b)\|a ) - 70b atanh(----------) +--R \| x +-+ +--R \|a +--R (328) ---------------------------------------------------------------- +--R 4 +-+ +--R 128a \|a +--R Type: Expression(Integer) +--E 359 + +--S 360 of 554 +d0267a:= D(m0267a,x) +--R +--R +--R (329) 0 +--R Type: Expression(Integer) +--E 360 + +--S 361 of 554 +m0267b:= a0267.2-r0267 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 4 +---+ \| x 4 +-+ \| x +--R - 35b \|- a atanh(----------) + 35b \|a atan(----------------) +--R +-+ a +--R \|a +--R (330) -------------------------------------------------------------- +--R 4 +---+ +-+ +--R 64a \|- a \|a +--R Type: Expression(Integer) +--E 361 + +--S 362 of 554 +d0267b:= D(m0267b,x) +--R +--R +--R (331) 0 +--R Type: Expression(Integer) +--E 362 + +--S 363 of 554 +t0268:= x^2/(a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (332) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 363 + +--S 364 of 554 +r0268:= 5/8*b^2*(a+b/x)^(1/2)*x/a^3-5/12*b*(a+b/x)^(1/2)*x^2/a^2+_ + 1/3*(a+b/x)^(1/2)*x^3/a-5/8*b^3*atanh((a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 3 \| x 2 3 2 2 +-+ |a x + b +--R - 15b atanh(----------) + (8a x - 10a b x + 15b x)\|a |------- +--R +-+ \| x +--R \|a +--R (333) ------------------------------------------------------------------ +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 364 + +--S 365 of 554 +a0268:= integrate(t0268,x) +--R +--R +--R (334) +--R [ +--R +-------+ +--R 3 |a x + b +-+ +--R 15b log(- 2a x |------- + (2a x + b)\|a ) +--R \| x +--R + +--R +-------+ +--R 2 3 2 2 +-+ |a x + b +--R (16a x - 20a b x + 30b x)\|a |------- +--R \| x +--R / +--R 3 +-+ +--R 48a \|a +--R , +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 3 \| x 2 3 2 2 +---+ |a x + b +--R - 15b atan(----------------) + (8a x - 10a b x + 15b x)\|- a |------- +--R a \| x +--R -------------------------------------------------------------------------] +--R 3 +---+ +--R 24a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 365 + +--S 366 of 554 +m0268a:= a0268.1-r0268 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 3 |a x + b +-+ 3 \| x +--R 5b log(- 2a x |------- + (2a x + b)\|a ) + 10b atanh(----------) +--R \| x +-+ +--R \|a +--R (335) ----------------------------------------------------------------- +--R 3 +-+ +--R 16a \|a +--R Type: Expression(Integer) +--E 366 + +--S 367 of 554 +d0268a:= D(m0268a,x) +--R +--R +--R (336) 0 +--R Type: Expression(Integer) +--E 367 + +--S 368 of 554 +m0268b:= a0268.2-r0268 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 3 +---+ \| x 3 +-+ \| x +--R 5b \|- a atanh(----------) - 5b \|a atan(----------------) +--R +-+ a +--R \|a +--R (337) ---------------------------------------------------------- +--R 3 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 368 + +--S 369 of 554 +d0268b:= D(m0268b,x) +--R +--R +--R (338) 0 +--R Type: Expression(Integer) +--E 369 + +--S 370 of 554 +t0269:= x/(a+b/x)^(1/2) +--R +--R +--R x +--R (339) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 370 + +--S 371 of 554 +r0269:= -3/4*b*(a+b/x)^(1/2)*x/a^2+1/2*(a+b/x)^(1/2)*x^2/a+_ + 3/4*b^2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R 2 \| x 2 +-+ |a x + b +--R 3b atanh(----------) + (2a x - 3b x)\|a |------- +--R +-+ \| x +--R \|a +--R (340) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 371 + +--S 372 of 554 +a0269:= integrate(t0269,x) +--R +--R +--R (341) +--R +-------+ +-------+ +--R 2 |a x + b +-+ 2 +-+ |a x + b +--R 3b log(2a x |------- + (2a x + b)\|a ) + (4a x - 6b x)\|a |------- +--R \| x \| x +--R [----------------------------------------------------------------------, +--R 2 +-+ +--R 8a \|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R 2 \| x 2 +---+ |a x + b +--R 3b atan(----------------) + (2a x - 3b x)\|- a |------- +--R a \| x +--R ----------------------------------------------------------] +--R 2 +---+ +--R 4a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 372 + +--S 373 of 554 +m0269a:= a0269.1-r0269 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R 2 |a x + b +-+ 2 \| x +--R 3b log(2a x |------- + (2a x + b)\|a ) - 6b atanh(----------) +--R \| x +-+ +--R \|a +--R (342) -------------------------------------------------------------- +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 373 + +--S 374 of 554 +d0269a:= D(m0269a,x) +--R +--R +--R (343) 0 +--R Type: Expression(Integer) +--E 374 + +--S 375 of 554 +m0269b:= a0269.2-r0269 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R 2 +---+ \| x 2 +-+ \| x +--R - 3b \|- a atanh(----------) + 3b \|a atan(----------------) +--R +-+ a +--R \|a +--R (344) ------------------------------------------------------------ +--R 2 +---+ +-+ +--R 4a \|- a \|a +--R Type: Expression(Integer) +--E 375 + +--S 376 of 554 +d0269b:= D(m0269b,x) +--R +--R +--R (345) 0 +--R Type: Expression(Integer) +--E 376 + +--S 377 of 554 +t0270:= 1/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (346) ---------- +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R Type: Expression(Integer) +--E 377 + +--S 378 of 554 +r0270:= (a+b/x)^(1/2)*x/a-b*atanh((a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +-------+ +--R \| x +-+ |a x + b +--R - b atanh(----------) + x\|a |------- +--R +-+ \| x +--R \|a +--R (347) --------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 378 + +--S 379 of 554 +a0270:= integrate(t0270,x) +--R +--R +--R (348) +--R +-------+ +-------+ +--R |a x + b +-+ +-+ |a x + b +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2x\|a |------- +--R \| x \| x +--R [-----------------------------------------------------------, +--R +-+ +--R 2a\|a +--R +-------+ +--R +---+ |a x + b +--R \|- a |------- +-------+ +--R \| x +---+ |a x + b +--R - b atan(----------------) + x\|- a |------- +--R a \| x +--R ----------------------------------------------] +--R +---+ +--R a\|- a +--R Type: Union(List(Expression(Integer)),...) +--E 379 + +--S 380 of 554 +m0270a:= a0270.1-r0270 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R b log(- 2a x |------- + (2a x + b)\|a ) + 2b atanh(----------) +--R \| x +-+ +--R \|a +--R (349) --------------------------------------------------------------- +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 380 + +--S 381 of 554 +d0270a:= D(m0270a,x) +--R +--R +--R (350) 0 +--R Type: Expression(Integer) +--E 381 + +--S 382 of 554 +m0270b:= a0270.2-r0270 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R b\|- a atanh(----------) - b\|a atan(----------------) +--R +-+ a +--R \|a +--R (351) ------------------------------------------------------ +--R +---+ +-+ +--R a\|- a \|a +--R Type: Expression(Integer) +--E 382 + +--S 383 of 554 +d0270b:= D(m0270b,x) +--R +--R +--R (352) 0 +--R Type: Expression(Integer) +--E 383 + +--S 384 of 554 +t0271:= 1/x/(a+b/x)^(1/2) +--R +--R +--R 1 +--R (353) ----------- +--R +-------+ +--R |a x + b +--R x |------- +--R \| x +--R Type: Expression(Integer) +--E 384 + +--S 385 of 554 +r0271:= 2*atanh((a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +-------+ +--R |a x + b +--R |------- +--R \| x +--R 2atanh(----------) +--R +-+ +--R \|a +--R (354) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 385 + +--S 386 of 554 +a0271:= integrate(t0271,x) +--R +--R +--R +-------+ +--R +---+ |a x + b +--R +-------+ \|- a |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) 2atan(----------------) +--R \| x a +--R (355) [------------------------------------,-----------------------] +--R +-+ +---+ +--R \|a \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 386 + +--S 387 of 554 +m0271a:= a0271.1-r0271 +--R +--R +--R +-------+ +--R |a x + b +--R +-------+ |------- +--R |a x + b +-+ \| x +--R log(2a x |------- + (2a x + b)\|a ) - 2atanh(----------) +--R \| x +-+ +--R \|a +--R (356) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 387 + +--S 388 of 554 +d0271a:= D(m0271a,x) +--R +--R +--R (357) 0 +--R Type: Expression(Integer) +--E 388 + +--S 389 of 554 +m0271b:= a0271.2-r0271 +--R +--R +--R +-------+ +-------+ +--R |a x + b +---+ |a x + b +--R |------- \|- a |------- +--R +---+ \| x +-+ \| x +--R - 2\|- a atanh(----------) + 2\|a atan(----------------) +--R +-+ a +--R \|a +--R (358) -------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 389 + +--S 390 of 554 +d0271b:= D(m0271b,x) +--R +--R +--R (359) 0 +--R Type: Expression(Integer) +--E 390 + +--S 391 of 554 +t0272:= x^3/(-a+b/x)^(1/2) +--R +--R +--R 3 +--R x +--R (360) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 391 + +--S 392 of 554 +r0272:= -35/64*b^3*(-a+b/x)^(1/2)*x/a^4-35/96*b^2*(-a+b/x)^(1/2)*x^2/a^3-_ + 7/24*b*(-a+b/x)^(1/2)*x^3/a^2-1/4*(-a+b/x)^(1/2)*x^4/a-_ + 35/64*b^4*atan((-a+b/x)^(1/2)/a^(1/2))/a^(9/2) +--R +--R +--R (361) +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 \| x +--R - 105b atan(------------) +--R +-+ +--R \|a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R Type: Expression(Integer) +--E 392 + +--S 393 of 554 +a0272:= integrate(t0272,x) +--R +--R +--R (362) +--R [ +--R +---------+ +--R 4 |- a x + b +---+ +--R 105b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 +---+ |- a x + b +--R (- 96a x - 112a b x - 140a b x - 210b x)\|- a |--------- +--R \| x +--R / +--R 4 +---+ +--R 384a \|- a +--R , +--R +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +--R 4 \| x +--R - 105b atan(----------------) +--R a +--R + +--R +---------+ +--R 3 4 2 3 2 2 3 |- a x + b +-+ +--R (- 48a x - 56a b x - 70a b x - 105b x) |--------- \|a +--R \| x +--R / +--R 4 +-+ +--R 192a \|a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 393 + +--S 394 of 554 +m0272a:= a0272.1-r0272 +--R +--R +--R (363) +--R +---------+ +--R 4 +-+ |- a x + b +---+ +--R 35b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 4 +---+ \| x +--R 70b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 4 +---+ +-+ +--R 128a \|- a \|a +--R Type: Expression(Integer) +--E 394 + +--S 395 of 554 +d0272a:= D(m0272a,x) +--R +--R +--R (364) 0 +--R Type: Expression(Integer) +--E 395 + +--S 396 of 554 +m0272b:= a0272.2-r0272 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 4 \| x 4 \| x +--R - 35b atan(----------------) + 35b atan(------------) +--R a +-+ +--R \|a +--R (365) ----------------------------------------------------- +--R 4 +-+ +--R 64a \|a +--R Type: Expression(Integer) +--E 396 + +--S 397 of 554 +d0272b:= D(m0272b,x) +--R +--R +--R (366) 0 +--R Type: Expression(Integer) +--E 397 + +--S 398 of 554 +t0273:= x^2/(-a+b/x)^(1/2) +--R +--R +--R 2 +--R x +--R (367) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 398 + +--S 399 of 554 +r0273:= -5/8*b^2*(-a+b/x)^(1/2)*x/a^3-5/12*b*(-a+b/x)^(1/2)*x^2/a^2-_ + 1/3*(-a+b/x)^(1/2)*x^3/a-5/8*b^3*atan((-a+b/x)^(1/2)/a^(1/2))/a^(7/2) +--R +--R +--R (368) +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R +-+ \| x +--R \|a +--R ----------------------------------------------------------------------- +--R 3 +-+ +--R 24a \|a +--R Type: Expression(Integer) +--E 399 + +--S 400 of 554 +a0273:= integrate(t0273,x) +--R +--R +--R (369) +--R [ +--R +---------+ +--R 3 |- a x + b +---+ +--R 15b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 3 2 2 +---+ |- a x + b +--R (- 16a x - 20a b x - 30b x)\|- a |--------- +--R \| x +--R / +--R 3 +---+ +--R 48a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 3 \| x 2 3 2 2 |- a x + b +-+ +--R - 15b atan(----------------) + (- 8a x - 10a b x - 15b x) |--------- \|a +--R a \| x +--R ---------------------------------------------------------------------------] +--R 3 +-+ +--R 24a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 400 + +--S 401 of 554 +m0273a:= a0273.1-r0273 +--R +--R +--R (370) +--R +---------+ +--R 3 +-+ |- a x + b +---+ +--R 5b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 3 +---+ \| x +--R 10b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 3 +---+ +-+ +--R 16a \|- a \|a +--R Type: Expression(Integer) +--E 401 + +--S 402 of 554 +d0273a:= D(m0273a,x) +--R +--R +--R (371) 0 +--R Type: Expression(Integer) +--E 402 + +--S 403 of 554 +m0273b:= a0273.2-r0273 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 3 \| x 3 \| x +--R - 5b atan(----------------) + 5b atan(------------) +--R a +-+ +--R \|a +--R (372) --------------------------------------------------- +--R 3 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 403 + +--S 404 of 554 +d0273b:= D(m0273b,x) +--R +--R +--R (373) 0 +--R Type: Expression(Integer) +--E 404 + +--S 405 of 554 +t0274:= x/(-a+b/x)^(1/2) +--R +--R +--R x +--R (374) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 405 + +--S 406 of 554 +r0274:= -3/4*b*(-a+b/x)^(1/2)*x/a^2-1/2*(-a+b/x)^(1/2)*x^2/a-_ + 3/4*b^2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(------------) + (- 2a x - 3b x) |--------- \|a +--R +-+ \| x +--R \|a +--R (375) ---------------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 406 + +--S 407 of 554 +a0274:= integrate(t0274,x) +--R +--R +--R (376) +--R [ +--R +---------+ +--R 2 |- a x + b +---+ +--R 3b log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R 2 +---+ |- a x + b +--R (- 4a x - 6b x)\|- a |--------- +--R \| x +--R / +--R 2 +---+ +--R 8a \|- a +--R , +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R 2 \| x 2 |- a x + b +-+ +--R - 3b atan(----------------) + (- 2a x - 3b x) |--------- \|a +--R a \| x +--R --------------------------------------------------------------] +--R 2 +-+ +--R 4a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 407 + +--S 408 of 554 +m0274a:= a0274.1-r0274 +--R +--R +--R (377) +--R +---------+ +--R 2 +-+ |- a x + b +---+ +--R 3b \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R 2 +---+ \| x +--R 6b \|- a atan(------------) +--R +-+ +--R \|a +--R / +--R 2 +---+ +-+ +--R 8a \|- a \|a +--R Type: Expression(Integer) +--E 408 + +--S 409 of 554 +d0274a:= D(m0274a,x) +--R +--R +--R (378) 0 +--R Type: Expression(Integer) +--E 409 + +--S 410 of 554 +m0274b:= a0274.2-r0274 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R 2 \| x 2 \| x +--R - 3b atan(----------------) + 3b atan(------------) +--R a +-+ +--R \|a +--R (379) --------------------------------------------------- +--R 2 +-+ +--R 4a \|a +--R Type: Expression(Integer) +--E 410 + +--S 411 of 554 +d0274b:= D(m0274b,x) +--R +--R +--R (380) 0 +--R Type: Expression(Integer) +--E 411 + +--S 412 of 554 +t0275:= 1/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (381) ------------ +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R Type: Expression(Integer) +--E 412 + +--S 413 of 554 +r0275:= -(-a+b/x)^(1/2)*x/a-b*atan((-a+b/x)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +---------+ +--R \| x |- a x + b +-+ +--R - b atan(------------) - x |--------- \|a +--R +-+ \| x +--R \|a +--R (382) ------------------------------------------ +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 413 + +--S 414 of 554 +a0275:= integrate(t0275,x) +--R +--R +--R (383) +--R +---------+ +---------+ +--R |- a x + b +---+ +---+ |- a x + b +--R b log(- 2a x |--------- + (- 2a x + b)\|- a ) - 2x\|- a |--------- +--R \| x \| x +--R [---------------------------------------------------------------------, +--R +---+ +--R 2a\|- a +--R +---------+ +--R |- a x + b +-+ +--R |--------- \|a +---------+ +--R \| x |- a x + b +-+ +--R - b atan(----------------) - x |--------- \|a +--R a \| x +--R ----------------------------------------------] +--R +-+ +--R a\|a +--R Type: Union(List(Expression(Integer)),...) +--E 414 + +--S 415 of 554 +m0275a:= a0275.1-r0275 +--R +--R +--R (384) +--R +---------+ +--R +-+ |- a x + b +---+ +--R b\|a log(- 2a x |--------- + (- 2a x + b)\|- a ) +--R \| x +--R + +--R +---------+ +--R |- a x + b +--R |--------- +--R +---+ \| x +--R 2b\|- a atan(------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R 2a\|- a \|a +--R Type: Expression(Integer) +--E 415 + +--S 416 of 554 +d0275a:= D(m0275a,x) +--R +--R +--R (385) 0 +--R Type: Expression(Integer) +--E 416 + +--S 417 of 554 +m0275b:= a0275.2-r0275 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - b atan(----------------) + b atan(------------) +--R a +-+ +--R \|a +--R (386) ------------------------------------------------- +--R +-+ +--R a\|a +--R Type: Expression(Integer) +--E 417 + +--S 418 of 554 +d0275b:= D(m0275b,x) +--R +--R +--R (387) 0 +--R Type: Expression(Integer) +--E 418 + +--S 419 of 554 +t0276:= 1/x/(-a+b/x)^(1/2) +--R +--R +--R 1 +--R (388) ------------- +--R +---------+ +--R |- a x + b +--R x |--------- +--R \| x +--R Type: Expression(Integer) +--E 419 + +--S 420 of 554 +r0276:= -2*atan((-a+b/x)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +---------+ +--R |- a x + b +--R |--------- +--R \| x +--R 2atan(------------) +--R +-+ +--R \|a +--R (389) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 420 + +--S 421 of 554 +a0276:= integrate(t0276,x) +--R +--R +--R (390) +--R +---------+ +--R |- a x + b +-+ +--R +---------+ |--------- \|a +--R |- a x + b +---+ \| x +--R log(- 2a x |--------- + (- 2a x + b)\|- a ) 2atan(----------------) +--R \| x a +--R [--------------------------------------------,- -----------------------] +--R +---+ +-+ +--R \|- a \|a +--R Type: Union(List(Expression(Integer)),...) +--E 421 + +--S 422 of 554 +m0276a:= a0276.1-r0276 +--R +--R +--R (391) +--R +---------+ +--R |- a x + b +--R +---------+ |--------- +--R +-+ |- a x + b +---+ +---+ \| x +--R \|a log(- 2a x |--------- + (- 2a x + b)\|- a ) + 2\|- a atan(------------) +--R \| x +-+ +--R \|a +--R ---------------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 422 + +--S 423 of 554 +d0276a:= D(m0276a,x) +--R +--R +--R (392) 0 +--R Type: Expression(Integer) +--E 423 + +--S 424 of 554 +m0276b:= a0276.2-r0276 +--R +--R +--R +---------+ +---------+ +--R |- a x + b +-+ |- a x + b +--R |--------- \|a |--------- +--R \| x \| x +--R - 2atan(----------------) + 2atan(------------) +--R a +-+ +--R \|a +--R (393) ----------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 424 + +--S 425 of 554 +d0276b:= D(m0276b,x) +--R +--R +--R (394) 0 +--R Type: Expression(Integer) +--E 425 + +--S 426 of 554 +t0277:= x^3/(a+b/x^2)^(1/2) +--R +--R +--R 3 +--R x +--R (395) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 426 + +--S 427 of 554 +r0277:= -3/8*b*(a+b/x^2)^(1/2)*x^2/a^2+1/4*(a+b/x^2)^(1/2)*x^4/a+_ + 3/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(5/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R 3b atanh(-----------) + (2a x - 3b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (396) ------------------------------------------------------ +--R 2 +-+ +--R 8a \|a +--R Type: Expression(Integer) +--E 427 + +--S 428 of 554 +a0277:= integrate(t0277,x) +--R +--R +--R (397) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((24a b x + 48b )\|b \|a x + b - 6a b x - 48a b x - 48b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|b +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 428 + +--S 429 of 554 +m0277a:= a0277.1-r0277 +--R +--R +--R (398) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((12a b x + 24b )\|b \|a x + b - 3a b x - 24a b x - 24b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 12a b x - 24b )\|b \|a x + b + 3a b x + 24a b x + 24b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +-+ +-+ | 2 4 4 3 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 429 + +--S 430 of 554 +d0277a:= D(m0277a,x) +--R +--R +--R (399) +--R 5 14 4 12 3 2 10 2 3 8 4 6 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 4 +--R 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 6 14 5 12 4 2 10 3 3 8 2 4 6 +--R - 11a x - 220a b x - 1232a b x - 2816a b x - 2816a b x +--R + +--R 5 4 +--R - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - a x - 60a b x - 560a b x - 1792a b x - 2304a b x +--R + +--R 5 5 +--R - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 5 6 3 +--R 3328a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 6 15 5 13 4 2 11 3 3 9 2 4 7 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 5 6 3 +--R - 3840a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 6 16 5 14 4 2 12 3 3 10 2 4 8 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 6 6 4 +--R - 3328a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 2 5 6 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x + 3328a b x +--R + +--R 6 4 +--R 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 5 2 6 +--R - 3328a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 5 2 6 +--R 3840a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 430 + +--S 431 of 554 +m0277b:= a0277.2-r0277 +--R +--R +--R (400) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (- 12a b x - 24b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (3a b x + 24a b x + 24b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (24a b x + 48b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (- 6a b x - 48a b x - 48b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 4a b x + 24b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 13a b x + 8a b x + 24b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 12a b x - 20a b x - 24b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 13a b x - 8a b x - 24b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 3 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 4 4 3 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 431 + +--S 432 of 554 +d0277b:= D(m0277b,x) +--R +--R +--R (401) +--R +--------+ +--R | 2 +--R 3 10 2 8 2 6 3 4 |a x + b +-+ 4 11 +--R (- 8a x - 80a b x - 192a b x - 128b x ) |-------- \|b - a x +--R | 2 +--R \| x +--R + +--R 3 9 2 2 7 3 5 4 3 +--R - 32a b x - 160a b x - 256a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 4 11 3 9 2 2 7 3 5 4 3 +-+ +--R (8a x + 88a b x + 272a b x + 320a b x + 128b x )\|b +--R + +--R +--------+ +--R | 2 +--R 4 12 3 10 2 2 8 3 6 4 4 |a x + b +--R (a x + 32a b x + 160a b x + 256a b x + 128b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 432 + +--S 433 of 554 +t0278:= x/(a+b/x^2)^(1/2) +--R +--R +--R x +--R (402) ----------- +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 433 + +--S 434 of 554 +r0278:= 1/2*(a+b/x^2)^(1/2)*x^2/a-1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R - b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (403) ------------------------------------------ +--R +-+ +--R 2a\|a +--R Type: Expression(Integer) +--E 434 + +--S 435 of 554 +a0278:= integrate(t0278,x) +--R +--R +--R (404) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R , +--R +--R +--------+ +--R +-+ | 2 2 2 +--R (- 4b\|b \|a x + b + 2a b x + 4b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 +---+ | 2 3 +---+ +-+ +--R (- a x - 2b x)\|- a \|a x + b + (2a x + 2b x)\|- a \|b +--R / +--R +--------+ +--R +---+ +-+ | 2 2 2 +---+ +--R 4a\|- a \|b \|a x + b + (- 2a x - 4a b)\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 435 + +--S 436 of 554 +m0278a:= a0278.1-r0278 +--R +--R +--R (405) +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +-+ | 2 2 2 \| x +--R (2b\|b \|a x + b - a b x - 2b )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +-+ |a x + b +-+ 3 +-+ | 2 +--R (- 2x \|a |-------- \|b + (- a x - 2b x)\|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +-+ +-+ 4 2 +-+ |a x + b +--R (2a x + 2b x)\|a \|b + (a x + 2b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R 4a\|a \|b \|a x + b + (- 2a x - 4a b)\|a +--R Type: Expression(Integer) +--E 436 + +--S 437 of 554 +d0278a:= D(m0278a,x) +--R +--R +--R (406) +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b 4 8 +--R (- 7a x - 56a b x - 112a b x - 64b x )\|a |-------- - 7a x +--R | 2 +--R \| x +--R + +--R 3 6 2 2 4 3 2 +--R - 56a b x - 112a b x - 64a b x +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (- a x - 24a b x - 80a b x - 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (- a x - 25a b x - 104a b x - 144a b x - 64b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 9 3 7 2 2 5 3 3 |a x + b +--R (7a x + 56a b x + 112a b x + 64a b x ) |-------- +--R | 2 +--R \| x +--R + +--R 4 9 3 7 2 2 5 3 3 4 +-+ +--R (7a x + 63a b x + 168a b x + 176a b x + 64b x)\|a +--R * +--R +-+ +--R \|b +--R + +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b x )\|a |-------- +--R | 2 +--R \| x +--R + +--R 5 10 4 8 3 2 6 2 3 4 4 2 +--R a x + 25a b x + 104a b x + 144a b x + 64a b x +--R / +--R +--------+ +--R | 2 +--R 4 7 3 5 2 2 3 3 |a x + b +-+ +--R (7a x + 56a b x + 112a b x + 64a b x) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +--R (a x + 25a b x + 104a b x + 144a b x + 64b )\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 +-+ |a x + b +-+ +--R (- 7a x - 63a b x - 168a b x - 176a b x - 64b )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 5 9 4 7 3 2 5 2 3 3 4 |a x + b +--R (- a x - 25a b x - 104a b x - 144a b x - 64a b x) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 437 + +--S 438 of 554 +m0278b:= a0278.2-r0278 +--R +--R +--R (407) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R +--------+ | 2 +--R +---+ +-+ | 2 2 2 +---+ \| x +--R (2b\|- a \|b \|a x + b + (- a b x - 2b )\|- a )atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R +-+ +-+ | 2 2 2 +-+ +--R (- 4b\|a \|b \|a x + b + (2a b x + 4b )\|a ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--------+ +--R 2 +---+ +-+ |a x + b +-+ 3 +---+ +-+ | 2 +--R (- 2x \|- a \|a |-------- \|b + (- a x - 2b x)\|- a \|a )\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 +---+ +-+ +-+ 4 2 +---+ +-+ |a x + b +--R (2a x + 2b x)\|- a \|a \|b + (a x + 2b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R +---+ +-+ +-+ | 2 2 2 +---+ +-+ +--R 4a\|- a \|a \|b \|a x + b + (- 2a x - 4a b)\|- a \|a +--R Type: Expression(Integer) +--E 438 + +--S 439 of 554 +d0278b:= D(m0278b,x) +--R +--R +--R (408) +--R +--------+ +--R | 2 +--------+ +--R 4 2 |a x + b +-+ 2 5 3 2 | 2 +--R ((- 4a x - 8b x ) |-------- \|b - a x - 8a b x - 8b x)\|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ 2 6 4 2 2 |a x + b +--R (4a x + 12a b x + 8b x)\|b + (a x + 8a b x + 8b x ) |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 2 4 2 2 |a x + b | 2 +--R (a x + 8a b x + 8b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 2 |a x + b +-+ +--R (- 4a x - 12a b x - 8b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 439 + +--S 440 of 554 +t0279:= 1/x/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (409) ------------ +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 440 + +--S 441 of 554 +r0279:= atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R (410) ------------------ +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 441 + +--S 442 of 554 +a0279:= integrate(t0279,x) +--R +--R +--R (411) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R [-------------------------------------------------------------, +--R +-+ +--R \|a +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R 2atan(------------------------------) +--R a x +--R -------------------------------------] +--R +---+ +--R \|- a +--R Type: Union(List(Expression(Integer)),...) +--E 442 + +--S 443 of 554 +m0279a:= a0279.1-r0279 +--R +--R +--R (412) +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R - atanh(-----------) +--R +-+ +--R \|a +--R / +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 443 + +--S 444 of 554 +d0279a:= D(m0279a,x) +--R +--R +--R (413) +--R +--------+ +--R | 2 +--R 3 +-+ |a x + b 2 3 +-+ +--R ((3a x + 4b x)\|a |-------- - 3a x - 4a b x)\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +--R (- a x - 4a b x ) |-------- + (a x + 5a b x + 4b )\|a +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b 2 4 2 2 +-+ +-+ +--R ((3a x + 4a b x ) |-------- + (- 3a x - 7a b x - 4b )\|a )\|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b 3 5 2 3 2 +--R (- a x - 5a b x - 4b x)\|a |-------- + a x + 5a b x + 4a b x +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--R 2 4 2 |a x + b +-+ +--R (3a x + 4a b x ) |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +--R (- a x - 5a b x - 4b x)\|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R +--------+ +--R | 2 +--R 2 5 3 2 +-+ |a x + b +-+ +--R (3a x + 7a b x + 4b x)\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 3 6 2 4 2 2 |a x + b +--R (- a x - 5a b x - 4a b x ) |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 444 + +--S 445 of 554 +m0279b:= a0279.2-r0279 +--R +--R +--R (414) +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 +---+ | 2 +---+ +-+ +--R +---+ \| x +-+ \|- a \|a x + b - \|- a \|b +--R - \|- a atanh(-----------) + 2\|a atan(------------------------------) +--R +-+ a x +--R \|a +--R ---------------------------------------------------------------------- +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 445 + +--S 446 of 554 +d0279b:= D(m0279b,x) +--R +--R +--R +--------+ +--R +--------+ | 2 +--R | 2 |a x + b +--R - \|a x + b + x |-------- +--R | 2 +--R \| x +--R (415) ---------------------------- +--R +--------+ +--R | 2 +--------+ +--R |a x + b | 2 +--R x |-------- \|a x + b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 446 + +--S 447 of 554 +t0280:= 1/x/(-a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (416) -------------- +--R +----------+ +--R | 2 +--R |- a x + b +--R x |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 447 + +--S 448 of 554 +r0280:= -atan((-a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R atan(-------------) +--R +-+ +--R \|a +--R (417) - ------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 448 + +--S 449 of 554 +a0280:= integrate(t0280,x) +--R +--R +--R (418) +--R +----------+ +----------+ +--R | 2 +---+ +-+ 2 +---+ | 2 +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a + a x\|- a x + b +--R log(---------------------------------------------------------------------) +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R [--------------------------------------------------------------------------, +--R +---+ +--R \|- a +--R +----------+ +--R +-+ +-+ | 2 +-+ +--R \|a \|b - \|- a x + b \|a +--R 2atan(----------------------------) +--R a x +--R -----------------------------------] +--R +-+ +--R \|a +--R Type: Union(List(Expression(Integer)),...) +--E 449 + +--S 450 of 554 +m0280a:= a0280.1-r0280 +--R +--R +--R (419) +--R +-+ +--R \|a +--R * +--R log +--R +----------+ +--R | 2 +---+ +-+ 2 +---+ +--R (\|- a x + b \|- a - a x)\|b + (a x - b)\|- a +--R + +--R +----------+ +--R | 2 +--R a x\|- a x + b +--R / +--R +----------+ +--R | 2 +-+ +--R \|- a x + b \|b - b +--R + +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R +---+ \| x +--R \|- a atan(-------------) +--R +-+ +--R \|a +--R / +--R +---+ +-+ +--R \|- a \|a +--R Type: Expression(Integer) +--E 450 + +--S 451 of 554 +d0280a:= D(m0280a,x) +--R +--R +--R (420) +--R +----------+ +--R +----------+ | 2 +--R 3 | 2 +---+ 2 4 2 |- a x + b +--R ((- 3a x + 4b x)\|- a x + b \|- a + 3a x - 4a b x ) |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 +---+ 2 3 | 2 +--R (- 3a x + 7a b x - 4b )\|- a + (- 3a x + 4a b x)\|- a x + b +--R * +--R +-+ +--R \|b +--R + +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((- a x + 5a b x - 4b x)\|- a + (- a x + 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 4 2 2 | 2 +---+ 3 5 2 3 2 +--R (a x - 5a b x + 4b )\|- a x + b \|- a - a x + 5a b x - 4a b x +--R / +--R +----------+ +--R 2 5 3 2 +---+ 2 4 2 | 2 +--R ((3a x - 7a b x + 4b x)\|- a + (3a x - 4a b x )\|- a x + b ) +--R * +--R +----------+ +--R | 2 +--R |- a x + b +-+ +--R |---------- \|b +--R | 2 +--R \| x +--R + +--R +----------+ +--R 2 5 3 2 | 2 +---+ 3 6 2 4 +--R (- a x + 5a b x - 4b x)\|- a x + b \|- a + a x - 5a b x +--R + +--R 2 2 +--R 4a b x +--R * +--R +----------+ +--R | 2 +--R |- a x + b +--R |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 451 + +--S 452 of 554 +m0280b:= a0280.2-r0280 +--R +--R +--R +----------+ +--R | 2 +--R |- a x + b +--R +----------+ |---------- +--R +-+ +-+ | 2 +-+ | 2 +--R \|a \|b - \|- a x + b \|a \| x +--R 2atan(----------------------------) + atan(-------------) +--R a x +-+ +--R \|a +--R (421) --------------------------------------------------------- +--R +-+ +--R \|a +--R Type: Expression(Integer) +--E 452 + +--S 453 of 554 +d0280b:= D(m0280b,x) +--R +--R +--R +----------+ +--R | 2 +----------+ +--R |- a x + b | 2 +--R x |---------- - \|- a x + b +--R | 2 +--R \| x +--R (422) ------------------------------ +--R +----------+ +--R +----------+ | 2 +--R | 2 |- a x + b +--R x\|- a x + b |---------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 453 + +--S 454 of 554 +t0281:= 1/x^2/(2+b/x^2)^(1/2) +--R +--R +--R 1 +--R (423) ------------ +--R +-------+ +--R | 2 +--R 2 |2x + b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 454 + +--S 455 of 554 +r0281:= -asinh(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asinh(--------) +--R 2x +--R (424) - --------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 455 + +--S 456 of 554 +a0281:= integrate(t0281,x) +--R +--R +--R +-------+ +--R | 2 +-+ +--R +-+ \|2x + b - \|b +--R \|b log(-----------------) +--R x +--R (425) -------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 456 + +--S 457 of 554 +m0281:= a0281-r0281 +--R +--R +--R +-------+ +--R | 2 +-+ +-+ +-+ +--R \|2x + b - \|b \|2 \|b +--R log(-----------------) + asinh(--------) +--R x 2x +--R (426) ---------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 457 + +--S 458 of 554 +d0281:= D(m0281,x) +--R +--R +--R (427) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R +-+ +-+ |2x + b | 2 |2x + b +-+ 2 +-+ +--R (- \|2 \|b - 2x |------- )\|2x + b + 2x |------- \|b + (2x + b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ------------------------------------------------------------------------ +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 |2x + b +-+ | 2 4 2 |2x + b +--R 2x |------- \|b \|2x + b + (- 4x - 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 458 + +--S 459 of 554 +t0282:= 1/x^2/(2-b/x^2)^(1/2) +--R +--R +--R 1 +--R (428) ------------ +--R +-------+ +--R | 2 +--R 2 |2x - b +--R x |------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 459 + +--S 460 of 554 +r0282:= -asin(1/2*b^(1/2)*2^(1/2)/x)/b^(1/2) +--R +--R +--R +-+ +-+ +--R \|2 \|b +--R asin(--------) +--R 2x +--R (429) - -------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 460 + +--S 461 of 554 +a0282:= integrate(t0282,x) +--R +--R +--R +-------+ +--R | 2 +---+ +--R +---+ \|2x - b - \|- b +--R \|- b log(-------------------) +--R x +--R (430) - ------------------------------ +--R b +--R Type: Union(Expression(Integer),...) +--E 461 + +--S 462 of 554 +m0282:= a0282-r0282 +--R +--R +--R +-------+ +--R | 2 +---+ +-+ +-+ +--R +---+ +-+ \|2x - b - \|- b \|2 \|b +--R - \|- b \|b log(-------------------) + b asin(--------) +--R x 2x +--R (431) ------------------------------------------------------- +--R +-+ +--R b\|b +--R Type: Expression(Integer) +--E 462 + +--S 463 of 554 +d0282:= D(m0282,x) +--R +--R +--R (432) +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R |2x - b +-+ +---+ | 2 +---+ |2x - b 2 +-+ +--R (- 2x |------- - \|2 \|- b )\|2x - b + 2x\|- b |------- + (2x - b)\|2 +--R | 2 | 2 +--R \| 2x \| 2x +--R ---------------------------------------------------------------------------- +--R +-------+ +-------+ +--R | 2 +-------+ | 2 +--R 2 +---+ |2x - b | 2 4 2 |2x - b +--R 2x \|- b |------- \|2x - b + (- 4x + 2b x ) |------- +--R | 2 | 2 +--R \| 2x \| 2x +--R Type: Expression(Integer) +--E 463 + +--S 464 of 554 +t0283:= 1/x^2/(a+b/x^2)^(1/2) +--R +--R +--R 1 +--R (433) ------------- +--R +--------+ +--R | 2 +--R 2 |a x + b +--R x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 464 + +--S 465 of 554 +r0283:= -atanh((a+b/x^2)^(1/2)*x/b^(1/2))/b^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R x |-------- +--R | 2 +--R \| x +--R atanh(------------) +--R +-+ +--R \|b +--R (434) - ------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 465 + +--S 466 of 554 +a0283:= integrate(t0283,x) +--R +--R +--R +--------+ +--R | 2 +-+ +--R +-+ \|a x + b - \|b +--R \|b log(------------------) +--R x +--R (435) --------------------------- +--R b +--R Type: Union(Expression(Integer),...) +--E 466 + +--S 467 of 554 +m0283:= a0283-r0283 +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R +--------+ x |-------- +--R | 2 +-+ | 2 +--R \|a x + b - \|b \| x +--R log(------------------) + atanh(------------) +--R x +-+ +--R \|b +--R (436) --------------------------------------------- +--R +-+ +--R \|b +--R Type: Expression(Integer) +--E 467 + +--S 468 of 554 +d0283:= D(m0283,x) +--R +--R +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R +-+ |a x + b | 2 |a x + b +-+ 2 +--R (- \|b - x |-------- )\|a x + b + x |-------- \|b + a x + b +--R | 2 | 2 +--R \| x \| x +--R (437) ---------------------------------------------------------------- +--R +--------+ +--------+ +--R | 2 +--------+ | 2 +--R 2 |a x + b +-+ | 2 4 2 |a x + b +--R x |-------- \|b \|a x + b + (- a x - b x ) |-------- +--R | 2 | 2 +--R \| x \| x +--R Type: Expression(Integer) +--E 468 + +--S 469 of 554 +t0284:= x^3*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R 3 |a x + b +--R (438) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 469 + +--S 470 of 554 +r0284:= 1/8*b*(a+b/x^2)^(1/2)*x^2/a+1/4*(a+b/x^2)^(1/2)*x^4-_ + 1/8*b^2*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(3/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R 2 \| x 4 2 +-+ |a x + b +--R - b atanh(-----------) + (2a x + b x )\|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (439) ------------------------------------------------------ +--R +-+ +--R 8a\|a +--R Type: Expression(Integer) +--E 470 + +--S 471 of 554 +a0284:= integrate(t0284,x) +--R +--R +--R (440) +--R [ +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +-+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R , +--R +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((- 8a b x - 16b )\|b \|a x + b + 2a b x + 16a b x + 16b ) +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R 3 7 2 5 2 3 3 +---+ | 2 +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|b +--R / +--R +--------+ +--R 2 2 +---+ +-+ | 2 +--R (32a x + 64a b)\|- a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +--R (- 8a x - 64a b x - 64a b )\|- a +--R ] +--R Type: Union(List(Expression(Integer)),...) +--E 471 + +--S 472 of 554 +m0284a:= a0284.1-r0284 +--R +--R +--R (441) +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b + a x)\|a x + b - a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 2 2 3 +-+ | 2 2 2 4 3 2 4 +--R ((4a b x + 8b )\|b \|a x + b - a b x - 8a b x - 8b ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +-+ +-+ | 2 3 4 2 2 2 +-+ +--R (32a x + 64a b)\|a \|b \|a x + b + (- 8a x - 64a b x - 64a b )\|a +--R Type: Expression(Integer) +--E 472 + +--S 473 of 554 +d0284a:= D(m0284a,x) +--R +--R +--R (442) +--R 6 14 5 12 4 2 10 3 3 8 +--R - 11a x - 231a b x - 1452a b x - 4048a b x +--R + +--R 2 4 6 5 4 6 2 +--R - 5632a b x - 3840a b x - 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 7 14 6 12 5 2 10 4 3 8 3 4 6 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 2 5 4 6 2 +--R - 3840a b x - 1024a b x +--R * +--R +-+ +--R \|b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 5 6 3 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R - a x - 62a b x - 681a b x - 2972a b x - 6448a b x +--R + +--R 2 5 5 6 3 7 +--R - 7424a b x - 4352a b x - 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 231a b x + 1452a b x + 4048a b x + 5632a b x +--R + +--R 2 5 5 6 3 +--R 3840a b x + 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R + +--R 7 15 6 13 5 2 11 4 3 9 3 4 7 +--R 11a x + 242a b x + 1683a b x + 5500a b x + 9680a b x +--R + +--R 2 5 5 6 3 7 +--R 9472a b x + 4864a b x + 1024b x +--R * +--R +-+ +--R \|a +--R * +--R +-+ +--R \|b +--R + +--R 7 16 6 14 5 2 12 4 3 10 3 4 8 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x +--R + +--R 2 5 6 6 4 7 2 +--R 7424a b x + 4352a b x + 1024b x +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R + +--R 8 16 7 14 6 2 12 5 3 10 4 4 8 3 5 6 +--R a x + 62a b x + 681a b x + 2972a b x + 6448a b x + 7424a b x +--R + +--R 2 6 4 7 2 +--R 4352a b x + 1024a b x +--R / +--R 6 11 5 9 4 2 7 3 3 5 2 4 3 +--R 11a x + 220a b x + 1232a b x + 2816a b x + 2816a b x +--R + +--R 5 +--R 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +-+ +--R |-------- \|b +--R | 2 +--R \| x +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R a x + 61a b x + 620a b x + 2352a b x + 4096a b x +--R + +--R 5 2 6 +--R 3328a b x + 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +--R \|a |-------- +--R | 2 +--R \| x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 6 12 5 10 4 2 8 3 3 6 2 4 4 +--R - 11a x - 231a b x - 1452a b x - 4048a b x - 5632a b x +--R + +--R 5 2 6 +--R - 3840a b x - 1024b +--R * +--R +--------+ +--R | 2 +--R +-+ |a x + b +-+ +--R \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 7 13 6 11 5 2 9 4 3 7 3 4 5 +--R - a x - 61a b x - 620a b x - 2352a b x - 4096a b x +--R + +--R 2 5 3 6 +--R - 3328a b x - 1024a b x +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 473 + +--S 474 of 554 +m0284b:= a0284.2-r0284 +--R +--R +--R (443) +--R +--------+ +--R 2 2 3 +---+ +-+ | 2 +--R (4a b x + 8b )\|- a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +---+ +--R (- a b x - 8a b x - 8b )\|- a +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R atanh(-----------) +--R +-+ +--R \|a +--R + +--R +--------+ +--R 2 2 3 +-+ +-+ | 2 +--R (- 8a b x - 16b )\|a \|b \|a x + b +--R + +--R 2 2 4 3 2 4 +-+ +--R (2a b x + 16a b x + 16b )\|a +--R * +--R +--------+ +--R +---+ | 2 +---+ +-+ +--R \|- a \|a x + b - \|- a \|b +--R atan(------------------------------) +--R a x +--R + +--R +--------+ +--R | 2 +--R 2 6 4 2 2 +---+ +-+ |a x + b +-+ +--R (- 8a x - 20a b x - 8b x )\|- a \|a |-------- \|b +--R | 2 +--R \| x +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +--R (- 2a x - 17a b x - 24a b x - 8b x)\|- a \|a +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 3 7 2 5 2 3 3 +---+ +-+ +-+ +--R (8a x + 28a b x + 28a b x + 8b x)\|- a \|a \|b +--R + +--R +--------+ +--R | 2 +--R 3 8 2 6 2 4 3 2 +---+ +-+ |a x + b +--R (2a x + 17a b x + 24a b x + 8b x )\|- a \|a |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R 2 2 +---+ +-+ +-+ | 2 +--R (32a x + 64a b)\|- a \|a \|b \|a x + b +--R + +--R 3 4 2 2 2 +---+ +-+ +--R (- 8a x - 64a b x - 64a b )\|- a \|a +--R Type: Expression(Integer) +--E 474 + +--S 475 of 554 +d0284b:= D(m0284b,x) +--R +--R +--R (444) +--R +--------+ +--R | 2 +--R 4 10 3 8 2 2 6 3 4 4 2 |a x + b +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b x ) |-------- +--R | 2 +--R \| x +--R * +--R +-+ +--R \|b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +--R - a x - 33a b x - 192a b x - 416a b x - 384a b x - 128b x +--R * +--R +--------+ +--R | 2 +--R \|a x + b +--R + +--R 5 11 4 9 3 2 7 2 3 5 4 3 5 +-+ +--R (8a x + 96a b x + 360a b x + 592a b x + 448a b x + 128b x)\|b +--R + +--R 5 12 4 10 3 2 8 2 3 6 4 4 5 2 +--R (a x + 33a b x + 192a b x + 416a b x + 384a b x + 128b x ) +--R * +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--R | 2 +--R \| x +--R / +--R +--------+ +--R | 2 +--------+ +--R 4 8 3 6 2 2 4 3 2 4 |a x + b | 2 +--R (a x + 32a b x + 160a b x + 256a b x + 128b ) |-------- \|a x + b +--R | 2 +--R \| x +--R + +--R +--------+ +--R | 2 +--R 4 8 3 6 2 2 4 3 2 4 |a x + b +-+ +--R (- 8a x - 88a b x - 272a b x - 320a b x - 128b ) |-------- \|b +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 475 + +--S 476 of 554 +t0285:= x*(a+b/x^2)^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R (445) x |-------- +--R | 2 +--R \| x +--R Type: Expression(Integer) +--E 476 + +--S 477 of 554 +r0285:= 1/2*x^2*(a+b/x^2)^(1/2)+1/2*b*atanh((a+b/x^2)^(1/2)/a^(1/2))/a^(1/2) +--R +--R +--R +--------+ +--R | 2 +--R |a x + b +--R |-------- +--------+ +--R | 2 | 2 +--R \| x 2 +-+ |a x + b +--R b atanh(-----------) + x \|a |-------- +--R +-+ | 2 +--R \|a \| x +--R (446) ---------------------------------------- +--R +-+ +--R 2\|a +--R Type: Expression(Integer) +--E 477 + +--S 478 of 554 +a0285:= integrate(t0285,x) +--R +--R +--R (447) +--R [ +--R +--------+ +--R +-+ | 2 2 2 +--R (2b\|b \|a x + b - a b x - 2b ) +--R * +--R +--------+ +--R +-+ +-+ | 2 +-+ 2 +-+ +--R (\|a \|b - a x)\|a x + b + a x\|b + (- a x - b)\|a +--R log(--------------------------------------------------------) +--R +--------+ +--R +-+ | 2 +--R \|b \|a x + b - b +--R + +--R +--------+ +--R 3 +-+ | 2 3 +-+ +-+ +--R (- a x - 2b x)\|a \|a x + b + (2a x + 2b x)\|a \|b +--R / +--R +--------+ +--R +-+ +-+ | 2 2 +-+ +--R 4\|a \|b \|a x + b + (- 2a x - 4b)\|a +--R , +--R +--R +--------+ +--R +--------+ +---+ | 2 +---+ +-+ +--R +-+ | 2 2 2 \|- a \|a x + b - \|- a \|b +--R (4b\|b \|a x + b - 2a b x - 4b )atan(------------------------------) +--R