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!set methtit=Integration by parts

!set methenv=ZZ QQ RR

!set methparmtype=parm function integrate, function, function

!set methhelp=This method applies integration by parts.

!if $wims_read_parm iswordof form check

  !goto $wims_read_parm

!endif

!exit

:form

 Apply integration by parts on

!read deduc/methparm.phtml 1

:

<div class="wimscenter">

	\(integrate(u*v'dx) = u*v - integrate(u'*v dx))

</div>

<table class="wimsnoborder">

<tr><td style="text-align:right"> where \(u = ) </td><td>

!read deduc/methparm.phtml 2,30

</td></tr>

<tr><td style="text-align:right"> and \(v = ) </td><td>

!read deduc/methparm.phtml 3,30

</td></tr>

</table>

!exit

:check

ker=!item 2 of $methparmobj1

ker=!mathsubst integrate= in $ker

ker=!trim $ker

ker=!declosing $ker

!distribute items $ker into iker,ivar

vartest=!varlist $ivar

!if $ivar != $vartest

  error=Fail

  !exit

!endif

mout=!exec maxima diff($methparm3,$ivar);\

	diff($methparm2,$ivar);

!distribute lines $mout into vprime,uprime

!if diff isvarof $vprime,$uprime or $vprime=$empty or $uprime=$empty

  :bad_data

  error=bad_data

  !exit

!endif

!read deduc/sub/checkzero ($iker)-($methparm2)*($vprime)\

	($uprime)*($methparm3)

!distribute lines $out into ztest1,ztest2

!if $ztest1=$empty or $ztest2=$empty

  !goto bad_data

!endif

!if $ztest1!=yes

    error=Bad function: \(uv') $m_neq \($iker)!

  !advance penalty

  !exit

!endif

!read deduc/sub/simplify ($methparm2)*($methparm3)\

	($uprime)*($methparm3)

!distribute lines $out into uv,uprimev

!if $ztest2=yes

  !if strictintegrate isin $m_options

    error=You don't have the right to take a constant for \(u).\

	  Please change your method.

    !exit

  !else

    newobject1=($uv)

  !endif

!else

  newobject1=($uv - integrate($uprimev,$ivar))

!endif

oldobject=1

methexp=\(u=$methparm2), \(v=$methparm3)

!exit