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!set methtit=Reverse change of variable

!set methenv=ZZ QQ RR

!set methparmtype=parm function integrate, function, function

!set methhelp=This method applies the reverse change of variable for an\

  indefinite integral.

!if $wims_read_parm iswordof form check

  !goto $wims_read_parm

!endif

!exit

:form

!set N=!linecnt $mtobj1

!if $N>1 and $methsubstep=1

  :first

  !set methsubstep=2

  Apply a reverse change of variable for:

  <p>

  !read deduc/methparm.phtml 1

  </p>

!else

  !bound methparm1 between integer 0 and $N default 1

  !if $methparm1=0 or $error!=$empty

    !goto first

  !endif

  <input type="hidden" name="methparm1" value="$methparm1">

  !set methsubstep=1

  !set l=!line $methparm1 of $mtobj1

  !set l=!item 2 to -1 of $l

  !set k=!mathsubst integrate= in $l

  !set k=!declosing $k

  !set v=!item 2 of $k

  !set nvar=!item 1 of $newvariables

  Reverse change of variable for \($l): putting <br>

  \($nvar = h($v) = )

  !read deduc/methparm.phtml 2,18

, one has

   <div class="wimscenter">

 	\($l = integrate(f(h($v))h'($v)d$v) = integrate(f($nvar)d$nvar)) ,

  </div>

  where

  \(f($nvar) = )

  !read deduc/methparm.phtml 3,36

  .

!endif

!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

newvar=!item 1 of $newvariables

vv=!varlist nofn $methparm2

vtest=!listcomplement $ivar,e,pi,euler in $vv

!if $vtest!=$empty

  error=\(h($ivar)) must be a function of \($ivar) only.

  !exit

!endif

hprime=!exec maxima diff($methparm2,$ivar);

!if $hprime=$empty

  :bad_data

  error=bad_data

  !exit

!endif

vv=!varlist nofn $methparm3

vtest=!listcomplement $newvar,e,pi,euler in $vv

!if $vtest!=$empty

  error=\(f($newvar)) doit être une fonction de \($newvar) uniquement.

  !exit

!endif

substed=!mathsubst $newvar=($methparm2) in $methparm3

!read deduc/sub/checkzero ($substed)*($hprime)-($iker)\

	diff($methparm3,$newvar)

!distribute lines $out into ztest,difftest

!if $ztest=$empty or $difftest=$empty

  !goto bad_data

!endif

!if $ztest!=yes

  error=Bad formula for the change of variable!

  !advance penalty

  !exit

!endif

!read deduc/sub/simplify $methparm3\

	($methparm3)*($newvar)

!distribute lines $out into newker,res

!if $newker=$empty or $res=$empty

  !goto bad_data

!endif

!if strictintegrate iswordof $m_options and $difftest=yes

  error=You don't have the right to put a constant for \(f($newvar)). \

	Please change the method.

  !exit

!endif

!if $difftest=yes

  newobject1=($res)

!else

  newobject1=integrate($newker,$newvar)

!endif

oldobject=0,1

newobject0=$newvar=$methparm2

methexp=\($newvar=$methparm2)

variables=$variables,$newvar

!exit