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!set methtit=Direct change of variable

!set methenv=ZZ QQ RR

!set methparmtype=parm function integrate, function

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

on 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 change of variable for: <p>

  !read deduc/methparm.phtml 1

!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

  Change of variable:

  <div class="wimscenter">

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

  </div>

  with

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

  !read deduc/methparm.phtml 2,36

.

!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 $newvar,e,pi,euler in $vv

!if $vtest!=$empty

  error=\($methparm2) must be a function of \($newvar) only.

  !exit

!endif

diff=!exec maxima diff($methparm2,$newvar);

!if $diff=$empty

  :bad_data

  error=bad_data

  !exit

!endif

inv=!exec maxima solve($ivar=$methparm2,$newvar);

inv=!declosing $inv

n=!itemcnt $inv

inv2=!nospace $inv

eq==

!if $n!=1 or +++**$newvar$eq notin +++**$inv2

  error=Impossible to find the inverse function of $methparm2, which is\

 	   for future substitution:\

	  use the reverse change of variable.

  !exit

!endif

substed=!mathsubst $ivar=($methparm2) in $iker

!read deduc/sub/checkzero diff(($substed)*($diff),$newvar)

difftest=$out

!read deduc/sub/simplify ($substed)*($diff)\

	($substed)*($diff)*$newvar

!distribute lines $out into newker,ktest

!if $newker=$empty or $ktest=$empty or $difftest=$empty

  !goto bad_data

!endif

!if strictintegrate iswordof $m_options and $difftest=yes

  error=This change of variable is not allowed for this environment.\

	  Please change the method.

  !exit

!endif

!if $difftest=yes

  newobject1=$ktest

!else

  newobject1=integrate($newker,$newvar)

!endif

newobject0=$inv

oldobject=0,1

methexp=\($ivar=$methparm2)

variables=$variables,$newvar

!exit