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!set methenv=ZZ QQ RR
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!set methenv=ZZ QQ RR
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!set methparmtype=parm function integrate, function
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!set methparmtype=parm function integrate, function
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!set methhelp=This method applies the change of variable on an indefinite\
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!set methhelp=This method applies the change of variable \
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integral.
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on an indefinite integral.
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!if $wims_read_parm iswordof form check
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!if $wims_read_parm iswordof form check
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 !goto $wims_read_parm
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  !goto $wims_read_parm
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!endif
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!endif
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!exit
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!exit
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:form
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:form
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!set N=!linecnt $mtobj1
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!set N=!linecnt $mtobj1
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  !set k=!mathsubst integrate= in $l
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  !set k=!mathsubst integrate= in $l
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  !set k=!declosing $k
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  !set k=!declosing $k
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  !set v=!item 2 of $k
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  !set v=!item 2 of $k
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  !set nvar=!item 1 of $newvariables
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  !set nvar=!item 1 of $newvariables
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  Change of variable:
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  Change of variable:
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   <div class="wimscenter">
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  <div class="wimscenter">
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 	\($l = integrate(f($v),$v) = integrate(f(h($nvar))h'($nvar),$nvar)) ,
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  \($l = integrate(f($v),$v) = integrate(f(h($nvar))h'($nvar),$nvar)) ,
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  </div>
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  </div>
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  with
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  with
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  \($v = h($nvar) = )
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  \($v = h($nvar) = )
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  !read deduc/methparm.phtml 2,36
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  !read deduc/methparm.phtml 2,36
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.
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.
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n=!itemcnt $inv
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n=!itemcnt $inv
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inv2=!nospace $inv
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inv2=!nospace $inv
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eq==
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eq==
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!if $n!=1 or +++**$newvar$eq notin +++**$inv2
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!if $n!=1 or +++**$newvar$eq notin +++**$inv2
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  error=Impossible to find the inverse function of $methparm2, which is\
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  error=Impossible to find the inverse function of $methparm2, which is\
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 	necessary for future substitution:\
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 	   for future substitution:\
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	use the reverse change of variable.
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	  use the reverse change of variable.
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  !exit
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  !exit
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!endif
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!endif
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 substed=!mathsubst $ivar=($methparm2) in $iker
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substed=!mathsubst $ivar=($methparm2) in $iker
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 !read deduc/sub/checkzero diff(($substed)*($diff),$newvar)
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!read deduc/sub/checkzero diff(($substed)*($diff),$newvar)
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 difftest=$out
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difftest=$out
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 !read deduc/sub/simplify ($substed)*($diff)\
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!read deduc/sub/simplify ($substed)*($diff)\
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	($substed)*($diff)*$newvar
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	($substed)*($diff)*$newvar
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!distribute lines $out into newker,ktest
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!distribute lines $out into newker,ktest
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!if $newker=$empty or $ktest=$empty or $difftest=$empty
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!if $newker=$empty or $ktest=$empty or $difftest=$empty
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  !goto bad_data
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  !goto bad_data
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!endif
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!endif
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!if strictintegrate iswordof $m_options and $difftest=yes
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!if strictintegrate iswordof $m_options and $difftest=yes
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  error=This change of variable is not allowed for this environment.\
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  error=This change of variable is not allowed for this environment.\
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	Please change the method.
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	  Please change the method.
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  !exit
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  !exit
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!endif
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!endif
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!if $difftest=yes
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!if $difftest=yes
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  newobject1=$ktest
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  newobject1=$ktest