The Change command performs a change of variables in the integrals involved in v.

The second parameter c is the transformation (or list of transformations or set of transformations) in the form x=f(u) (assuming x is the original variable and u is the new variable). Implicit transformations (g(x)=h(u)) can be given as long as it is possible to unambiguously rewrite it as an explicit transformation.

The third parameter y is required only if the number of new symbols in the transformation is not equal to the number of old variables in v.

$\mathrm{with}\left(\mathrm{IntegrationTools}\right)\:$

$V≔\mathrm{Int}\left(f\left(x^2\right)\,x=a..b\right)$

$V≔{\int }_a^{b}f\left(x^2\right)\ⅆx$

$\mathrm{Change}\left(V\,x=u^2\right)$

${\int }_{\sqrt{a}}^{\sqrt{b}}2f\left(u^4\right)u\ⅆu$

$V≔\mathrm{Int}\left(f\left(x\right)\,x=a..b\right)$

$V≔{\int }_a^{b}f\left(x\right)\ⅆx$

$\mathrm{Change}\left(V\,x=u-c\,u\right)$

${\int }_{c+a}^{c+b}f\left(u-c\right)\ⅆu$

$V≔\mathrm{Int}\left(\mathrm{Int}\left(f\left(x^2\right)g\left(y\right)\,x=a..b\right)\,y=c..d\right)$

$V≔{\int }_c^d\left({\int }_a^{b}f\left(x^2\right)g\left(y\right)\ⅆx\right)\ⅆy$

$\mathrm{Change}\left(V\,\left\{x=u^2\,y=v^2\right\}\right)$

${\int }_{\sqrt{c}}^{\sqrt{d}}2\left({\int }_{\sqrt{a}}^{\sqrt{b}}2f\left(u^4\right)g\left(v^2\right)u\ⅆu\right)v\ⅆv$