Important: The student package has been deprecated. Use the superseding commands, IntegrationTools[Change] and Student[MultivariateCalculus][ChangeOfVariables], instead.

The changevar function performs a ``change of variables'' for integrals, sums, or limits.

The first argument is an equation defining the new variable in terms of the old variable. If more than two variables are involved, the new variable must be given as the third argument. The second argument is the expression to be rewritten and usually contains Int, Sum, or Limit.

The changevar command acts like powsubs if none of Int, Sum, or Limit appears in f.

The change of variables may be implicitly defined, for example, $x^2+2=2u^2$.

The unevaluated forms Int, Limit, and Sum should be used, rather than int, limit, and sum. They can be evaluated later by using the value command.

Limited capabilities exist in connection with double and triple integrals. In this case, the equations defining the multivariate change of variables are given as a set, and the new variables are given in a list.

The command with(student,changevar) allows the use of the abbreviated form of this command.

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

$\mathrm{changevar}\left(\cos \left(x\right)+1=u\,\mathrm{Int}\left({\left(\cos \left(x\right)+1\right)}^3\sin \left(x\right)\,x\right)\,u\right)$

$\int -u^3\ⅆu$

$\mathrm{changevar}\left(x=\sin \left(u\right)\,\mathrm{Int}\left(\mathrm{sqrt}\left(1-x^2\right)\,x=a..b\right)\,u\right)$

${\int }_{\arcsin \left(a\right)}^{\arcsin \left(b\right)}\sqrt{-{\sin \left(u\right)}^2+1}\cos \left(u\right)\ⅆu$

$\mathrm{changevar}\left(\left\{x=r\cos \left(t\right)\,y=r\sin \left(t\right)\right\}\,\mathrm{Doubleint}\left(1\,x\,y\right)\,\left[t\,r\right]\right)$

$\int \left(\int \left|r\right|\ⅆt\right)\ⅆr$