The function ExpandMultiple expands a multiple integral given as a single Int function call into a nested series of Int function calls.

ExpandMultiple will also work similarly on unevaluated int function calls.

This command is primarily intended for programmers who need to manipulate integrals as data structures.  In most cases, multiple integrals should be computed from a single function call.  The output of ExpandMultiple can be transformed back into a single function call using IntegrationTools[CollapseNested].

If stripoptions is given, none of the options in the integral v will appear in the output

If v is a nested Int or int function call, only the outermost function call will be expanded.

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

$\mathrm{lprint}\left(\mathrm{Int}\left(f\left(x\,y\right)\,\left[x\,y\right]\right)\right)$

Int(f(x,y),[x, y])

$\mathrm{ExpandMultiple}\left(\mathrm{Int}\left(f\left(x\,y\right)\,\left[x\,y\right]\right)\right)$

$\int \left(\int f\left(x\,y\right)\ⅆx\right)\ⅆy$

$\mathrm{lprint}\left(\right)$

Int(Int(f(x,y),x),y)

$\mathrm{ExpandMultiple}\left(\mathrm{Int}\left(f\left(x\,y\right)\,x\,y\right)\right)$

$\int \left(\int f\left(x\,y\right)\ⅆx\right)\ⅆy$

$\mathrm{lprint}\left(\right)$

Int(Int(f(x,y),x),y)

$\mathrm{ExpandMultiple}\left(\mathrm{Int}\left(f\left(x\,y\right)\,\left[x=a..b\,y=c..d\right]\right)\right)$

${\int }_c^d\left({\int }_a^{b}f\left(x\,y\right)\ⅆx\right)\ⅆy$

$\mathrm{lprint}\left(\right)$

Int(Int(f(x,y),x = a .. b),y = c .. d)

$\mathrm{CollapseNested}\left(\right)$

${\int }_c^d{\int }_a^{b}f\left(x\,y\right)\ⅆx\ⅆy$

$\mathrm{lprint}\left(\right)$

Int(f(x,y),[x = a .. b, y = c .. d])

$\mathrm{ExpandMultiple}\left('\mathrm{int}'\left(f\left(x\,y\right)\,\left[x=a..b\,y=c..d\right]\right)\right)$

${\int }_c^d\left({\int }_a^{b}f\left(x\,y\right)\ⅆx\right)\ⅆy$

$\mathrm{lprint}\left(\right)$

int(int(f(x,y),x = a .. b),y = c .. d)

$\mathrm{ExpandMultiple}\left(\mathrm{Int}\left(f\left(x\,y\right)\,\left[x=a..b\,y=c..d\right]\,\mathrm{CauchyPrincipalValue}\right)\right)$

${{\int }_c^d\mathrm{Typesetting}:-\mathrm{\_Hold}\left(\left[\mathrm{Int}\left(f\left(x\,y\right)\,x\=a..b\,\mathrm{CauchyPrincipalValue}\right)\right]\right)\ⅆy}_{\mathrm{CauchyPrincipalValue}}$

$\mathrm{lprint}\left(\right)$

Int(Int(f(x,y),x = a .. b,CauchyPrincipalValue),y = c .. d,CauchyPrincipalValue)

$\mathrm{ExpandMultiple}\left(\mathrm{Int}\left(f\left(x\,y\right)\,\left[x=a..b\,y=c..d\right]\,\mathrm{CauchyPrincipalValue}\right)\,\mathrm{stripoptions}\right)$

${\int }_c^d\left({\int }_a^{b}f\left(x\,y\right)\ⅆx\right)\ⅆy$

$\mathrm{lprint}\left(\right)$

Int(Int(f(x,y),x = a .. b),y = c .. d)