Answer: Currently there is no predefined function that will do this but it can be easily accomplished given Maple's design. Greg Fee of the Maple Symbolic Computation Lab suggests you define a function `expand/Int` as follows:
> `expand/Int` := proc(a,r) > local x,f,y,c; > if type(r,name) then x := r > elif type(r,`=`) then x := op(1,r) > else ERROR(`bad 2nd arg`) > fi; > if type(a,`*`) then > c := 1; > y := 1; > for f in a do if has(f,x) then y := y*f else c := c*f fi od; > c*Int(y,r) > elif type(a,`+`) then map(procname,a,r) > else Int(a,r) > fi > end;Maple is designed so that users may add their own special routines for dealing with special functions. Functions such as expand, simplify, combine, int and others have a specially designed interface to make this easy. For example, when expand is passed an argument such as Int(something), Maple will invoke the routine `expand/Int`, if it exists, on something.
> Int(a*x^n+a*f(x)*sin(1)*Pi,x);
/
| n
| a x + a f(x) sin(1) Pi dx
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/
> expand(");
/ /
| n |
a | x dx + a sin(1) Pi | f(x) dx
| |
/ /
Related help files include: expand, combine, Int, simplify