Now I compute the integral 

0<int((abs(c-x)/x)^n,x=a..b)=int((c-x)/x)^n,x=a..c),symbolic)+int((x-c)/x)^n,x=c..b)

assuming c>0,b>c,n>-1.

As it is not possible directly, I split this apparently real integral in two parts. Both parts are real for n>0. Look, what's happens!!!

> Za:=simplify(int(((c-x)/x)^n,x=a..c),symbolic) assuming a>0,c>a,n>-1;

How to compute the integral: int((c-x)/x)^n,x=a..c) ?

This integral is an incomplete beta function and could be expressed in terms of hypergeometric function, but my Maple refuse to deal is. Pleas help