How to integrate an expression with multiple factors ? for example sin(x)*cos(y)*x^3*ln(x)*g^x?

I am trying to write a program to do some calculus, and i got stuck at integrating expressions that are multiplications of multiple functions (like sin(x)*cos(y)*x^3*ln(x) etc), the algorithm for finding the derivative is simple,(sum of multiplications with one derivative per element) but I can't find any good way for integrating. I have never seen integration by parts to be used for more than two factors and its still more of guessing. Any ideas how I can tackle this problem or is it even possible?