Solving Integrals of Product Functions: A Comprehensive Guide

[satxer]

How do I find the integral for any integral of the type: f(x)g(x)dx

I've looked every where, and the closest I've seen is integration by parts which is apparently for the integral of f(x)g'(x)dx, which, to my inexpert eyes, is a completely different integral than the first one

Also, this is probably harder and I think I'm less likely to get an answer, but how about the integral of (x^n)(e^(x^(m+p)))dx

 

[TMM]

It's similar to a convolution, which has some nice properties, but other than that they usually need to be dealt with on a case by case basis. On the other hand if you wish to perform a contour integral you can get the residues of f(z)g(z) with the Laurent series for f(z) and g(z) in certain cases.

 

[Whitishcube]

Nono, integration by parts is what you're looking for I'm pretty sure. The only difference is that you would treat either g(x) or f(x) as a derivative, like g'(x). To use integration by parts only one of the functions you're given has to be integrable, where the other needs to be differentiable. Integration by parts is pretty malleable. (Sp?)

Hope this helps.