Integrating e^f(x): A Simple Explanation and Common Pitfalls

[tetris11]

Homework Statement

Hi there, really easy question but I can't get a straight answer online.

What's $$\int$$x e^f(x) dx

The Attempt at a Solution

I get (e^f(x) x)/f'(x) - $$\int$$ (e^f(x))/f'(x) dx

And when I try to do parts on the last component it will proably just go one forever.

Help?

 

[rock.freak667]

You really won't get a straight answer as that depends on exactly what f(x) is.
You'd need to have u=e^f(x) and dv=x dx.

Since you can't integrate e^f(x) without knowing what f(x) is. For example if f(x)=x², then you'd have dv=e^x2 dx, which has no elementary integral.