# Integration Problem

• November 22nd 2009, 05:30 PM
csawyer1109
Integration Problem
Hi again,

Can anyone help me integrate the following problem:

$\int_{1}^{2}\frac{e^\frac{1}{x} - x^2}{x^2e^\frac{1}{x} + x^3}dx$

I'm not sure what to use for my substitution (if I even need to use the substitution method)

Thanks guys!

-Christian
• November 22nd 2009, 06:09 PM
csawyer1109
The answer on the solution sheet is:

$\ln(\frac{e+1}{\sqrt e+2})$

If that helps any...

Didn't seem to help me much!
• November 22nd 2009, 06:34 PM
songoku
Hi csawyer1109

$\int_{1}^{2}\frac{e^\frac{1}{x} - x^2}{x^2e^\frac{1}{x} + x^3}dx$

$=\int_{1}^{2}\frac{e^\frac{1}{x} - x^2}{x^2(e^\frac{1}{x} + x)}dx$

let : $u = e^\frac{1}{x} + x$