Integrating $\int\frac{xe^{2x}}{(2x+1)^2}dx$

[aznshark4]

Homework Statement

$$\int\frac{xe^{2x}}{(2x+1)^2}dx$$ where "e" is the natural number

Homework Equations

(none)

The Attempt at a Solution

I tried many ways to solve this problem, but to no avail.
the hint on the book said to use substitution and make $$u=xe^{2x}$$ and $$du=2xe^{2x}+e^{2x}dx$$ but I don't see how that would work out; there is no way to change all the x's into u's.

 

[Dick]

I don't think they meant a simple substitution. They meant to integrate by parts with u=x*exp(2x). Pick dv=dx/(2x+1)^2. That works.