# Integrate (xe^(2x))/(1+2x)^2

1. Feb 17, 2013

### autodidude

1. The problem statement, all variables and given/known data
Integrate $$\frac{xe^{2x}}{(1+2x)^2}$$ with respect to x

Didn't get anywhere with integration by parts or substitution using u=xe^(2x)
A push in the right direction would be much appreciated.

2. Feb 17, 2013

### voko

Try v = 1 + 2x.

3. Feb 17, 2013

### autodidude

As a second substitution?

4. Feb 17, 2013

### voko

5. Feb 17, 2013

### autodidude

Ok, I now have the following:

$$\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}$$

6. Feb 17, 2013

### Karnage1993

Allow me to fix that for you:

$\displaystyle \frac{1}{4} \int \frac{(u-1)e^{(u-1)}}{u^2} \ du$

Last edited: Feb 17, 2013
7. Feb 17, 2013

### voko

where is du?

8. Feb 17, 2013

### ehild

Integrate by parts

∫uv'dx=uv-∫u'vdx,

using u=xe2x and v'=1/(1+2x)2.

ehild

9. Feb 17, 2013

### Karnage1993

Parts requires u,v to be continuous.

10. Feb 17, 2013

### voko

Now that we have reinstated du, observe that e^(u - 1) = (e^u)/e; the 1/e constant goes outside, and what's inside can be simplified into ((e^u)/u - (e^u)/u^2).