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

by autodidude
Tags: integrate, xe2x or 1
 P: 333 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.
 PF Patron Thanks P: 4,448 Try v = 1 + 2x.
 P: 333 As a second substitution?
PF Patron
Thanks
P: 4,448

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

 P: 333 Ok, I now have the following: $$\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}$$
P: 132
 Quote by autodidude Ok, I now have the following: $$\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}$$
Allow me to fix that for you:

##\displaystyle \frac{1}{4} \int \frac{(u-1)e^{(u-1)}}{u^2} \ du##
 PF Patron Thanks P: 4,448 where is du?
HW Helper
Thanks
P: 9,255
 Quote by 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.
Integrate by parts

∫uv'dx=uv-∫u'vdx,

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

ehild
P: 132
 Quote by ehild Integrate by parts ∫uv'dx=uv-∫u'vdx, using u=xe2x and v'=1/(1+2x)2. ehild
Parts requires u,v to be continuous.
 PF Patron Thanks P: 4,448 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).

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