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

## Homework Statement

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.

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Try v = 1 + 2x.

As a second substitution?

Ok, I now have the following:

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

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##

Last edited:
where is du?

ehild
Homework Helper

## Homework Statement

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

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.

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).