- #1

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## Homework Statement

Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] 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.

- Thread starter autodidude
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- #1

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Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] 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

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Try v = 1 + 2x.

- #3

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As a second substitution?

- #4

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No, just start with it.

- #5

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Ok, I now have the following:

[tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]

[tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]

- #6

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Allow me to fix that for you:Ok, I now have the following:

[tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]

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

Last edited:

- #7

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where is du?

- #8

ehild

Homework Helper

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Integrate by parts## Homework Statement

Integrate [tex]\frac{xe^{2x}}{(1+2x)^2}[/tex] 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.

∫uv'dx=uv-∫u'vdx,

using u=xe

ehild

- #9

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Parts requires u,v to be continuous.Integrate by parts

∫uv'dx=uv-∫u'vdx,

using u=xe^{2x}and v'=1/(1+2x)^{2}.

ehild

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