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

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  • #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.
 

Answers and Replies

  • #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]
 
  • #6
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Ok, I now have the following:

[tex]\frac{1}{4} \int \frac{(u-1)e^{(u-1)}{u^2}[/tex]
Allow me to fix that for you:

##\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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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.
Integrate by parts

∫uv'dx=uv-∫u'vdx,

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

ehild
 
  • #9
133
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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.
 
  • #10
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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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