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Integrate (xe^(2x))/(1+2x)^2 
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#1
Feb1713, 12:04 AM

P: 333

1. The problem statement, all variables and given/known data
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
Feb1713, 01:13 AM

Thanks
P: 5,687

Try v = 1 + 2x.



#3
Feb1713, 10:27 AM

P: 333

As a second substitution?



#4
Feb1713, 10:29 AM

Thanks
P: 5,687

Integrate (xe^(2x))/(1+2x)^2
No, just start with it.



#5
Feb1713, 02:41 PM

P: 333

Ok, I now have the following:
[tex]\frac{1}{4} \int \frac{(u1)e^{(u1)}{u^2}[/tex] 


#6
Feb1713, 02:45 PM

P: 132

##\displaystyle \frac{1}{4} \int \frac{(u1)e^{(u1)}}{u^2} \ du## 


#7
Feb1713, 02:50 PM

Thanks
P: 5,687

where is du?



#8
Feb1713, 03:43 PM

HW Helper
Thanks
P: 10,387

∫uv'dx=uv∫u'vdx, using u=xe^{2x} and v'=1/(1+2x)^{2}. ehild 


#9
Feb1713, 03:52 PM

P: 132




#10
Feb1713, 04:05 PM

Thanks
P: 5,687

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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