# integration by parts

by CellCoree
Tags: integration, parts
 P: 42 hi, i would like help on a problem i am currently stuck on. $$\int(e^x)/(1+e^(2x))dx$$ <-- it's suppose to be $$\int$$ (e^x)/(1+e^(2x))dx using integration by parts, here's what i done: u=e^x du=e^x dv=(1+e^(2x)) v = (need to use anti-differentiation, which i dont remeber....) can i use integration by parts with this? this is cal 2.
P: 135
 Quote by CellCoree hi, i would like help on a problem i am currently stuck on. dv=(1+e^(2x)) v = (need to use anti-differentiation, which i dont remeber....)
Yes, v would be the integral of (1+e^(2x))
 Sci Advisor HW Helper P: 1,123 Erm, by-parts doesn't seem to make sense because actually: $$u = e^x$$ $$dv = \frac{1}{1 + e^{2x}}$$ To me, it just looks like it is going to get nastier and nastier. I would suggest using the substitution $t = e^x$ because $dt = e^xdx$ and if you look at the integral like this it becomes quite simple: $$\int \frac{e^x dx}{1 + \left( e^x \right)^2}$$
HW Helper
P: 2,886

## integration by parts

 Quote by CellCoree hi, i would like help on a problem i am currently stuck on. $$\int(e^x)/(1+e^(2x))dx$$ <-- it's suppose to be $$\int$$ (e^x)/(1+e^(2x))dx using integration by parts, here's what i done: u=e^x du=e^x dv=(1+e^(2x)) v = (need to use anti-differentiation, which i dont remeber....) can i use integration by parts with this? this is cal 2.
Hi,

I would not try an integration by parts. I would simply do a simple substitution u= e^x. Then you have the integral of du/(1+u^2) which is a basic one.

Pat

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