# Integration by parts

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 don't remeber...)

can i use integration by parts with this? this is cal 2.

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Crumbles
CellCoree said:
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 don't remeber...)

Yes, v would be the integral of (1+e^(2x))

Homework Helper
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:

$$\int \frac{e^x dx}{1 + \left( e^x \right)^2}$$

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Homework Helper
Gold Member
CellCoree said:
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 don't 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