integration by parts

CellCoree

hi, i would like help on a problem i am currently stuck on.

[tex]\int(e^x)/(1+e^(2x))dx[/tex] <-- it's suppose to be [tex]\int[/tex] (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.

Crumbles

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

Zurtex

Erm, by-parts doesn't seem to make sense because actually:

[tex]u = e^x[/tex]

[tex]dv = \frac{1}{1 + e^{2x}}[/tex]

To me, it just looks like it is going to get nastier and nastier.

I would suggest using the substitution [itex]t = e^x[/itex] because [itex]dt = e^xdx[/itex] and if you look at the integral like this it becomes quite simple:

[tex]\int \frac{e^x dx}{1 + \left( e^x \right)^2} [/tex]

nrqed

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