Question

Can some one help me evaluate the integral ?

Answer 1

\[\int\limits e^x/(1+e^{2x}) dx\]

Answer 2

I thought the answer should be arctan(e^x) +c

but somehow the answer tells me that there is a 1/2 multiplied to it.
I can't figure out where it got that from.

Answer 3

\[\int\limits \frac{e^x}{1+e^{2x}} dx\]\[= \int\limits \frac{e^x}{1+(e^x)^2} dx\]

let u = e^x and solve, how come? I got arcTan(e^x) too

Answer 4

1/2 can come from \[u=e ^{2x}\]