taking an indefinite integral?

Question

how do u take the integral of S (e^2x)/(1+e^2x) dx ?
i brought the denominator up, neg exponent, set that as u, took the derivative, mult. the integral by 1/2, but then when i integrate i get U^0/0....whcih throws everything off?
am i doing this u substitution right?

Answer 1

(e^2x)/(1+e^2x) dx ?
Let u = 1+e^2x
Then du = 2e^2x dx so dx = du/2 = e^2x dx
So we now ar integrating du/2u = 1/2 integral du/u = 1/2 lnu +C.
So required integral is 1/2ln(1+e^2x) + C

Answer 2

I believe the derivative of ln (1+e^2x) is equal to 1/(1+e^2x) times the derivative of the (1+e^2x) which is 2e^2x so the final answer would be
2(e^2x)/(1+e^2x).
Therefore the integral of (e^2x)/(1+e^2x) is (1/2)ln(1+e^2x) +C.

Answer 3

Use u=1+e^2x for your substitution.
I think du= ((e^2x)/2)dx

Try this and see if it works.

You would be integrating (2/u) du or something like that

P.S
Ironduke did it correctly below.