Question

how do you find the integral of (e^2x) / (1+(e^2x))^2 ?

Answer 1

\[\int\limits \frac{e^{2 x}}{\left(1+e^{2 x}\right)^2} \, dx=-\frac{1}{2 \left(1+e^{2 x}\right)}+c \]

Answer 2

i got an extra (1+e^2x) on the denominator...

Answer 3

use u substitution. let u = 1+ e^2x ---> du= 2e^2xdx or 1/2du = e^2xdx

Answer 4

then you have the integral of 1/u^2

Answer 5

or 1/2 times that integral

Answer 6

i used the formula for (u^n+1) / (n+1) + c .... did i use the formula correctly?

Answer 7

once you do the substitution then yes

Answer 8

oh! now i get what i did wrong....

Answer 9

int[u^(-2)] is -u^(-1)

Answer 10

thanks!

Answer 11

no prob