Evaluate the integral? : int e^(2x)/(1+e^(2x))^2 dx

1 Answer
Feb 1, 2017

int \ e^(2x)/(1+e^(2x))^2 \ dx = -1/(2(1+e^(2x))) + C

Explanation:

We want to find;

int \ e^(2x)/(1+e^(2x))^2 \ dx

Let u =1+e^(2x) => (du)/dx = 2e^(2x)

Substituting into the integral we get:

int \ e^(2x)/(1+e^(2x))^2 \ dx = int \ (1/2)/u^2 \ du
" " = 1/2int \ 1/u^2 \ du
" " = -1/2 1/u + C
" " = -1/(2(1+e^(2x))) + C