Question

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

Answer 1

`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`