Question

How do you find the integral of `e^(2x) sqrt(1 + e^(2x)) dx`?

Answer 1

`1/3 (1+e^(2x))^(3/2)` +C

Explanation:

Let u=`1+e^(2x)`, du= 2`e^(2x)`dx

Accordingly, `int e^(2x) sqrt(1+e^(2x) dx`=`1/2int u^(1/2) du`

=`1/3 u^(3/2)` +C

=`1/3 (1+e^(2x))^(3/2)` +C