evaluate the integral

Question

∫ e^x ((1-e^(2x))^(1/2) dx

Answer 1

Given that

Substitute the value of u = e^2x and du = e^xdx

For

Substitute u = sins and du = cos(s)ds then

Write

Integrate the sum terms by term and constant

For integral cos2s substitute p = 2s ===> dp = 2ds

The integral of cosp is sinp

The integration of 1 is s

Substitute back for p = 2s

Substitute back

Substitute the value that

Take common

The integral of the given equation is