Question

Evaluate the integral.

Answer 1

Step 1:

The integral function is .

Consider .

Partial fractions decomposition of the function :

Step 2:

Compare coefficients on each side.

.                                Equation (1)

Compare coefficients on each side.

.        Equation (2)

Compare coefficients on each side.

.                Equation (3)

Substitute equation (1) in equation (3).

Compare constant coefficients on each side.

.                Equation (4)

Substitute equation (4) in equation (2)

Substitute in equation (1).

Substitute and in equation (4).

Therefore .

Step 3:

                                   

Solution :

.