Question

Evaluate the integral.

Answer 1

Step 1:

.

Apply the partial fractions.

--------> (1)

Multiply each side by .

Equate the coefficients.

                       -----> equation (2)

Equate the coefficients.

          -----> equation (3)

Equate the constants.

            -----> equation (4)

Add the equations (3) and (4).

                 -----> equation (5)

Rewrite the equation (3).

Substitute  in above equation.

    -----> equation (6)   

Add the equations (5) and (6).

Substitute  in equation (6).

Substitute in equation (2).

Substitute the values  and in equation (1).

Step 2:

Use the power rule of integration:.

Use the property :.

Solution:

.