Question

Make a substitution to express the integrand as a rational function and then evaluate the integral.

Answer 1

Step 1 :

The expression is

Rewrite the expression :

Let , then

Substitute corresponding values.

Step 2 :

Solve the above integral by using partial fractions.

Partial fractions decomposition.

Equate u coefficients and equate constants.

Multiply equation (2) by 2 and then subtract two equations.

Substitute in equation (2)

Substitute and in equation 1.

Apply integration with respect u on each side.

Use the formula :

Substitute and in above equation.

The value of the integration :

Solution :