4)

Step 1:

The integral is .

Definition of improper integeral :

If has a discontinuity at , where , and both and are convergent, then

.

Here the third term in the integrand function has a discontinuity at ,

.

Consider .

Sum property of Integrals :.

.

Step 2:

Consider .

.

.

.

5)

Step 3:

The integral is .

Rewrite the integral as .

Sum property of Integrals :.

 .

.

6)

The integral is .

Sum property of Integrals :.

Rewrite the integral as

.

.

Solution:

4)

.

5) .

6)