The integral is .

The integral is can have three cases.

They are , is negative, and is positive.

Case 1 :

Evaluate the integral for .

If , then .

Thus, .

Case 2 :

Evaluate the integral for , where is some constant.

If , then .

.

Consider .

Partial fraction decomposition.

Compare coefficients of terms on both sides.

Compare constant terms on both sides.

Substitute in .

.

If , then .

Substitute and in equation (1).

.

.

Case 3 :

Evaluate the integral for , where is some constant.

If , then .

.

.

If , then .

If , then .

If , then .