(5)

Step 1:

The integral is .

Sum and difference rule of integral : .

Integral formula of sine function : .

Integral formula of exponential function : .

.

Solution :

.

(6)

Step 1:

The integral is .

Rewrite the integral.

Consider .

Substitute and in the above integral.

Power rule of integral formula : .

Replace in the above expression.

.

Solution :

.

(7)

Step 1:

The integral is .

Consider

Substitute and in the above integral.

Power rule of integral formula : .

Replace in the above expression.

.

Solution :

.

(8)

Step 1:

The integral is .

Rewrite the integral.

Consider the function .

Now use the partial fraction method :

Compare the coefficients of x terms.

                    (1)

Compare the constant terms.

          (2)

Multiple equation (1) with 3.

            (3)

Slove equation (2) and (3).

.

Substitute in equation (1).

.

Step 2:

Integral formula : .

.

Solution :

.