(1)

Step 1 :

The integral is.

Determine the integral by using integration by parts.

Integration by parts: .

Let and .

Find by integrating .

.

.

Differentiate on each side.

.

Substitute corresponding values in integration by parts.

Consider .

Integration by parts: .

Let and .

Find by integrating .

.

Differentiate on each side.

.

Substitute corresponding values in integration by parts.

Substitute the result of in .

.

2)

Step 1: 

The integral is.

Determine the integral by using integration by parts.

Integration by parts: .

Let and .

Find by integrating .

.

.

Differentiate on each side.

.

Substitute corresponding values in integration by parts.

.

Consider .

Integration by parts: .

Let and .

Find by integrating .

.

Differentiate on each side.

.

Substitute corresponding values in integration by parts.

Substitute the result of in .

Consider .

Differentiate with respect to .

.

Property of integration : .

Substitute and in equation (1).

Step 2 :

Integration by parts: .

 let and .

Differentiate with respect .

Substite and in above formula.

Integration of exponential function :.

Substitute   in equation (2).

.

Solution :

.

(2)

The integration function is

Integration by parts: .

Let and .

Differentiate with respect .