help-substitution rule-integrals.

Question

Answer 1

1)

Step 1:

The integral is .

Consider .

Differentiate on each side with respect to .

Substitue and in the integral.

.

Power rule of integration: .

 

.

Replace in above expression.

.

Solution:

.

Answer 2

2)

Step 1:

The integral is .

Consider .

Differentiate on each side with respect to .

Substitue and in the integral.

.

Power rule of integration: .

 

Replace in above expression.

.

Solution:

.

Answer 3

3)

Step 1:

The integral is .

Consider .

Differentiate on each side with respect to .

Substitue and in the integral.

Integral formula: .

Replace in above expression.

.

Solution:

.

Answer 4

4)

Step 1:

The integral is .

Consider .

Differentiate on each side with respect to .

Substitue and in the integral.

Integral formula: .

 

Replace in above expression.

.

Solution:

.