help? [substitution rule-integrals.]

Question

Answer 1

5)

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 2

6)

Step 1:

The integral is .

Sum and difference of the integral:.

Consider the integral .

Assume .

Differentiate on each side with respect to .

Substitue and in the integral.

Integral formula: . 

Replace in above expression.

.

Comments

Continued...

Step 2:

Consider the integral .

Assume .

Differentiate on each side with respect to .

Substitue and in the integral.

Power rule of integration: .

.

Replace in above expression.

Substitute the results of in .

Solution:

.