use substitution to find the indefinite integral

Question

a) ∫ (6x+7)/(12x^2+28x) dx

b) ∫ (6x+5)/(12x^2+20x) dx

c) ∫  p(p+8)^6 dp

Answer 1

(a)

Step 1:

The indefinite integral is .

Solve the integral using substitution method.

Let .

Apply derivative on each side with respect to .

.

Step 2:

Substitute and in the integral.

Apply formula:.

Substitute .

.

.

Solution:

.

Answer 2

(b)

Step 1:

The indefinite integral is .

Solve the integral using substitution method.

Let .

Apply derivative on each side with respect to .

.

Step 2:

Substitute and in the integral.

Apply formula: .

Substitute .

.

.

Solution:

.

Answer 3

(c)

Step 1:

The indefinite integral is .

Solve the integral using substitution method.

Let .

Apply derivative on each side with respect to .

.

Step 2:

Substitute , and in the integral.

Apply power rule of integration: .

Substitute .

.

.

Solution:

.