find the antiderivative

Question

∫ (6x+7)/(12x^2+28x)^5 dx

∫ (6x+5)/(12x^2+20x)^5 dx

Answer 1

(1)

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:

.

Answer 2

(2)

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:

.