evaluate each of the following integrals

Question

1. ∫ x^4 ln(x^5+6) dx

2. ∫ ln(3x+4) dx

Answer 1

(1)

Step 1:

The integral is .

Consider .

Substitute in the integral.

Constant multiple rule of integral : .

.

Step 2:

Integration by parts: .

Assume and .

Consider .

Differentiate on each side.

.

Consider .

Integrate on each side.

.

Substitute corresponding value in the integral.

Substitute .

Solution:

Answer 2

(2)

Step1:

The integral is .

Consider .

Substitute in the integral.

Constant multiple rule of integral : .

Step 2:

Integration by parts: .

Assume and .

Consider .

Differentiate on each side.

.

Consider .

Integrate on each side.

.

Substitute corresponding value in the integral.

Substitute .

Solution: