help-integrals?

Question

Answer 1

(1)

Step 1:

The integral function is .

Sum and difference rule of integral : .

Power rule of integral :.

.

.

Solution :

.

Answer 2

(2)

Step 1:

The integral function is .

Power rule of integral :.

.

Solution :

.

Answer 3

(3)

Step 1:

The integral function is .

Let .

Differentiate on each side with respect to .

.

Substitute and in the integral function.

Integral of logarithm function is  .

.

Substitute in the integral function.

.

Solution :

.

Answer 4

(4)

Step 1:

The integral function is .

Let .

.

Differentiate on each side with respect to .

 

Substitute , and in the integral function.

.

Sum and difference rule of integral : .

Integral of logarithm function is .

Power rule of integral :.

Substitute in integral function.

.

.

Solution :

.