# Calculus Examples

Step 1

Integrate by parts using the formula , where and .

Step 2

Step 2.1

Combine and .

Step 2.2

Combine and .

Step 3

Since is constant with respect to , move out of the integral.

Step 4

Step 4.1

Multiply by .

Step 4.2

Multiply by .

Step 5

Step 5.1

Let . Find .

Step 5.1.1

Differentiate .

Step 5.1.2

Since is constant with respect to , the derivative of with respect to is .

Step 5.1.3

Differentiate using the Power Rule which states that is where .

Step 5.1.4

Multiply by .

Step 5.2

Rewrite the problem using and .

Step 6

Combine and .

Step 7

Since is constant with respect to , move out of the integral.

Step 8

Step 8.1

Multiply by .

Step 8.2

Multiply by .

Step 9

The integral of with respect to is .

Step 10

Step 10.1

Rewrite as .

Step 10.2

Simplify.

Step 10.2.1

Combine and .

Step 10.2.2

Combine and .

Step 11

Replace all occurrences of with .

Step 12

Reorder factors in .