# Calculus Examples

Step 1

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

Step 2

Step 2.1

Let . Find .

Step 2.1.1

Differentiate .

Step 2.1.2

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

Step 2.1.3

Differentiate using the Power Rule which states that is where .

Step 2.1.4

Multiply by .

Step 2.2

Rewrite the problem using and .

Step 3

Combine and .

Step 4

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

Step 5

Step 5.1

Simplify.

Step 5.1.1

Combine and .

Step 5.1.2

Cancel the common factor of and .

Step 5.1.2.1

Factor out of .

Step 5.1.2.2

Cancel the common factors.

Step 5.1.2.2.1

Factor out of .

Step 5.1.2.2.2

Cancel the common factor.

Step 5.1.2.2.3

Rewrite the expression.

Step 5.1.2.2.4

Divide by .

Step 5.2

Use to rewrite as .

Step 6

By the Power Rule, the integral of with respect to is .

Step 7

Step 7.1

Rewrite as .

Step 7.2

Simplify.

Step 7.2.1

Combine and .

Step 7.2.2

Multiply by .

Step 8

Replace all occurrences of with .