# Calculus Examples

Step 1

Step 1.1

Let . Find .

Step 1.1.1

Differentiate .

Step 1.1.2

By the Sum Rule, the derivative of with respect to is .

Step 1.1.3

Differentiate using the Power Rule which states that is where .

Step 1.1.4

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

Step 1.1.5

Add and .

Step 1.2

Rewrite the problem using and .

Step 2

Combine and .

Step 3

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

Step 4

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

Step 5

Step 5.1

Rewrite as .

Step 5.2

Simplify.

Step 5.2.1

Multiply by .

Step 5.2.2

Multiply by .

Step 6

Replace all occurrences of with .