# Calculus Examples

Evaluate the Integral
Step 1
Let . Then , so . Rewrite using and .
Let . Find .
Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
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
Simplify.
Rewrite as .
Simplify.
Multiply by .
Multiply by .
Step 6
Replace all occurrences of with .