# Calculus Examples

Find the Integral With Respect to x
Step 1
Since is constant with respect to , move out of the integral.
Step 2
Let . Then , so . Rewrite using and .
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
Simplify the expression.
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
Simplify.
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 .