# Calculus Examples

Factor the numerator and denominator of .

Write the fraction using partial fraction decomposition.

Simplify.

Split the single integral into multiple integrals.

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

The integral of with respect to is .

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

Let . Find .

Rewrite.

Divide by .

Rewrite the problem using and .

Multiply and .

Move to the left of .

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

Multiply and .

Multiply by .

The integral of with respect to is .

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

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

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 .

Add and .

Rewrite the problem using and .

The integral of with respect to is .

Simplify.

Combine and .

To write as a fraction with a common denominator, multiply by .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Combine and .

Combine and .

Move to the left of .

Cancel the common factor.

Divide by .

Replace all occurrences of with .

Replace all occurrences of with .