# Calculus Examples

Divide by .

Split the single integral into multiple integrals.

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

Rewrite as .

Since both terms are perfect cubes, factor using the difference of cubes formula, where and .

Simplify.

Multiply by .

One to any power is one.

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.

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 .

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 .

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.

Replace all occurrences of with .

Replace all occurrences of with .