# Calculus Examples

Divide by .

Since integration is linear, the integral of with respect to is .

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

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 as .

Simplify.

Since integration is linear, the integral of with respect to is .

Remove unnecessary parentheses.

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

Let . Then . Rewrite using and .

The integral of with respect to is .

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

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

Remove parentheses around .

Let . Then , so . Rewrite using and .

The integral of with respect to is .

Simplify.

Write as a fraction with denominator .

Multiply and .

Replace all occurrences of with .

Replace all occurrences of with .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Move to the left of the expression .

Multiply by .

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

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Combine.

Multiply by .

Combine the numerators over the common denominator.

Simplify the numerator.

Simplify .

Reorder and .

Simplify by moving inside the logarithm.

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Cancel the common factor of .

Write as a fraction with denominator .

Factor out the greatest common factor .

Cancel the common factor.

Rewrite the expression.

Simplify.

Multiply and .

Divide by .

Simplify by moving inside the logarithm.

Rewrite the expression using the negative exponent rule .

Use the product property of logarithms, .

Simplify the log argument.

Write as a fraction with denominator .

Multiply and .

Reorder terms.