# Calculus Examples

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

Let . Then , so . Rewrite using and .

Write as a fraction with denominator .

Multiply and .

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

Write as a fraction with denominator .

Multiply and .

Reduce the expression by cancelling the common factors.

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Rewrite as .

By the Power Rule, the integral of with respect to is .

Write as a fraction with denominator .

Multiply and .

Simplify.

Write as a fraction with denominator .

Multiply and .

Multiply by .

Replace all occurrences of with .

Simplify each term.

Factor.

Apply the product rule to .

Remove unnecessary parentheses.

Move to the numerator using the negative exponent rule .

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

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.

Multiply by .

Add and .