# Calculus Examples

Integrate by parts using the formula , where and .

Write as a fraction with denominator .

Multiply and to get .

Write as a fraction with denominator .

Multiply and to get .

Write as a fraction with denominator .

Multiply and to get .

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

Multiply by to get .

Multiply by to get .

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 to get .

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

Multiply and to get .

Multiply by to get .

The integral of with respect to is .

Rewrite as .

Replace all occurrences of with .

Reorder terms.

Remove parentheses around .

Remove parentheses around .