# Calculus Examples

Integrate by parts using the formula , where and .
Combine fractions.
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.
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 .
Combine fractions.
Write as a fraction with denominator .
Multiply and to get .
Since is constant with respect to , the integral of with respect to is .
Combine fractions.
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 .