# Calculus Examples

Evaluate the Integral
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 .
By the Power Rule, the integral of with respect to is .
Write as a fraction with denominator .
Multiply and to get .
Simplify.
Multiply and to get .
Multiply by to get .
Replace all occurrences of with .
Simplify each term.
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Reorder terms.

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