Calculus Examples

Evaluate the Integral
Let . Then , so . Rewrite using and .
Combine fractions.
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Write as a fraction with denominator .
Multiply and .
Since is constant with respect to , the integral of with respect to is .
By the Power Rule, the integral of with respect to is .
Simplify the answer.
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Write as a fraction with denominator .
Multiply and .
Simplify.
Multiply and .
Multiply by .
Replace all occurrences of with .
Simplify each term.
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Simplify the numerator.
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Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Apply the product rule to .
Reorder terms.
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