Calculus Examples

Evaluate the Integral
Let . Then , so . Rewrite using and .
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Let . Find .
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Differentiate .
By the Sum Rule, the derivative of with respect to is .
Differentiate using the Power Rule which states that is where .
Since is constant with respect to , the derivative of with respect to is .
Add and .
Rewrite the problem using and .
Combine and .
Since is constant with respect to , move out of the integral.
By the Power Rule, the integral of with respect to is .
Simplify.
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Simplify.
Combine fractions.
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Combine and .
Multiply and .
Multiply by .
Replace all occurrences of with .
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