Calculus Examples

Divide by .
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Factor the numerator and denominator of .
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Rewrite as .
Since both terms are perfect cubes, factor using the difference of cubes formula, where and .
Simplify.
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Multiply by .
One to any power is one.
Write the fraction using partial fraction decomposition.
Simplify.
Split the single integral into multiple integrals.
Since is constant with respect to , move out of the integral.
Let . Then . 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 .
The integral of with respect to is .
Since is constant with respect to , move out of the integral.
Since is constant with respect to , move out of 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 .
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 .
The integral of with respect to is .
Simplify.
Substitute back in for each integration substitution variable.
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Replace all occurrences of with .
Replace all occurrences of with .
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