This gives us the equation " title="Rendered by QuickLaTeX.com"/>First, we can find the values of and by evaluating at and , r" />

Evaluate Integral 8X^2/(X^3+2)^3, Find The Integral 8X^3

Since the denominator is already factored into linear terms we can proceed directly with the partial fraction decomposition. We write,

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This gives us the equation

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First, we can find the values of and by evaluating at

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and

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, respectively. This gives us

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Then using these values of and we evaluate at

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and

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(these are just convenient values, there isn’t anything special about them) to obtain the two equations

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Solving these two equations we obtain

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and

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. Therefore, we have the following partial fraction decomposition:

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We can now evaluate the integral,

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If you are having trouble with math proofs a great book to learn from is How to Prove It by Daniel Velleman:

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A really awesome book that I highly recommend on how to study math and be a math major is Laura Alcock”s, How to Study as a Mathematics Major:

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