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Express rational functions as a sum of fractions with simpler denominators. You can apply this to telescoping series to mass cancel terms in a seemingly complicated sum.
Evaluate \[\int_6^{18}\frac{6x^2}{x^3+15x^2+72x+108}dx.\]
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What is \[\int\frac{1}{x^2+7x+6}dx?\]
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Suppose that \(f(x)\) is a function whose derivative is \[f'(x)=\frac{1}{x^2-2x}\] and that \(f(-2)=\frac{1}{2}\ln2.\) What is the value of \(f(8)?\)
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What is \[\int\frac{x+6}{x^2-9x+20}dx?\]
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What is \[\int\frac{1}{x^2-16}dx?\]
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