Integration of Rational Functions Practice Problems Online

Given \(\displaystyle{f(x) = \int \frac{2x + 49}{x^2+9x+14} dx}\) and \(f(0) = 1,\) find the function \(f(x).\)

\[7\ln \lvert \frac{x+2}{2} \rvert + 5\ln \lvert \frac{7}{x+7} \rvert +1\] \[9\ln \lvert \frac{x+2}{2} \rvert + 7\ln \lvert \frac{7}{x+7} \rvert +1\] \[8\ln \lvert \frac{x+2}{2} \rvert + 6\ln \lvert \frac{7}{x+7} \rvert +1\] \[10\ln \lvert \frac{x+2}{2} \rvert + 8\ln \lvert \frac{7}{x+7} \rvert +1\]

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Evaluate \[\int_{1}^{8} \frac{4}{x^3} dx .\]

\[\frac{65}{32}\] \[\frac{251}{128}\] \[\frac{31}{8}\] \[\frac{63}{32}\]

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If \(\displaystyle{f(x) = \int \frac{8x-9}{(x-3)(x-8)} dx},\) what is \(f(5)-f(1)?\)

\[11 \ln \frac{3}{7}\] \[11 \ln \frac{3}{8}\] \[11 \ln \frac{4}{7}\] \[11 \ln \frac{1}{3}\]

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If \(\displaystyle{f(x)=\int \frac{38x-2}{19x^2-2x-2e}dx}\) and \(f(0)=1+\ln 2-\ln 19,\) what is the value of \(f(-e)?\)

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Evaluate the indefinite integral \[\int \frac{x^2+17}{x-3}dx.\] (Use \(C\) as the constant of integration.)

\[\frac{1}{2}x^2+3x+26\ln \lvert{x-3}\rvert+C \] \[x^2+3x+26\ln \lvert{x-3}\rvert+C \] \[\frac{1}{2}x^2-3x-26\ln \lvert{x-3}\rvert+C \] \[\frac{1}{2}x^2+26\ln \lvert{x-3}\rvert+C \]

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Learn from a vibrant community of students and enthusiasts,
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Master advanced concepts through explanations,
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Learn from a vibrant community of students and enthusiasts,
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Master advanced concepts through explanations,
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Learn from a vibrant community of students and enthusiasts,
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Master advanced concepts through explanations,
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Learn from a vibrant community of students and enthusiasts,
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Learn from a vibrant community of students and enthusiasts,
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Learn from a vibrant community of students and enthusiasts,
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