Optimal. Leaf size=23 \[ 4 \left (\log (x)+\log \left (-4+x+\frac {x^2}{1+x+2 (8+x)}\right )\right ) \]
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Rubi [A] time = 0.05, antiderivative size = 26, normalized size of antiderivative = 1.13, number of steps used = 3, number of rules used = 2, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.054, Rules used = {2074, 628} \begin {gather*} 4 \log \left (-4 x^2-5 x+68\right )+4 \log (x)-4 \log (3 x+17) \end {gather*}
Antiderivative was successfully verified.
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Rule 628
Rule 2074
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {4}{x}-\frac {12}{17+3 x}+\frac {4 (5+8 x)}{-68+5 x+4 x^2}\right ) \, dx\\ &=4 \log (x)-4 \log (17+3 x)+4 \int \frac {5+8 x}{-68+5 x+4 x^2} \, dx\\ &=4 \log (x)-4 \log (17+3 x)+4 \log \left (68-5 x-4 x^2\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 26, normalized size = 1.13 \begin {gather*} 4 \log (x)-4 \log (17+3 x)+4 \log \left (68-5 x-4 x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.71, size = 26, normalized size = 1.13 \begin {gather*} 4 \, \log \left (4 \, x^{3} + 5 \, x^{2} - 68 \, x\right ) - 4 \, \log \left (3 \, x + 17\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 29, normalized size = 1.26 \begin {gather*} 4 \, \log \left ({\left | 4 \, x^{2} + 5 \, x - 68 \right |}\right ) - 4 \, \log \left ({\left | 3 \, x + 17 \right |}\right ) + 4 \, \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 27, normalized size = 1.17
method | result | size |
default | \(-4 \ln \left (17+3 x \right )+4 \ln \relax (x )+4 \ln \left (4 x^{2}+5 x -68\right )\) | \(27\) |
norman | \(-4 \ln \left (17+3 x \right )+4 \ln \relax (x )+4 \ln \left (4 x^{2}+5 x -68\right )\) | \(27\) |
risch | \(-4 \ln \left (17+3 x \right )+4 \ln \left (4 x^{3}+5 x^{2}-68 x \right )\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 26, normalized size = 1.13 \begin {gather*} 4 \, \log \left (4 \, x^{2} + 5 \, x - 68\right ) - 4 \, \log \left (3 \, x + 17\right ) + 4 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.28, size = 22, normalized size = 0.96 \begin {gather*} 4\,\ln \left (x\,\left (4\,x^2+5\,x-68\right )\right )-4\,\ln \left (x+\frac {17}{3}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 24, normalized size = 1.04 \begin {gather*} - 4 \log {\left (3 x + 17 \right )} + 4 \log {\left (4 x^{3} + 5 x^{2} - 68 x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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