Optimal. Leaf size=27 \[ \log \left (8 \left (5+\frac {x+\frac {1}{4} (-4+2 x+x \log (4))}{4 x^2}\right )\right ) \]
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Rubi [A] time = 0.06, antiderivative size = 20, normalized size of antiderivative = 0.74, number of steps used = 6, number of rules used = 4, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.121, Rules used = {6, 1594, 800, 628} \begin {gather*} \log \left (-80 x^2-x (6+\log (4))+4\right )-2 \log (x) \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 628
Rule 800
Rule 1594
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {8+x (-6-\log (4))}{-4 x+6 x^2+80 x^3+x^2 \log (4)} \, dx\\ &=\int \frac {8+x (-6-\log (4))}{-4 x+80 x^3+x^2 (6+\log (4))} \, dx\\ &=\int \frac {8+x (-6-\log (4))}{x \left (-4+80 x^2+x (6+\log (4))\right )} \, dx\\ &=\int \left (-\frac {2}{x}+\frac {-6-160 x-\log (4)}{4-80 x^2-x (6+\log (4))}\right ) \, dx\\ &=-2 \log (x)+\int \frac {-6-160 x-\log (4)}{4-80 x^2+x (-6-\log (4))} \, dx\\ &=-2 \log (x)+\log \left (4-80 x^2-x (6+\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 21, normalized size = 0.78 \begin {gather*} -2 \log (x)+\log \left (4-6 x-80 x^2-x \log (4)\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.76, size = 20, normalized size = 0.74 \begin {gather*} \log \left (40 \, x^{2} + x \log \relax (2) + 3 \, x - 2\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.22, size = 22, normalized size = 0.81 \begin {gather*} \log \left ({\left | 40 \, x^{2} + x \log \relax (2) + 3 \, x - 2 \right |}\right ) - 2 \, \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 = 0.07, size = 20, normalized size = 0.74
method | result | size |
risch | \(-2 \ln \relax (x )+\ln \left (-2+40 x^{2}+x \left (3+\ln \relax (2)\right )\right )\) | \(20\) |
default | \(-2 \ln \relax (x )+\ln \left (x \ln \relax (2)+40 x^{2}+3 x -2\right )\) | \(21\) |
norman | \(-2 \ln \relax (x )+\ln \left (x \ln \relax (2)+40 x^{2}+3 x -2\right )\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.35, size = 19, normalized size = 0.70 \begin {gather*} \log \left (40 \, x^{2} + x {\left (\log \relax (2) + 3\right )} - 2\right ) - 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.00, size = 21, normalized size = 0.78 \begin {gather*} \ln \left (6-3\,x\,\ln \relax (2)-120\,x^2-9\,x\right )-2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.41, size = 22, normalized size = 0.81 \begin {gather*} - 2 \log {\relax (x )} + \log {\left (x^{2} + x \left (\frac {\log {\relax (2 )}}{40} + \frac {3}{40}\right ) - \frac {1}{20} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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