Optimal. Leaf size=19 \[ \frac {-10+\log (4)}{\frac {4 x^2}{3}-\log (5)} \]
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Rubi [A] time = 0.01, antiderivative size = 20, normalized size of antiderivative = 1.05, number of steps used = 4, number of rules used = 4, integrand size = 31, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.129, Rules used = {6, 12, 28, 261} \begin {gather*} -\frac {3 (10-\log (4))}{4 x^2-3 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 12
Rule 28
Rule 261
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x (240-24 \log (4))}{16 x^4-24 x^2 \log (5)+9 \log ^2(5)} \, dx\\ &=(24 (10-\log (4))) \int \frac {x}{16 x^4-24 x^2 \log (5)+9 \log ^2(5)} \, dx\\ &=(384 (10-\log (4))) \int \frac {x}{\left (16 x^2-12 \log (5)\right )^2} \, dx\\ &=-\frac {3 (10-\log (4))}{4 x^2-3 \log (5)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.00, size = 18, normalized size = 0.95 \begin {gather*} \frac {3 (-10+\log (4))}{4 x^2-3 \log (5)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.11, size = 18, normalized size = 0.95 \begin {gather*} \frac {6 \, {\left (\log \relax (2) - 5\right )}}{4 \, x^{2} - 3 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.99, size = 37, normalized size = 1.95 \begin {gather*} \frac {6 \, {\left (\log \relax (2)^{2} - 10 \, \log \relax (2) + 25\right )}}{4 \, x^{2} \log \relax (2) - 20 \, x^{2} - 3 \, \log \relax (5) \log \relax (2) + 15 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 19, normalized size = 1.00
method | result | size |
gosper | \(-\frac {6 \left (\ln \relax (2)-5\right )}{-4 x^{2}+3 \ln \relax (5)}\) | \(19\) |
default | \(\frac {-30+6 \ln \relax (2)}{-3 \ln \relax (5)+4 x^{2}}\) | \(19\) |
norman | \(\frac {30-6 \ln \relax (2)}{-4 x^{2}+3 \ln \relax (5)}\) | \(20\) |
risch | \(-\frac {2 \ln \relax (2)}{-\frac {4 x^{2}}{3}+\ln \relax (5)}+\frac {10}{-\frac {4 x^{2}}{3}+\ln \relax (5)}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.51, size = 18, normalized size = 0.95 \begin {gather*} \frac {6 \, {\left (\log \relax (2) - 5\right )}}{4 \, x^{2} - 3 \, \log \relax (5)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.42, size = 113, normalized size = 5.95 \begin {gather*} -\frac {30\,\mathrm {atanh}\left (\frac {4\,x^2\,\sqrt {3\,\ln \relax (5)+\ln \left (125\right )}\,\sqrt {3\,\ln \relax (5)-\ln \left (125\right )}}{12\,x^2\,\ln \relax (5)-{\ln \left (125\right )}^2}\right )-2\,\ln \relax (8)\,\mathrm {atanh}\left (\frac {4\,x^2\,\sqrt {3\,\ln \relax (5)+\ln \left (125\right )}\,\sqrt {3\,\ln \relax (5)-\ln \left (125\right )}}{12\,x^2\,\ln \relax (5)-{\ln \left (125\right )}^2}\right )}{\sqrt {3\,\ln \relax (5)+\ln \left (125\right )}\,\sqrt {3\,\ln \relax (5)-\ln \left (125\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 17, normalized size = 0.89 \begin {gather*} - \frac {240 - 48 \log {\relax (2 )}}{32 x^{2} - 24 \log {\relax (5 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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