Optimal. Leaf size=33 \[ \frac {-e^5 \left (4+\frac {12 \log (3)}{x}\right )+\log \left (\frac {1}{25} (-\log (4)+\log (5))^2\right )}{x} \]
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Rubi [A] time = 0.01, antiderivative size = 41, normalized size of antiderivative = 1.24, number of steps used = 2, number of rules used = 2, integrand size = 41, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.049, Rules used = {6, 37} \begin {gather*} -\frac {\left (x \left (4 e^5+\log (25)-2 \log \left (\log \left (\frac {5}{4}\right )\right )\right )+24 e^5 \log (3)\right )^2}{48 e^5 x^2 \log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 37
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {24 e^5 \log (3)+x \left (4 e^5-\log \left (\frac {1}{25} \left (\log ^2(4)-2 \log (4) \log (5)+\log ^2(5)\right )\right )\right )}{x^3} \, dx\\ &=-\frac {\left (24 e^5 \log (3)+x \left (4 e^5+\log (25)-2 \log \left (\log \left (\frac {5}{4}\right )\right )\right )\right )^2}{48 e^5 x^2 \log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 29, normalized size = 0.88 \begin {gather*} -\frac {2 e^5 (2 x+\log (729))+x \left (\log (25)-2 \log \left (\log \left (\frac {5}{4}\right )\right )\right )}{x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.77, size = 40, normalized size = 1.21 \begin {gather*} -\frac {4 \, x e^{5} + 12 \, e^{5} \log \relax (3) - x \log \left (\frac {1}{25} \, \log \relax (5)^{2} - \frac {4}{25} \, \log \relax (5) \log \relax (2) + \frac {4}{25} \, \log \relax (2)^{2}\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.27, size = 40, normalized size = 1.21 \begin {gather*} -\frac {4 \, x e^{5} + 12 \, e^{5} \log \relax (3) - x \log \left (\frac {1}{25} \, \log \relax (5)^{2} - \frac {4}{25} \, \log \relax (5) \log \relax (2) + \frac {4}{25} \, \log \relax (2)^{2}\right )}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 33, normalized size = 1.00
method | result | size |
risch | \(\frac {\left (-2 \ln \relax (5)+2 \ln \left (\ln \relax (5)-2 \ln \relax (2)\right )-4 \,{\mathrm e}^{5}\right ) x -12 \,{\mathrm e}^{5} \ln \relax (3)}{x^{2}}\) | \(33\) |
gosper | \(-\frac {12 \,{\mathrm e}^{5} \ln \relax (3)+4 x \,{\mathrm e}^{5}-x \ln \left (\frac {\ln \relax (5)^{2}}{25}-\frac {4 \ln \relax (2) \ln \relax (5)}{25}+\frac {4 \ln \relax (2)^{2}}{25}\right )}{x^{2}}\) | \(41\) |
norman | \(\frac {\left (-2 \ln \relax (5)+\ln \left (\ln \relax (5)^{2}-4 \ln \relax (2) \ln \relax (5)+4 \ln \relax (2)^{2}\right )-4 \,{\mathrm e}^{5}\right ) x -12 \,{\mathrm e}^{5} \ln \relax (3)}{x^{2}}\) | \(41\) |
default | \(-\frac {12 \,{\mathrm e}^{5} \ln \relax (3)}{x^{2}}-\frac {-\ln \left (\frac {\ln \relax (5)^{2}}{25}-\frac {4 \ln \relax (2) \ln \relax (5)}{25}+\frac {4 \ln \relax (2)^{2}}{25}\right )+4 \,{\mathrm e}^{5}}{x}\) | \(43\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 41, normalized size = 1.24 \begin {gather*} -\frac {x {\left (4 \, e^{5} - \log \left (\frac {1}{25} \, \log \relax (5)^{2} - \frac {4}{25} \, \log \relax (5) \log \relax (2) + \frac {4}{25} \, \log \relax (2)^{2}\right )\right )} + 12 \, e^{5} \log \relax (3)}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 39, normalized size = 1.18 \begin {gather*} \frac {\ln \left (\frac {4\,{\ln \relax (2)}^2}{25}-\frac {4\,\ln \relax (2)\,\ln \relax (5)}{25}+\frac {{\ln \relax (5)}^2}{25}\right )-4\,{\mathrm {e}}^5}{x}-\frac {12\,{\mathrm {e}}^5\,\ln \relax (3)}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.24, size = 44, normalized size = 1.33 \begin {gather*} \frac {x \left (- 4 e^{5} - 2 \log {\relax (5 )} + \log {\left (- 4 \log {\relax (2 )} \log {\relax (5 )} + 4 \log {\relax (2 )}^{2} + \log {\relax (5 )}^{2} \right )}\right ) - 12 e^{5} \log {\relax (3 )}}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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