Optimal. Leaf size=28 \[ \left (-\frac {1}{x}+x \log \left (5+\frac {1}{5} \left (\frac {1}{8 \log (3)}+\log (5)\right )\right )\right )^2 \]
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Rubi [A] time = 0.01, antiderivative size = 27, normalized size of antiderivative = 0.96, number of steps used = 2, number of rules used = 1, integrand size = 34, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {14} \begin {gather*} \frac {1}{x^2}+x^2 \log ^2\left (5+\frac {1}{40 \log (3)}+\frac {\log (5)}{5}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 14
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {2}{x^3}+2 x \log ^2\left (5+\frac {1}{40 \log (3)}+\frac {\log (5)}{5}\right )\right ) \, dx\\ &=\frac {1}{x^2}+x^2 \log ^2\left (5+\frac {1}{40 \log (3)}+\frac {\log (5)}{5}\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 27, normalized size = 0.96 \begin {gather*} \frac {1}{x^2}+x^2 \log ^2\left (5+\frac {1}{40 \log (3)}+\frac {\log (5)}{5}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.61, size = 31, normalized size = 1.11 \begin {gather*} \frac {x^{4} \log \left (\frac {8 \, \log \relax (5) \log \relax (3) + 200 \, \log \relax (3) + 1}{40 \, \log \relax (3)}\right )^{2} + 1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.13, size = 29, normalized size = 1.04 \begin {gather*} x^{2} \log \left (\frac {8 \, \log \relax (5) \log \relax (3) + 200 \, \log \relax (3) + 1}{40 \, \log \relax (3)}\right )^{2} + \frac {1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 30, normalized size = 1.07
method | result | size |
default | \(\ln \left (\frac {8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1}{40 \ln \relax (3)}\right )^{2} x^{2}+\frac {1}{x^{2}}\) | \(30\) |
gosper | \(\frac {x^{4} \ln \left (\frac {8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1}{40 \ln \relax (3)}\right )^{2}+1}{x^{2}}\) | \(32\) |
norman | \(\frac {1+\left (\ln \left (40\right )^{2}-2 \ln \left (40\right ) \ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right )+2 \ln \left (40\right ) \ln \left (\ln \relax (3)\right )+\ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right )^{2}-2 \ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right ) \ln \left (\ln \relax (3)\right )+\ln \left (\ln \relax (3)\right )^{2}\right ) x^{4}}{x^{2}}\) | \(78\) |
risch | \(\ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right )^{2} x^{2}-6 \ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right ) \ln \relax (2) x^{2}-2 \ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right ) \ln \relax (5) x^{2}-2 \ln \left (8 \ln \relax (3) \ln \relax (5)+200 \ln \relax (3)+1\right ) \ln \left (\ln \relax (3)\right ) x^{2}+9 x^{2} \ln \relax (2)^{2}+6 x^{2} \ln \relax (2) \ln \relax (5)+6 \ln \relax (2) \ln \left (\ln \relax (3)\right ) x^{2}+x^{2} \ln \relax (5)^{2}+2 \ln \relax (5) \ln \left (\ln \relax (3)\right ) x^{2}+\ln \left (\ln \relax (3)\right )^{2} x^{2}+\frac {1}{x^{2}}\) | \(140\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 29, normalized size = 1.04 \begin {gather*} x^{2} \log \left (\frac {8 \, \log \relax (5) \log \relax (3) + 200 \, \log \relax (3) + 1}{40 \, \log \relax (3)}\right )^{2} + \frac {1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.09, size = 47, normalized size = 1.68 \begin {gather*} x^2\,\left ({\ln \left (5\,\ln \relax (3)+\frac {\ln \relax (3)\,\ln \relax (5)}{5}+\frac {1}{40}\right )}^2-2\,\ln \left (5\,\ln \relax (3)+\frac {\ln \relax (3)\,\ln \relax (5)}{5}+\frac {1}{40}\right )\,\ln \left (\ln \relax (3)\right )+{\ln \left (\ln \relax (3)\right )}^2\right )+\frac {1}{x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.12, size = 60, normalized size = 2.14 \begin {gather*} x^{2} \left (- 2 \log {\left (\frac {1}{40} + \frac {\log {\relax (3 )} \log {\relax (5 )}}{5} + 5 \log {\relax (3 )} \right )} \log {\left (\log {\relax (3 )} \right )} + \log {\left (\log {\relax (3 )} \right )}^{2} + \log {\left (\frac {1}{40} + \frac {\log {\relax (3 )} \log {\relax (5 )}}{5} + 5 \log {\relax (3 )} \right )}^{2}\right ) + \frac {1}{x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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