Optimal. Leaf size=23 \[ 5 x \log (3) \log \left (3+\log \left (\frac {1}{2} \left (-10-\frac {3}{x^2}-x\right )\right )\right ) \]
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Rubi [F]
time = 0.83, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps
used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {}
\begin {gather*} \int \frac {\left (-30+5 x^3\right ) \log (3)+\left (\left (45+150 x^2+15 x^3\right ) \log (3)+\left (15+50 x^2+5 x^3\right ) \log (3) \log \left (\frac {-3-10 x^2-x^3}{2 x^2}\right )\right ) \log \left (3+\log \left (\frac {-3-10 x^2-x^3}{2 x^2}\right )\right )}{9+30 x^2+3 x^3+\left (3+10 x^2+x^3\right ) \log \left (\frac {-3-10 x^2-x^3}{2 x^2}\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {5 \log (3) \left (-6+x^3+\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )\right )}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx\\ &=(5 \log (3)) \int \frac {-6+x^3+\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx\\ &=(5 \log (3)) \int \left (\frac {-6+x^3}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )}+\log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )\right ) \, dx\\ &=(5 \log (3)) \int \frac {-6+x^3}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx+(5 \log (3)) \int \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \, dx\\ &=(5 \log (3)) \int \left (\frac {1}{3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )}+\frac {-9-10 x^2}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )}\right ) \, dx+(5 \log (3)) \int \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \, dx\\ &=(5 \log (3)) \int \frac {1}{3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )} \, dx+(5 \log (3)) \int \frac {-9-10 x^2}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx+(5 \log (3)) \int \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \, dx\\ &=(5 \log (3)) \int \frac {1}{3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )} \, dx+(5 \log (3)) \int \left (-\frac {9}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )}-\frac {10 x^2}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )}\right ) \, dx+(5 \log (3)) \int \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \, dx\\ &=(5 \log (3)) \int \frac {1}{3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )} \, dx+(5 \log (3)) \int \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \, dx-(45 \log (3)) \int \frac {1}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx-(50 \log (3)) \int \frac {x^2}{\left (3+10 x^2+x^3\right ) \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 23, normalized size = 1.00 \begin {gather*} 5 x \log (3) \log \left (3+\log \left (-5-\frac {3}{2 x^2}-\frac {x}{2}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 0.29, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (5 x^{3}+50 x^{2}+15\right ) \ln \left (3\right ) \ln \left (\frac {-x^{3}-10 x^{2}-3}{2 x^{2}}\right )+\left (15 x^{3}+150 x^{2}+45\right ) \ln \left (3\right )\right ) \ln \left (\ln \left (\frac {-x^{3}-10 x^{2}-3}{2 x^{2}}\right )+3\right )+\left (5 x^{3}-30\right ) \ln \left (3\right )}{\left (x^{3}+10 x^{2}+3\right ) \ln \left (\frac {-x^{3}-10 x^{2}-3}{2 x^{2}}\right )+3 x^{3}+30 x^{2}+9}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 29, normalized size = 1.26 \begin {gather*} 5 \, x \log \left (3\right ) \log \left (-\log \left (2\right ) + \log \left (-x^{3} - 10 \, x^{2} - 3\right ) - 2 \, \log \left (x\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 24, normalized size = 1.04 \begin {gather*} 5 \, x \log \left (3\right ) \log \left (\log \left (-\frac {x^{3} + 10 \, x^{2} + 3}{2 \, x^{2}}\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [B] Leaf count of result is larger than twice the leaf count of optimal. 66 vs.
\(2 (24) = 48\).
time = 0.53, size = 66, normalized size = 2.87 \begin {gather*} \left (5 x \log {\left (3 \right )} + \frac {5 \log {\left (3 \right )}}{2}\right ) \log {\left (\log {\left (\frac {- \frac {x^{3}}{2} - 5 x^{2} - \frac {3}{2}}{x^{2}} \right )} + 3 \right )} - \frac {5 \log {\left (3 \right )} \log {\left (\log {\left (\frac {- \frac {x^{3}}{2} - 5 x^{2} - \frac {3}{2}}{x^{2}} \right )} + 3 \right )}}{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.66, size = 24, normalized size = 1.04 \begin {gather*} 5 \, x \log \left (3\right ) \log \left (\log \left (-\frac {x^{3} + 10 \, x^{2} + 3}{2 \, x^{2}}\right ) + 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.53, size = 26, normalized size = 1.13 \begin {gather*} 5\,x\,\ln \left (\ln \left (-\frac {\frac {x^3}{2}+5\,x^2+\frac {3}{2}}{x^2}\right )+3\right )\,\ln \left (3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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