Optimal. Leaf size=27 \[ \frac {x^2}{\log \left (\frac {x}{3}-\log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )} \]
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Rubi [F]
time = 3.30, 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 {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^3-x \log \left (\frac {16}{5}\right )+\left (-3 x^2+3 \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\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 {3 x^3-x^4+\left (3 x+x^2\right ) \log \left (\frac {16}{5}\right )+\left (2 x^4-2 x^2 \log \left (\frac {16}{5}\right )+\left (-6 x^3+6 x \log \left (\frac {16}{5}\right )\right ) \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log \left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (\frac {x^2-\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=\int \left (-\frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {2 x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x \left (-3 x^2+x^3-3 \log \left (\frac {16}{5}\right )-x \log \left (\frac {16}{5}\right )\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \left (-\frac {3 x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}-\frac {6 x \log \left (\frac {16}{5}\right )}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \frac {x}{\left (x^2-\log \left (\frac {16}{5}\right )\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (6 \log \left (\frac {16}{5}\right )\right ) \int \left (-\frac {1}{2 \left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}+\frac {1}{2 \left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )}\right ) \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ &=2 \int \frac {x}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+3 \int \frac {x}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (-x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx+\left (3 \log \left (\frac {16}{5}\right )\right ) \int \frac {1}{\left (x+\sqrt {\log \left (\frac {16}{5}\right )}\right ) \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx-\int \frac {x^2}{\left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right ) \log ^2\left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.04, size = 27, normalized size = 1.00 \begin {gather*} \frac {x^2}{\log \left (\frac {1}{3} \left (x-3 \log \left (x-\frac {\log \left (\frac {16}{5}\right )}{x}\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Maple [F]
time = 1.29, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (6 x \ln \left (\frac {16}{5}\right )-6 x^{3}\right ) \ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )-2 x^{2} \ln \left (\frac {16}{5}\right )+2 x^{4}\right ) \ln \left (-\ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )+\frac {x}{3}\right )+\left (x^{2}+3 x \right ) \ln \left (\frac {16}{5}\right )-x^{4}+3 x^{3}}{\left (\left (3 \ln \left (\frac {16}{5}\right )-3 x^{2}\right ) \ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )-x \ln \left (\frac {16}{5}\right )+x^{3}\right ) \ln \left (-\ln \left (\frac {-\ln \left (\frac {16}{5}\right )+x^{2}}{x}\right )+\frac {x}{3}\right )^{2}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.55, size = 32, normalized size = 1.19 \begin {gather*} -\frac {x^{2}}{\log \left (3\right ) - \log \left (x - 3 \, \log \left (x^{2} + \log \left (5\right ) - 4 \, \log \left (2\right )\right ) + 3 \, \log \left (x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 26, normalized size = 0.96 \begin {gather*} \frac {x^{2}}{\log \left (\frac {1}{3} \, x - \log \left (\frac {x^{2} - \log \left (\frac {16}{5}\right )}{x}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.30, size = 19, normalized size = 0.70 \begin {gather*} \frac {x^{2}}{\log {\left (\frac {x}{3} - \log {\left (\frac {x^{2} - \log {\left (\frac {16}{5} \right )}}{x} \right )} \right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 1559 vs.
\(2 (23) = 46\).
time = 1.09, size = 1559, normalized size = 57.74 \begin {gather*} \text {Too large to display} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [F]
time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )\,\left (2\,x^4-2\,x^2\,\ln \left (\frac {16}{5}\right )+\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (6\,x\,\ln \left (\frac {16}{5}\right )-6\,x^3\right )\right )+3\,x^3-x^4+\ln \left (\frac {16}{5}\right )\,\left (x^2+3\,x\right )}{{\ln \left (\frac {x}{3}-\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\right )}^2\,\left (\ln \left (-\frac {\ln \left (\frac {16}{5}\right )-x^2}{x}\right )\,\left (3\,\ln \left (\frac {16}{5}\right )-3\,x^2\right )-x\,\ln \left (\frac {16}{5}\right )+x^3\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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