Optimal. Leaf size=23 \[ -x+\frac {x^2}{\log ^2\left (\frac {3}{11} \log \left (\frac {4}{x^2}+x\right )\right )} \]
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Rubi [F] time = 2.33, 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 {16 x-2 x^4+\left (8 x+2 x^4\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log \left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )+\left (-4-x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}{\left (4+x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\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 \left (-1-\frac {2 x \left (-8+x^3\right )}{\left (4+x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}+\frac {2 x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}\right ) \, dx\\ &=-x-2 \int \frac {x \left (-8+x^3\right )}{\left (4+x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx+2 \int \frac {x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx\\ &=-x-2 \int \left (\frac {x}{\log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}+\frac {12 x}{\left (-4-x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}\right ) \, dx+2 \int \frac {x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx\\ &=-x-2 \int \frac {x}{\log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx+2 \int \frac {x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx-24 \int \frac {x}{\left (-4-x^3\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx\\ &=-x-2 \int \frac {x}{\log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx+2 \int \frac {x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx-24 \int \left (\frac {1}{3\ 2^{2/3} \left (2^{2/3}+x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}+\frac {\left (-\frac {1}{2}\right )^{2/3}}{3 \left (2^{2/3}-\sqrt [3]{-1} x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}-\frac {\sqrt [3]{-1}}{3\ 2^{2/3} \left (2^{2/3}+(-1)^{2/3} x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )}\right ) \, dx\\ &=-x-2 \int \frac {x}{\log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx+2 \int \frac {x}{\log ^2\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx+\left (4 \sqrt [3]{-2}\right ) \int \frac {1}{\left (2^{2/3}+(-1)^{2/3} x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx-\left (4 \sqrt [3]{2}\right ) \int \frac {1}{\left (2^{2/3}+x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx-\left (4 (-1)^{2/3} \sqrt [3]{2}\right ) \int \frac {1}{\left (2^{2/3}-\sqrt [3]{-1} x\right ) \log \left (\frac {4+x^3}{x^2}\right ) \log ^3\left (\frac {3}{11} \log \left (\frac {4+x^3}{x^2}\right )\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.57, size = 23, normalized size = 1.00 \begin {gather*} -x+\frac {x^2}{\log ^2\left (\frac {3}{11} \log \left (\frac {4}{x^2}+x\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.58, size = 40, normalized size = 1.74 \begin {gather*} -\frac {x \log \left (\frac {3}{11} \, \log \left (\frac {x^{3} + 4}{x^{2}}\right )\right )^{2} - x^{2}}{\log \left (\frac {3}{11} \, \log \left (\frac {x^{3} + 4}{x^{2}}\right )\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 4.54, size = 1412, normalized size = 61.39 result too large to display
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.08, size = 0, normalized size = 0.00 \[\int \frac {\left (-x^{3}-4\right ) \ln \left (\frac {x^{3}+4}{x^{2}}\right ) \ln \left (\frac {3 \ln \left (\frac {x^{3}+4}{x^{2}}\right )}{11}\right )^{3}+\left (2 x^{4}+8 x \right ) \ln \left (\frac {x^{3}+4}{x^{2}}\right ) \ln \left (\frac {3 \ln \left (\frac {x^{3}+4}{x^{2}}\right )}{11}\right )-2 x^{4}+16 x}{\left (x^{3}+4\right ) \ln \left (\frac {x^{3}+4}{x^{2}}\right ) \ln \left (\frac {3 \ln \left (\frac {x^{3}+4}{x^{2}}\right )}{11}\right )^{3}}\, dx\]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.55, size = 114, normalized size = 4.96 \begin {gather*} \frac {2 \, x {\left (\log \left (11\right ) - \log \relax (3)\right )} \log \left (\log \left (x^{3} + 4\right ) - 2 \, \log \relax (x)\right ) - x \log \left (\log \left (x^{3} + 4\right ) - 2 \, \log \relax (x)\right )^{2} - {\left (\log \left (11\right )^{2} - 2 \, \log \left (11\right ) \log \relax (3) + \log \relax (3)^{2}\right )} x + x^{2}}{\log \left (11\right )^{2} - 2 \, \log \left (11\right ) \log \relax (3) + \log \relax (3)^{2} - 2 \, {\left (\log \left (11\right ) - \log \relax (3)\right )} \log \left (\log \left (x^{3} + 4\right ) - 2 \, \log \relax (x)\right ) + \log \left (\log \left (x^{3} + 4\right ) - 2 \, \log \relax (x)\right )^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.12, size = 254, normalized size = 11.04 \begin {gather*} \frac {x^2}{{\ln \left (\frac {3\,\ln \left (\frac {1}{x^2}\right )}{11}+\frac {3\,\ln \left (x^3+4\right )}{11}\right )}^2}-x+\frac {4\,x^2\,\ln \left (\frac {1}{x^2}\right )}{x^3-8}+\frac {x^5\,\ln \left (\frac {1}{x^2}\right )}{x^3-8}+\frac {4\,x^2\,\ln \left (x^3+4\right )}{x^3-8}+\frac {x^5\,\ln \left (x^3+4\right )}{x^3-8}-\frac {256\,x^2\,\ln \left (\frac {1}{x^2}\right )}{x^9-24\,x^6+192\,x^3-512}+\frac {12\,x^8\,\ln \left (\frac {1}{x^2}\right )}{x^9-24\,x^6+192\,x^3-512}-\frac {x^{11}\,\ln \left (\frac {1}{x^2}\right )}{x^9-24\,x^6+192\,x^3-512}-\frac {256\,x^2\,\ln \left (x^3+4\right )}{x^9-24\,x^6+192\,x^3-512}+\frac {12\,x^8\,\ln \left (x^3+4\right )}{x^9-24\,x^6+192\,x^3-512}-\frac {x^{11}\,\ln \left (x^3+4\right )}{x^9-24\,x^6+192\,x^3-512} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.46, size = 20, normalized size = 0.87 \begin {gather*} \frac {x^{2}}{\log {\left (\frac {3 \log {\left (\frac {x^{3} + 4}{x^{2}} \right )}}{11} \right )}^{2}} - x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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