Optimal. Leaf size=28 \[ \frac {1}{3} \left (x^2+\frac {x}{-1+\frac {10}{x^2}+\log \left (e^{x^4} \log (x)\right )}\right ) \]
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Rubi [F] time = 1.01, 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 {-x^4+\left (200 x+30 x^2-40 x^3-x^4+2 x^5-4 x^8\right ) \log (x)+\left (40 x^3+x^4-4 x^5\right ) \log (x) \log \left (e^{x^4} \log (x)\right )+2 x^5 \log (x) \log ^2\left (e^{x^4} \log (x)\right )}{\left (300-60 x^2+3 x^4\right ) \log (x)+\left (60 x^2-6 x^4\right ) \log (x) \log \left (e^{x^4} \log (x)\right )+3 x^4 \log (x) \log ^2\left (e^{x^4} \log (x)\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 {-x^4+x \log (x) \left (200+30 x-40 x^2-x^3+2 x^4-4 x^7+x^2 \left (40+x-4 x^2\right ) \log \left (e^{x^4} \log (x)\right )+2 x^4 \log ^2\left (e^{x^4} \log (x)\right )\right )}{3 \log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx\\ &=\frac {1}{3} \int \frac {-x^4+x \log (x) \left (200+30 x-40 x^2-x^3+2 x^4-4 x^7+x^2 \left (40+x-4 x^2\right ) \log \left (e^{x^4} \log (x)\right )+2 x^4 \log ^2\left (e^{x^4} \log (x)\right )\right )}{\log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx\\ &=\frac {1}{3} \int \left (2 x-\frac {x^2 \left (x^2-20 \log (x)+4 x^6 \log (x)\right )}{\log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2}+\frac {x^2}{10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )}\right ) \, dx\\ &=\frac {x^2}{3}-\frac {1}{3} \int \frac {x^2 \left (x^2-20 \log (x)+4 x^6 \log (x)\right )}{\log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx+\frac {1}{3} \int \frac {x^2}{10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )} \, dx\\ &=\frac {x^2}{3}+\frac {1}{3} \int \frac {x^2}{10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )} \, dx-\frac {1}{3} \int \left (-\frac {20 x^2}{\left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2}+\frac {4 x^8}{\left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2}+\frac {x^4}{\log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2}\right ) \, dx\\ &=\frac {x^2}{3}-\frac {1}{3} \int \frac {x^4}{\log (x) \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx+\frac {1}{3} \int \frac {x^2}{10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )} \, dx-\frac {4}{3} \int \frac {x^8}{\left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx+\frac {20}{3} \int \frac {x^2}{\left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 50, normalized size = 1.79 \begin {gather*} \frac {x^2 \left (10+x-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )}{3 \left (10-x^2+x^2 \log \left (e^{x^4} \log (x)\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.56, size = 49, normalized size = 1.75 \begin {gather*} \frac {x^{4} \log \left (e^{\left (x^{4}\right )} \log \relax (x)\right ) - x^{4} + x^{3} + 10 \, x^{2}}{3 \, {\left (x^{2} \log \left (e^{\left (x^{4}\right )} \log \relax (x)\right ) - x^{2} + 10\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 30, normalized size = 1.07 \begin {gather*} \frac {1}{3} \, x^{2} + \frac {x^{3}}{3 \, {\left (x^{6} + x^{2} \log \left (\log \relax (x)\right ) - x^{2} + 10\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.13, size = 140, normalized size = 5.00
method | result | size |
risch | \(\frac {x^{2}}{3}+\frac {2 i x^{3}}{3 \left (\pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{x^{4}}\right ) \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i {\mathrm e}^{x^{4}} \ln \relax (x )\right )-\pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{x^{4}}\right ) \mathrm {csgn}\left (i {\mathrm e}^{x^{4}} \ln \relax (x )\right )^{2}-\pi \,x^{2} \mathrm {csgn}\left (i \ln \relax (x )\right ) \mathrm {csgn}\left (i {\mathrm e}^{x^{4}} \ln \relax (x )\right )^{2}+\pi \,x^{2} \mathrm {csgn}\left (i {\mathrm e}^{x^{4}} \ln \relax (x )\right )^{3}+2 i x^{2} \ln \left (\ln \relax (x )\right )+2 i x^{2} \ln \left ({\mathrm e}^{x^{4}}\right )-2 i x^{2}+20 i\right )}\) | \(140\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.39, size = 45, normalized size = 1.61 \begin {gather*} \frac {x^{8} + x^{4} \log \left (\log \relax (x)\right ) - x^{4} + x^{3} + 10 \, x^{2}}{3 \, {\left (x^{6} + x^{2} \log \left (\log \relax (x)\right ) - x^{2} + 10\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.47, size = 32, normalized size = 1.14 \begin {gather*} \frac {x^3}{3\,\left (x^2\,\ln \left (\ln \relax (x)\right )-x^2+x^6+10\right )}+\frac {x^2}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.48, size = 29, normalized size = 1.04 \begin {gather*} \frac {x^{3}}{3 x^{2} \log {\left (e^{x^{4}} \log {\relax (x )} \right )} - 3 x^{2} + 30} + \frac {x^{2}}{3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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