Optimal. Leaf size=35 \[ x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \]
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Rubi [F] time = 31.30, 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 {\left (2 e^{e^x+x} x^4+12 x^5+\left (-12 x^5+6 x^6+e^{e^x} \left (-4 x^3+2 x^4\right )\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log \left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )+\left (\left (-2 e^{e^x} x^3-6 x^5\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (10 e^{e^x+x} x+30 e^x x^3\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right ) \log ^2\left (\frac {e^{-x} \left (x^2-5 e^x \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )\right )}{\log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right )}{\left (-e^{e^x} x^2-3 x^4\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )+\left (5 e^{e^x+x}+15 e^x x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=2 \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (-x^3 \left (e^{e^x+x}+6 x\right )-\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \left ((-2+x) x^2-\left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=2 \int \left (\frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}+\frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{5 \left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )}\right ) \, dx\\ &=\frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+10 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 e^{e^x} x \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )+30 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-15 x^3 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int \frac {x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (e^{e^x} x^3+5 e^{e^x} \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )+15 x^2 \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx\\ &=\frac {2}{5} \int \frac {x^3 \left (-e^{e^x} x^3-30 x^2 \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )-5 (-2+x) \left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right ) \left (x^2-5 e^x \log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )\right ) \log ^2\left (\log \left (\frac {1}{3} \left (e^{e^x}+3 x^2\right )\right )\right )} \, dx+\frac {2}{5} \int x \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \left (\frac {e^{e^x} x^3}{\left (e^{e^x}+3 x^2\right ) \log \left (\frac {e^{e^x}}{3}+x^2\right ) \log ^2\left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}+5 \log \left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right )\right ) \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [A] time = 0.38, size = 35, normalized size = 1.00 \begin {gather*} x^2 \log ^2\left (-5+\frac {e^{-x} x^2}{\log \left (\log \left (\frac {e^{e^x}}{3}+x^2\right )\right )}\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.75, size = 64, normalized size = 1.83 \begin {gather*} x^{2} \log \left (\frac {{\left (x^{2} - 5 \, e^{x} \log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )} e^{\left (-x\right )}}{\log \left (\log \left (\frac {1}{3} \, {\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.56, size = 211, normalized size = 6.03 \begin {gather*} x^{4} - 2 \, x^{3} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) - 2 \, x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left ({\left (3 \, x^{2} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )\right )\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 1.36, size = 5397, normalized size = 154.20
method | result | size |
risch | \(\text {Expression too large to display}\) | \(5397\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.29, size = 132, normalized size = 3.77 \begin {gather*} x^{4} + x^{2} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} + 2 \, x^{3} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )^{2} - 2 \, {\left (x^{3} + x^{2} \log \left (\log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right )\right )} \log \left (x^{2} - 5 \, e^{x} \log \left (-\log \relax (3) + \log \left (3 \, x^{2} + e^{\left (e^{x}\right )}\right )\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 6.20, size = 45, normalized size = 1.29 \begin {gather*} x^2\,{\ln \left (-\frac {5\,\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )-x^2\,{\mathrm {e}}^{-x}}{\ln \left (\ln \left (\frac {{\mathrm {e}}^{{\mathrm {e}}^x}}{3}+x^2\right )\right )}\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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