Optimal. Leaf size=25 \[ \frac {1}{27} x^2 \log ^2\left (-e^{e^{e^{x+x^2}}}+x\right ) \]
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Rubi [A]
time = 6.64, antiderivative size = 25, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 6, integrand size = 118, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {6820, 12, 14,
6874, 2631, 6819} \begin {gather*} \frac {1}{27} x^2 \log ^2\left (x-e^{e^{e^{x^2+x}}}\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 14
Rule 2631
Rule 6819
Rule 6820
Rule 6874
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2}{27} x \log \left (-e^{e^{e^{x+x^2}}}+x\right ) \left (\frac {x \left (-1+e^{e^{e^{x+x^2}}+e^{x+x^2}+x+x^2} (1+2 x)\right )}{e^{e^{e^{x+x^2}}}-x}+\log \left (-e^{e^{e^{x+x^2}}}+x\right )\right ) \, dx\\ &=\frac {2}{27} \int x \log \left (-e^{e^{e^{x+x^2}}}+x\right ) \left (\frac {x \left (-1+e^{e^{e^{x+x^2}}+e^{x+x^2}+x+x^2} (1+2 x)\right )}{e^{e^{e^{x+x^2}}}-x}+\log \left (-e^{e^{e^{x+x^2}}}+x\right )\right ) \, dx\\ &=\frac {1}{27} x^2 \log ^2\left (-e^{e^{e^{x+x^2}}}+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [F]
time = 0.59, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {\left (-2 x^2+e^{e^{e^{x+x^2}}+e^{x+x^2}+x+x^2} \left (2 x^2+4 x^3\right )\right ) \log \left (-e^{e^{e^{x+x^2}}}+x\right )+\left (2 e^{e^{e^{x+x^2}}} x-2 x^2\right ) \log ^2\left (-e^{e^{e^{x+x^2}}}+x\right )}{27 e^{e^{e^{x+x^2}}}-27 x} \, dx \end {gather*}
Verification is not applicable to the result.
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Maple [A]
time = 0.18, size = 21, normalized size = 0.84
method | result | size |
risch | \(\frac {x^{2} \ln \left (-{\mathrm e}^{{\mathrm e}^{{\mathrm e}^{\left (x +1\right ) x}}}+x \right )^{2}}{27}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.37, size = 20, normalized size = 0.80 \begin {gather*} \frac {1}{27} \, x^{2} \log \left (x - e^{\left (e^{\left (e^{\left (x^{2} + x\right )}\right )}\right )}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [B] Leaf count of result is larger than twice the leaf count of optimal. 63 vs.
\(2 (20) = 40\).
time = 0.41, size = 63, normalized size = 2.52 \begin {gather*} \frac {1}{27} \, x^{2} \log \left ({\left (x e^{\left (x^{2} + x + e^{\left (x^{2} + x\right )}\right )} - e^{\left (x^{2} + x + e^{\left (x^{2} + x\right )} + e^{\left (e^{\left (x^{2} + x\right )}\right )}\right )}\right )} e^{\left (-x^{2} - x - e^{\left (x^{2} + x\right )}\right )}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 4.60, size = 19, normalized size = 0.76 \begin {gather*} \frac {x^{2} \log {\left (x - e^{e^{e^{x^{2} + x}}} \right )}^{2}}{27} \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. 63 vs.
\(2 (20) = 40\).
time = 0.72, size = 63, normalized size = 2.52 \begin {gather*} \frac {1}{27} \, x^{2} \log \left ({\left (x e^{\left (x^{2} + x + e^{\left (x^{2} + x\right )}\right )} - e^{\left (x^{2} + x + e^{\left (x^{2} + x\right )} + e^{\left (e^{\left (x^{2} + x\right )}\right )}\right )}\right )} e^{\left (-x^{2} - x - e^{\left (x^{2} + x\right )}\right )}\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 2.17, size = 21, normalized size = 0.84 \begin {gather*} \frac {x^2\,{\ln \left (x-{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x^2}\,{\mathrm {e}}^x}}\right )}^2}{27} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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