Optimal. Leaf size=27 \[ e^{-3+e^{\left (1+e^5\right ) (4+x)}} x^2 \log ^2(1-x) \]
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Rubi [F] time = 11.90, 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 {e^{-3+e^{4+x+e^5 (4+x)}} \left (2 x^2 \log (1-x)+\left (-2 x+2 x^2+e^{4+x+e^5 (4+x)} \left (-x^2+x^3+e^5 \left (-x^2+x^3\right )\right )\right ) \log ^2(1-x)\right )}{-1+x} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\exp \left (-3+e^{4+x+e^5 (4+x)}+4 \left (1+e^5\right )+\left (1+e^5\right ) x\right ) (1+e) \left (1-e+e^2-e^3+e^4\right ) x^2 \log ^2(1-x)+\frac {2 e^{-3+e^{4+x+e^5 (4+x)}} x \log (1-x) (x-\log (1-x)+x \log (1-x))}{-1+x}\right ) \, dx\\ &=2 \int \frac {e^{-3+e^{4+x+e^5 (4+x)}} x \log (1-x) (x-\log (1-x)+x \log (1-x))}{-1+x} \, dx+\left (1+e^5\right ) \int \exp \left (-3+e^{4+x+e^5 (4+x)}+4 \left (1+e^5\right )+\left (1+e^5\right ) x\right ) x^2 \log ^2(1-x) \, dx\\ &=2 \int \left (\frac {e^{-3+e^{4+x+e^5 (4+x)}} x^2 \log (1-x)}{-1+x}+e^{-3+e^{4+x+e^5 (4+x)}} x \log ^2(1-x)\right ) \, dx+\left (1+e^5\right ) \int \exp \left (e^{4+x+e^5 (4+x)}-3 \left (1-\frac {4}{3} \left (1+e^5\right )\right )+\left (1+e^5\right ) x\right ) x^2 \log ^2(1-x) \, dx\\ &=2 \int \frac {e^{-3+e^{4+x+e^5 (4+x)}} x^2 \log (1-x)}{-1+x} \, dx+2 \int e^{-3+e^{4+x+e^5 (4+x)}} x \log ^2(1-x) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} x^2 \log ^2(1-x) \, dx\\ &=\frac {2 \text {Ei}\left (e^{4+x+e^5 (4+x)}\right ) \log (1-x)}{e^3 \left (1+e^5\right )}+2 \int \left (e^{-3+e^{4+x+e^5 (4+x)}} \log ^2(1-x)-e^{-3+e^{4+x+e^5 (4+x)}} (1-x) \log ^2(1-x)\right ) \, dx-2 \int \frac {-\frac {\text {Ei}\left (e^{\left (1+e^5\right ) (4+x)}\right )}{e^3+e^8}-\int \frac {e^{-3+e^{\left (1+e^5\right ) (4+x)}}}{-1+x} \, dx-\int e^{-3+e^{\left (1+e^5\right ) (4+x)}} x \, dx}{1-x} \, dx+\left (1+e^5\right ) \int \left (e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} \log ^2(1-x)-2 e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x) \log ^2(1-x)+e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x)^2 \log ^2(1-x)\right ) \, dx+(2 \log (1-x)) \int \frac {e^{-3+e^{4+x+e^5 (4+x)}}}{-1+x} \, dx+(2 \log (1-x)) \int e^{-3+e^{4+x+e^5 (4+x)}} x \, dx\\ &=\frac {2 \text {Ei}\left (e^{4+x+e^5 (4+x)}\right ) \log (1-x)}{e^3 \left (1+e^5\right )}+2 \int e^{-3+e^{4+x+e^5 (4+x)}} \log ^2(1-x) \, dx-2 \int e^{-3+e^{4+x+e^5 (4+x)}} (1-x) \log ^2(1-x) \, dx-2 \int \left (\frac {-\text {Ei}\left (e^{\left (1+e^5\right ) (4+x)}\right )-e^3 \left (1+e^5\right ) \int \frac {e^{-3+e^{\left (1+e^5\right ) (4+x)}}}{-1+x} \, dx}{e^3 \left (1+e^5\right ) (1-x)}+\frac {\int e^{-3+e^{\left (1+e^5\right ) (4+x)}} x \, dx}{-1+x}\right ) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} \log ^2(1-x) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x)^2 \log ^2(1-x) \, dx-\left (2 \left (1+e^5\right )\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x) \log ^2(1-x) \, dx+(2 \log (1-x)) \int \frac {e^{-3+e^{4+x+e^5 (4+x)}}}{-1+x} \, dx+(2 \log (1-x)) \int e^{-3+e^{4+x+e^5 (4+x)}} x \, dx\\ &=\frac {2 \text {Ei}\left (e^{4+x+e^5 (4+x)}\right ) \log (1-x)}{e^3 \left (1+e^5\right )}+2 \int e^{-3+e^{4+x+e^5 (4+x)}} \log ^2(1-x) \, dx-2 \int e^{-3+e^{4+x+e^5 (4+x)}} (1-x) \log ^2(1-x) \, dx-2 \int \frac {\int e^{-3+e^{\left (1+e^5\right ) (4+x)}} x \, dx}{-1+x} \, dx-\frac {2 \int \frac {-\text {Ei}\left (e^{\left (1+e^5\right ) (4+x)}\right )-e^3 \left (1+e^5\right ) \int \frac {e^{-3+e^{\left (1+e^5\right ) (4+x)}}}{-1+x} \, dx}{1-x} \, dx}{e^3 \left (1+e^5\right )}+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} \log ^2(1-x) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x)^2 \log ^2(1-x) \, dx-\left (2 \left (1+e^5\right )\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x) \log ^2(1-x) \, dx+(2 \log (1-x)) \int \frac {e^{-3+e^{4+x+e^5 (4+x)}}}{-1+x} \, dx+(2 \log (1-x)) \int e^{-3+e^{4+x+e^5 (4+x)}} x \, dx\\ &=\frac {2 \text {Ei}\left (e^{4+x+e^5 (4+x)}\right ) \log (1-x)}{e^3 \left (1+e^5\right )}+2 \int e^{-3+e^{4+x+e^5 (4+x)}} \log ^2(1-x) \, dx-2 \int e^{-3+e^{4+x+e^5 (4+x)}} (1-x) \log ^2(1-x) \, dx-2 \int \frac {\int e^{-3+e^{\left (1+e^5\right ) (4+x)}} x \, dx}{-1+x} \, dx-\frac {2 \int \left (\frac {\text {Ei}\left (e^{4 \left (1+e^5\right )+\left (1+e^5\right ) x}\right )}{-1+x}+\frac {e^3 (1+e) \left (1-e+e^2-e^3+e^4\right ) \int \frac {e^{-3+e^{\left (1+e^5\right ) (4+x)}}}{-1+x} \, dx}{-1+x}\right ) \, dx}{e^3 \left (1+e^5\right )}+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} \log ^2(1-x) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x)^2 \log ^2(1-x) \, dx-\left (2 \left (1+e^5\right )\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x) \log ^2(1-x) \, dx+(2 \log (1-x)) \int \frac {e^{-3+e^{4+x+e^5 (4+x)}}}{-1+x} \, dx+(2 \log (1-x)) \int e^{-3+e^{4+x+e^5 (4+x)}} x \, dx\\ &=\frac {2 \text {Ei}\left (e^{4+x+e^5 (4+x)}\right ) \log (1-x)}{e^3 \left (1+e^5\right )}+2 \int e^{-3+e^{4+x+e^5 (4+x)}} \log ^2(1-x) \, dx-2 \int e^{-3+e^{4+x+e^5 (4+x)}} (1-x) \log ^2(1-x) \, dx-2 \int \frac {\int \frac {e^{-3+e^{\left (1+e^5\right ) (4+x)}}}{-1+x} \, dx}{-1+x} \, dx-2 \int \frac {\int e^{-3+e^{\left (1+e^5\right ) (4+x)}} x \, dx}{-1+x} \, dx-\frac {2 \int \frac {\text {Ei}\left (e^{4 \left (1+e^5\right )+\left (1+e^5\right ) x}\right )}{-1+x} \, dx}{e^3 \left (1+e^5\right )}+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} \log ^2(1-x) \, dx+\left (1+e^5\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x)^2 \log ^2(1-x) \, dx-\left (2 \left (1+e^5\right )\right ) \int e^{1+e^{\left (1+e^5\right ) (4+x)}+x+e^5 (4+x)} (1-x) \log ^2(1-x) \, dx+(2 \log (1-x)) \int \frac {e^{-3+e^{4+x+e^5 (4+x)}}}{-1+x} \, dx+(2 \log (1-x)) \int e^{-3+e^{4+x+e^5 (4+x)}} x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 9.99, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{-3+e^{4+x+e^5 (4+x)}} \left (2 x^2 \log (1-x)+\left (-2 x+2 x^2+e^{4+x+e^5 (4+x)} \left (-x^2+x^3+e^5 \left (-x^2+x^3\right )\right )\right ) \log ^2(1-x)\right )}{-1+x} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.99, size = 25, normalized size = 0.93 \begin {gather*} x^{2} e^{\left (e^{\left ({\left (x + 4\right )} e^{5} + x + 4\right )} - 3\right )} \log \left (-x + 1\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {{\left (2 \, x^{2} \log \left (-x + 1\right ) + {\left (2 \, x^{2} + {\left (x^{3} - x^{2} + {\left (x^{3} - x^{2}\right )} e^{5}\right )} e^{\left ({\left (x + 4\right )} e^{5} + x + 4\right )} - 2 \, x\right )} \log \left (-x + 1\right )^{2}\right )} e^{\left (e^{\left ({\left (x + 4\right )} e^{5} + x + 4\right )} - 3\right )}}{x - 1}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.23, size = 25, normalized size = 0.93
method | result | size |
risch | \(\ln \left (1-x \right )^{2} x^{2} {\mathrm e}^{{\mathrm e}^{\left (4+x \right ) \left ({\mathrm e}^{5}+1\right )}-3}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.69, size = 27, normalized size = 1.00 \begin {gather*} x^{2} e^{\left (e^{\left (x e^{5} + x + 4 \, e^{5} + 4\right )} - 3\right )} \log \left (-x + 1\right )^{2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.25, size = 30, normalized size = 1.11 \begin {gather*} x^2\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{{\mathrm {e}}^{4\,{\mathrm {e}}^5}\,{\mathrm {e}}^4\,{\mathrm {e}}^{x\,{\mathrm {e}}^5}\,{\mathrm {e}}^x}\,{\ln \left (1-x\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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