Optimal. Leaf size=22 \[ e^{-e^{\left (-1+e^{16}+x\right )^2}} x^2 (-2+\log (x)) \]
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Rubi [F] time = 15.73, 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 e^{-e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)}} \left (-3 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (-4 x^2+4 e^{16} x^2+4 x^3\right )+\left (2 x+e^{1+e^{32}-2 x+x^2+e^{16} (-2+2 x)} \left (2 x^2-2 e^{16} x^2-2 x^3\right )\right ) \log (x)\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \left (-3+4 e^{\left (-1+e^{16}+x\right )^2} x \left (-1+e^{16}+x\right )+2 \left (1-e^{\left (-1+e^{16}+x\right )^2} x \left (-1+e^{16}+x\right )\right ) \log (x)\right ) \, dx\\ &=\int \left (2 \exp \left (-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}+\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x))+e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x (-3+2 \log (x))\right ) \, dx\\ &=2 \int \exp \left (-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}+\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x)) \, dx+\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x (-3+2 \log (x)) \, dx\\ &=2 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) \left (1-e^{16}-x\right ) x^2 (-2+\log (x)) \, dx+\int \left (-3 e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x+2 e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \log (x)\right ) \, dx\\ &=2 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \log (x) \, dx+2 \int \left (2 \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right )-\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \log (x)\right ) \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx\\ &=-\left (2 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \log (x) \, dx\right )-2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \left (-1+e^{16}+x\right ) \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \frac {\left (-1+e^{16}\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \left (\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) \left (-1+e^{16}\right ) x^2+\exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3\right ) \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \left (\frac {(-1+e) (1+e) \left (1+e^2\right ) \left (1+e^4\right ) \left (1+e^8\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx}{x}+\frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x}\right ) \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx-\left (4 \left (1-e^{16}\right )\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ &=-\left (2 \int \frac {\int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx}{x} \, dx\right )+2 \int \frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx}{x} \, dx-3 \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx+4 \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx-\left (2 \left (1-e^{16}\right )\right ) \int \frac {\int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx}{x} \, dx-\left (4 \left (1-e^{16}\right )\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx+(2 \log (x)) \int e^{-e^{\left (-1+e^{16}\right )^2-2 \left (1-e^{16}\right ) x+x^2}} x \, dx-(2 \log (x)) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^3 \, dx+\left (2 \left (1-e^{16}\right ) \log (x)\right ) \int \exp \left (e^{32}-e^{\left (-1+e^{16}+x\right )^2}+2 e^{16} (-1+x)+(-1+x)^2\right ) x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 4.19, size = 22, normalized size = 1.00 \begin {gather*} e^{-e^{\left (-1+e^{16}+x\right )^2}} x^2 (-2+\log (x)) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.13, size = 34, normalized size = 1.55 \begin {gather*} {\left (x^{2} \log \relax (x) - 2 \, x^{2}\right )} e^{\left (-e^{\left (x^{2} + 2 \, {\left (x - 1\right )} e^{16} - 2 \, x + e^{32} + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.36, size = 121, normalized size = 5.50 \begin {gather*} {\left (x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )} \log \relax (x) - 2 \, x^{2} e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} - e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )} + 1\right )}\right )} e^{\left (-x^{2} - 2 \, x e^{16} + 2 \, x - e^{32} + 2 \, e^{16} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 32, normalized size = 1.45
method | result | size |
risch | \(\left (\ln \relax (x )-2\right ) x^{2} {\mathrm e}^{-{\mathrm e}^{2 x \,{\mathrm e}^{16}+x^{2}-2 \,{\mathrm e}^{16}+{\mathrm e}^{32}-2 x +1}}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.06, size = 36, normalized size = 1.64 \begin {gather*} {\left (x^{2} \log \relax (x) - 2 \, x^{2}\right )} e^{\left (-e^{\left (x^{2} + 2 \, x e^{16} - 2 \, x + e^{32} - 2 \, e^{16} + 1\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.72, size = 35, normalized size = 1.59 \begin {gather*} x^2\,{\mathrm {e}}^{-{\mathrm {e}}^{-2\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{-2\,x}\,{\mathrm {e}}^{x^2}\,\mathrm {e}\,{\mathrm {e}}^{2\,x\,{\mathrm {e}}^{16}}\,{\mathrm {e}}^{{\mathrm {e}}^{32}}}\,\left (\ln \relax (x)-2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 49.25, size = 34, normalized size = 1.55 \begin {gather*} \left (x^{2} \log {\relax (x )} - 2 x^{2}\right ) e^{- e^{x^{2} - 2 x + \left (2 x - 2\right ) e^{16} + 1 + e^{32}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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