Optimal. Leaf size=26 \[ e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \]
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Rubi [F] time = 1.90, 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 e^{-6+e^{5 x}-e^{32 e^{-1+e^{5 x}}} x^2} \left (e^{32 e^{-1+e^{5 x}}} x^x \left (-2 e^{1-e^{5 x}} x-160 e^{5 x} x^2\right )+e^{1-e^{5 x}} x^x (1+\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 \left (-2 \exp \left (-6+32 e^{-1+e^{5 x}}-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{1+x} \left (e+80 e^{e^{5 x}+5 x} x\right )+e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x (1+\log (x))\right ) \, dx\\ &=-\left (2 \int \exp \left (-6+32 e^{-1+e^{5 x}}-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{1+x} \left (e+80 e^{e^{5 x}+5 x} x\right ) \, dx\right )+\int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x (1+\log (x)) \, dx\\ &=-\left (2 \int \left (\exp \left (-5+32 e^{-1+e^{5 x}}-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{1+x}+80 \exp \left (-6+32 e^{-1+e^{5 x}}+e^{5 x}+5 x-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{2+x}\right ) \, dx\right )+\int \left (e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x+e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \log (x)\right ) \, dx\\ &=-\left (2 \int \exp \left (-5+32 e^{-1+e^{5 x}}-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{1+x} \, dx\right )-160 \int \exp \left (-6+32 e^{-1+e^{5 x}}+e^{5 x}+5 x-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{2+x} \, dx+\int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \, dx+\int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \log (x) \, dx\\ &=-\left (2 \int \exp \left (-5+32 e^{-1+e^{5 x}}-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{1+x} \, dx\right )-160 \int \exp \left (-6+32 e^{-1+e^{5 x}}+e^{5 x}+5 x-e^{32 e^{-1+e^{5 x}}} x^2\right ) x^{2+x} \, dx+\log (x) \int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \, dx+\int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \, dx-\int \frac {\int e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \, dx}{x} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.45, size = 26, normalized size = 1.00 \begin {gather*} e^{-5-e^{32 e^{-1+e^{5 x}}} x^2} x^x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 22, normalized size = 0.85 \begin {gather*} x^{x} e^{\left (-x^{2} e^{\left (32 \, e^{\left (e^{\left (5 \, x\right )} - 1\right )}\right )} - 5\right )} \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 -{\left (2 \, {\left (80 \, x^{2} e^{\left (5 \, x\right )} + x e^{\left (-e^{\left (5 \, x\right )} + 1\right )}\right )} x^{x} e^{\left (32 \, e^{\left (e^{\left (5 \, x\right )} - 1\right )}\right )} - x^{x} {\left (\log \relax (x) + 1\right )} e^{\left (-e^{\left (5 \, x\right )} + 1\right )}\right )} e^{\left (-x^{2} e^{\left (32 \, e^{\left (e^{\left (5 \, x\right )} - 1\right )}\right )} + e^{\left (5 \, x\right )} - 6\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.10, size = 23, normalized size = 0.88
method | result | size |
risch | \(x^{x} {\mathrm e}^{-x^{2} {\mathrm e}^{32 \,{\mathrm e}^{{\mathrm e}^{5 x}-1}}-5}\) | \(23\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 22, normalized size = 0.85 \begin {gather*} e^{\left (-x^{2} e^{\left (32 \, e^{\left (e^{\left (5 \, x\right )} - 1\right )}\right )} + x \log \relax (x) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.19, size = 22, normalized size = 0.85 \begin {gather*} x^x\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^{32\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{{\mathrm {e}}^{5\,x}}}} \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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