Optimal. Leaf size=24 \[ e^{e^{-e^x+2 x} (-2+x) x^2 \log ^4(2)} \]
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Rubi [F] time = 7.65, 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 {\exp \left (-e^x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) \left (-2 x+x^2\right ) \left (e^{3 x} \left (2 x-x^2\right ) \log ^4(2)+e^{2 x} \left (-4-x+2 x^2\right ) \log ^4(2)\right )}{-2+x} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \exp \left (-e^x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \left (e^{3 x} \left (2 x-x^2\right ) \log ^4(2)+e^{2 x} \left (-4-x+2 x^2\right ) \log ^4(2)\right ) \, dx\\ &=\int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \left (-4-x+2 e^x x+2 x^2-e^x x^2\right ) \log ^4(2) \, dx\\ &=\log ^4(2) \int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \left (-4-x+2 e^x x+2 x^2-e^x x^2\right ) \, dx\\ &=\log ^4(2) \int \left (-\exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) (-2+x) x^2+\exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \left (-4-x+2 x^2\right )\right ) \, dx\\ &=-\left (\log ^4(2) \int \exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) (-2+x) x^2 \, dx\right )+\log ^4(2) \int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \left (-4-x+2 x^2\right ) \, dx\\ &=\log ^4(2) \int \left (-4 \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x-\exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^2+2 \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^3\right ) \, dx-\log ^4(2) \int \left (-2 \exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^2+\exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^3\right ) \, dx\\ &=-\left (\log ^4(2) \int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^2 \, dx\right )-\log ^4(2) \int \exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^3 \, dx+\left (2 \log ^4(2)\right ) \int \exp \left (-e^x+3 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^2 \, dx+\left (2 \log ^4(2)\right ) \int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x^3 \, dx-\left (4 \log ^4(2)\right ) \int \exp \left (-e^x+2 x+e^{-e^x+2 x} x \left (-2 x+x^2\right ) \log ^4(2)\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.54, size = 24, normalized size = 1.00 \begin {gather*} e^{e^{-e^x+2 x} (-2+x) x^2 \log ^4(2)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.98, size = 24, normalized size = 1.00 \begin {gather*} e^{\left (x e^{\left (2 \, x - e^{x} + \log \left (x^{2} - 2 \, x\right )\right )} \log \relax (2)^{4}\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 -\frac {{\left ({\left (x^{2} - 2 \, x\right )} e^{\left (3 \, x\right )} \log \relax (2)^{4} - {\left (2 \, x^{2} - x - 4\right )} e^{\left (2 \, x\right )} \log \relax (2)^{4}\right )} e^{\left (x e^{\left (2 \, x - e^{x} + \log \left (x^{2} - 2 \, x\right )\right )} \log \relax (2)^{4} - e^{x} + \log \left (x^{2} - 2 \, x\right )\right )}}{x - 2}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [C] time = 0.22, size = 100, normalized size = 4.17
method | result | size |
risch | \({\mathrm e}^{\ln \relax (2)^{4} \left (x -2\right ) x^{2} {\mathrm e}^{2 x -\frac {i \pi \mathrm {csgn}\left (i x \left (x -2\right )\right )^{3}}{2}+\frac {i \pi \mathrm {csgn}\left (i x \left (x -2\right )\right )^{2} \mathrm {csgn}\left (i x \right )}{2}+\frac {i \pi \mathrm {csgn}\left (i x \left (x -2\right )\right )^{2} \mathrm {csgn}\left (i \left (x -2\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x \left (x -2\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x -2\right )\right )}{2}-{\mathrm e}^{x}}}\) | \(100\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.53, size = 37, normalized size = 1.54 \begin {gather*} e^{\left (x^{3} e^{\left (2 \, x - e^{x}\right )} \log \relax (2)^{4} - 2 \, x^{2} e^{\left (2 \, x - e^{x}\right )} \log \relax (2)^{4}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.48, size = 38, normalized size = 1.58 \begin {gather*} {\mathrm {e}}^{x^3\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\ln \relax (2)}^4}\,{\mathrm {e}}^{-2\,x^2\,{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\ln \relax (2)}^4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.60, size = 24, normalized size = 1.00 \begin {gather*} e^{x \left (x^{2} - 2 x\right ) e^{2 x} e^{- e^{x}} \log {\relax (2 )}^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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