Optimal. Leaf size=29 \[ e^{2-(4-x) (-4+x) \left (-5-e^x+x\right )} \left (-1+e^3+x\right ) \]
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Rubi [F] time = 4.72, 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 \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-55+82 x-29 x^2+3 x^3+e^3 \left (56-26 x+3 x^2\right )+e^x \left (8-14 x+7 x^2-x^3+e^3 \left (-8+6 x-x^2\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-55 \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right )+82 \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x-29 \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2+3 \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3-\exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-1+e^3+x\right ) \left (8-6 x+x^2\right )+\exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (56-26 x+3 x^2\right )\right ) \, dx\\ &=3 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3 \, dx-29 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2 \, dx-55 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \, dx+82 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x \, dx-\int \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-1+e^3+x\right ) \left (8-6 x+x^2\right ) \, dx+\int \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (56-26 x+3 x^2\right ) \, dx\\ &=3 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3 \, dx-29 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2 \, dx-55 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \, dx+82 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x \, dx+\int \left (56 \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right )-26 \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x+3 \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2\right ) \, dx-\int \left (8 \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-1+e^3\right )-2 \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-7+3 e^3\right ) x+\exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \left (-7+e^3\right ) x^2+\exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3\right ) \, dx\\ &=3 \int \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2 \, dx+3 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3 \, dx-26 \int \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x \, dx-29 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2 \, dx-55 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \, dx+56 \int \exp \left (-75+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \, dx+82 \int \exp \left (-78+56 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x \, dx-\left (2 \left (7-3 e^3\right )\right ) \int \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x \, dx+\left (8 \left (1-e^3\right )\right ) \int \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) \, dx-\left (-7+e^3\right ) \int \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^2 \, dx-\int \exp \left (-78+57 x-13 x^2+x^3+e^x \left (-16+8 x-x^2\right )\right ) x^3 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.08, size = 32, normalized size = 1.10 \begin {gather*} e^{-78-e^x (-4+x)^2+56 x-13 x^2+x^3} \left (-1+e^3+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 32, normalized size = 1.10 \begin {gather*} {\left (x + e^{3} - 1\right )} e^{\left (x^{3} - 13 \, x^{2} - {\left (x^{2} - 8 \, x + 16\right )} e^{x} + 56 \, x - 78\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 (3 \, x^{3} - 29 \, x^{2} + {\left (3 \, x^{2} - 26 \, x + 56\right )} e^{3} - {\left (x^{3} - 7 \, x^{2} + {\left (x^{2} - 6 \, x + 8\right )} e^{3} + 14 \, x - 8\right )} e^{x} + 82 \, x - 55\right )} e^{\left (x^{3} - 13 \, x^{2} - {\left (x^{2} - 8 \, x + 16\right )} e^{x} + 56 \, x - 78\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 = 37, normalized size = 1.28
method | result | size |
risch | \(\left ({\mathrm e}^{3}+x -1\right ) {\mathrm e}^{-{\mathrm e}^{x} x^{2}+x^{3}+8 \,{\mathrm e}^{x} x -13 x^{2}-16 \,{\mathrm e}^{x}+56 x -78}\) | \(37\) |
norman | \(x \,{\mathrm e}^{\left (-x^{2}+8 x -16\right ) {\mathrm e}^{x}+x^{3}-13 x^{2}+56 x -78}+\left ({\mathrm e}^{3}-1\right ) {\mathrm e}^{\left (-x^{2}+8 x -16\right ) {\mathrm e}^{x}+x^{3}-13 x^{2}+56 x -78}\) | \(63\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 33.82, size = 36, normalized size = 1.24 \begin {gather*} {\left (x + e^{3} - 1\right )} e^{\left (x^{3} - x^{2} e^{x} - 13 \, x^{2} + 8 \, x e^{x} + 56 \, x - 16 \, e^{x} - 78\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.15, size = 111, normalized size = 3.83 \begin {gather*} {\mathrm {e}}^{8\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{56\,x}\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{-75}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-13\,x^2}\,{\mathrm {e}}^{-16\,{\mathrm {e}}^x}-{\mathrm {e}}^{8\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{56\,x}\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{-78}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-13\,x^2}\,{\mathrm {e}}^{-16\,{\mathrm {e}}^x}+x\,{\mathrm {e}}^{8\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{56\,x}\,{\mathrm {e}}^{x^3}\,{\mathrm {e}}^{-78}\,{\mathrm {e}}^{-x^2\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-13\,x^2}\,{\mathrm {e}}^{-16\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 32, normalized size = 1.10 \begin {gather*} \left (x - 1 + e^{3}\right ) e^{x^{3} - 13 x^{2} + 56 x + \left (- x^{2} + 8 x - 16\right ) e^{x} - 78} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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