Optimal. Leaf size=29 \[ e^2 \left (e^{2 x}-e^{3 \left (2-e^x-\frac {4}{x}\right ) x}\right ) \]
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Rubi [F] time = 0.47, 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^2 \left (e^{2 x}-e^{-12+6 x-3 e^x x}\right ) \left (-2 e^{2 x}+e^{-12+6 x-3 e^x x} \left (6+e^x (-3-3 x)\right )\right )}{-e^{2 x}+e^{-12+6 x-3 e^x x}} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^2 \int \frac {\left (e^{2 x}-e^{-12+6 x-3 e^x x}\right ) \left (-2 e^{2 x}+e^{-12+6 x-3 e^x x} \left (6+e^x (-3-3 x)\right )\right )}{-e^{2 x}+e^{-12+6 x-3 e^x x}} \, dx\\ &=e^2 \int \left (2 e^{2 x}-6 e^{-3 \left (4+\left (-2+e^x\right ) x\right )}+3 e^{-12+7 x-3 e^x x} (1+x)\right ) \, dx\\ &=\left (2 e^2\right ) \int e^{2 x} \, dx+\left (3 e^2\right ) \int e^{-12+7 x-3 e^x x} (1+x) \, dx-\left (6 e^2\right ) \int e^{-3 \left (4+\left (-2+e^x\right ) x\right )} \, dx\\ &=e^{2+2 x}+\left (3 e^2\right ) \int \left (e^{-12+7 x-3 e^x x}+e^{-12+7 x-3 e^x x} x\right ) \, dx-\left (6 e^2\right ) \int e^{-3 \left (4+\left (-2+e^x\right ) x\right )} \, dx\\ &=e^{2+2 x}+\left (3 e^2\right ) \int e^{-12+7 x-3 e^x x} \, dx+\left (3 e^2\right ) \int e^{-12+7 x-3 e^x x} x \, dx-\left (6 e^2\right ) \int e^{-3 \left (4+\left (-2+e^x\right ) x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.34, size = 23, normalized size = 0.79 \begin {gather*} e^{2+2 x}-e^{-10+6 x-3 e^x x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 20, normalized size = 0.69 \begin {gather*} -e^{\left (-3 \, x e^{x} + 6 \, x - 10\right )} + e^{\left (2 \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [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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maple [A] time = 0.05, size = 21, normalized size = 0.72
method | result | size |
risch | \(-{\mathrm e}^{-10-3 \,{\mathrm e}^{x} x +6 x}+{\mathrm e}^{2 x +2}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 23, normalized size = 0.79 \begin {gather*} -{\left (e^{\left (-3 \, x e^{x} + 6 \, x\right )} - e^{\left (2 \, x + 12\right )}\right )} e^{\left (-10\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 = 0.76 \begin {gather*} {\mathrm {e}}^{2\,x}\,{\mathrm {e}}^2-{\mathrm {e}}^{-3\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{6\,x}\,{\mathrm {e}}^{-10} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.37, size = 24, normalized size = 0.83 \begin {gather*} e^{2} e^{2 x} - e^{2} e^{- 3 x e^{x} + 6 x - 12} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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