Optimal. Leaf size=37 \[ -4 e^{-e^{-3-x+e^{-x} x}}-x-\frac {4-e^x+x}{x} \]
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Rubi [F] time = 1.89, 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^{-e^{e^{-x} \left (e^x (-3-x)+x\right )}-x} \left (e^{e^{-x} \left (e^x (-3-x)+x\right )} \left (4 x^2-4 e^x x^2-4 x^3\right )+e^{e^{e^{-x} \left (e^x (-3-x)+x\right )}} \left (e^{2 x} (-1+x)+e^x \left (4-x^2\right )\right )\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-1+\frac {4}{x^2}+\frac {e^x (-1+x)}{x^2}-4 \exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right ) \left (-1+e^x+x\right )\right ) \, dx\\ &=-\frac {4}{x}-x-4 \int \exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right ) \left (-1+e^x+x\right ) \, dx+\int \frac {e^x (-1+x)}{x^2} \, dx\\ &=-\frac {4}{x}+\frac {e^x}{x}-x-4 \int \left (-\exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right )+e^{-3-e^{-3+\left (-1+e^{-x}\right ) x}-x+e^{-x} x}+\exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right ) x\right ) \, dx\\ &=-\frac {4}{x}+\frac {e^x}{x}-x+4 \int \exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right ) \, dx-4 \int e^{-3-e^{-3+\left (-1+e^{-x}\right ) x}-x+e^{-x} x} \, dx-4 \int \exp \left (-3-e^{-3+\left (-1+e^{-x}\right ) x}-2 x+e^{-x} x\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.67, size = 36, normalized size = 0.97 \begin {gather*} -4 e^{-e^{-3-x+e^{-x} x}}-\frac {4}{x}+\frac {e^x}{x}-x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.57, size = 57, normalized size = 1.54 \begin {gather*} -\frac {{\left ({\left (x^{2} - e^{x} + 4\right )} e^{\left (e^{\left (-{\left ({\left (x + 3\right )} e^{x} - x\right )} e^{\left (-x\right )}\right )}\right )} + 4 \, x\right )} e^{\left (-e^{\left (-{\left ({\left (x + 3\right )} e^{x} - x\right )} e^{\left (-x\right )}\right )}\right )}}{x} \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 (4 \, {\left (x^{3} + x^{2} e^{x} - x^{2}\right )} e^{\left (-{\left ({\left (x + 3\right )} e^{x} - x\right )} e^{\left (-x\right )}\right )} - {\left ({\left (x - 1\right )} e^{\left (2 \, x\right )} - {\left (x^{2} - 4\right )} e^{x}\right )} e^{\left (e^{\left (-{\left ({\left (x + 3\right )} e^{x} - x\right )} e^{\left (-x\right )}\right )}\right )}\right )} e^{\left (-x - e^{\left (-{\left ({\left (x + 3\right )} e^{x} - x\right )} e^{\left (-x\right )}\right )}\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 40, normalized size = 1.08
method | result | size |
risch | \(-x -\frac {4}{x}+\frac {{\mathrm e}^{x}}{x}-4 \,{\mathrm e}^{-{\mathrm e}^{-\left ({\mathrm e}^{x} x +3 \,{\mathrm e}^{x}-x \right ) {\mathrm e}^{-x}}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.72, size = 35, normalized size = 0.95 \begin {gather*} -x - \frac {4}{x} + {\rm Ei}\relax (x) - 4 \, e^{\left (-e^{\left (x e^{\left (-x\right )} - x - 3\right )}\right )} - \Gamma \left (-1, -x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.13, size = 33, normalized size = 0.89 \begin {gather*} \frac {{\mathrm {e}}^x}{x}-4\,{\mathrm {e}}^{-{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-3}\,{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}}}-x-\frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.56, size = 27, normalized size = 0.73 \begin {gather*} - x - 4 e^{- e^{\left (x + \left (- x - 3\right ) e^{x}\right ) e^{- x}}} + \frac {e^{x}}{x} - \frac {4}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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