Optimal. Leaf size=27 \[ -3+e+\frac {2 (-2+x)}{x \left (e^{-3 e} x-e^x x\right )} \]
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Rubi [F] time = 1.18, 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^{3 e} (8-2 x)+e^{6 e+x} \left (-8-2 x+2 x^2\right )}{x^3-2 e^{3 e+x} x^3+e^{6 e+2 x} x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {2 e^{3 e} \left (4-x+e^{3 e+x} \left (-4-x+x^2\right )\right )}{\left (1-e^{3 e+x}\right )^2 x^3} \, dx\\ &=\left (2 e^{3 e}\right ) \int \frac {4-x+e^{3 e+x} \left (-4-x+x^2\right )}{\left (1-e^{3 e+x}\right )^2 x^3} \, dx\\ &=\left (2 e^{3 e}\right ) \int \left (\frac {-2+x}{\left (-1+e^{3 e+x}\right )^2 x^2}+\frac {-4-x+x^2}{\left (-1+e^{3 e+x}\right ) x^3}\right ) \, dx\\ &=\left (2 e^{3 e}\right ) \int \frac {-2+x}{\left (-1+e^{3 e+x}\right )^2 x^2} \, dx+\left (2 e^{3 e}\right ) \int \frac {-4-x+x^2}{\left (-1+e^{3 e+x}\right ) x^3} \, dx\\ &=\left (2 e^{3 e}\right ) \int \left (-\frac {2}{\left (-1+e^{3 e+x}\right )^2 x^2}+\frac {1}{\left (-1+e^{3 e+x}\right )^2 x}\right ) \, dx+\left (2 e^{3 e}\right ) \int \left (-\frac {4}{\left (-1+e^{3 e+x}\right ) x^3}-\frac {1}{\left (-1+e^{3 e+x}\right ) x^2}+\frac {1}{\left (-1+e^{3 e+x}\right ) x}\right ) \, dx\\ &=-\left (\left (2 e^{3 e}\right ) \int \frac {1}{\left (-1+e^{3 e+x}\right ) x^2} \, dx\right )+\left (2 e^{3 e}\right ) \int \frac {1}{\left (-1+e^{3 e+x}\right )^2 x} \, dx+\left (2 e^{3 e}\right ) \int \frac {1}{\left (-1+e^{3 e+x}\right ) x} \, dx-\left (4 e^{3 e}\right ) \int \frac {1}{\left (-1+e^{3 e+x}\right )^2 x^2} \, dx-\left (8 e^{3 e}\right ) \int \frac {1}{\left (-1+e^{3 e+x}\right ) x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.19, size = 26, normalized size = 0.96 \begin {gather*} \frac {2 e^{3 e} (2-x)}{\left (-1+e^{3 e+x}\right ) x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.63, size = 34, normalized size = 1.26 \begin {gather*} -\frac {2 \, {\left (x - 2\right )} e^{\left (6 \, e\right )}}{x^{2} e^{\left (x + 6 \, e\right )} - x^{2} e^{\left (3 \, e\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.32, size = 36, normalized size = 1.33 \begin {gather*} -\frac {2 \, {\left (x e^{\left (3 \, e\right )} - 2 \, e^{\left (3 \, e\right )}\right )}}{x^{2} e^{\left (x + 3 \, e\right )} - x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.25, size = 25, normalized size = 0.93
method | result | size |
risch | \(-\frac {2 \,{\mathrm e}^{3 \,{\mathrm e}} \left (x -2\right )}{x^{2} \left ({\mathrm e}^{x +3 \,{\mathrm e}}-1\right )}\) | \(25\) |
norman | \(\frac {4 \,{\mathrm e}^{3 \,{\mathrm e}}-2 \,{\mathrm e}^{3 \,{\mathrm e}} x}{x^{2} \left ({\mathrm e}^{x} {\mathrm e}^{3 \,{\mathrm e}}-1\right )}\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.05, size = 36, normalized size = 1.33 \begin {gather*} -\frac {2 \, {\left (x e^{\left (3 \, e\right )} - 2 \, e^{\left (3 \, e\right )}\right )}}{x^{2} e^{\left (x + 3 \, e\right )} - x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.60, size = 24, normalized size = 0.89 \begin {gather*} -\frac {2\,{\mathrm {e}}^{3\,\mathrm {e}}\,\left (x-2\right )}{x^2\,\left ({\mathrm {e}}^{x+3\,\mathrm {e}}-1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 34, normalized size = 1.26 \begin {gather*} \frac {- 2 x e^{3 e} + 4 e^{3 e}}{x^{2} e^{3 e} e^{x} - x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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