Optimal. Leaf size=21 \[ e^{\frac {216 e}{\left (x+\frac {x}{-2-x+e x}\right )^2}} \]
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Rubi [F] time = 9.13, 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 (\frac {216 e^3 x^2+e^2 \left (-864 x-432 x^2\right )+e \left (864+864 x+216 x^2\right )}{x^2+2 x^3+x^4+e^2 x^4+e \left (-2 x^3-2 x^4\right )}\right ) \left (-432 e^4 x^3+e^2 \left (-4320 x-5184 x^2-1296 x^3\right )+e \left (1728+4320 x+2592 x^2+432 x^3\right )+e^3 \left (2592 x^2+1296 x^3\right )\right )}{-x^3-3 x^4-3 x^5-x^6+e^3 x^6+e^2 \left (-3 x^5-3 x^6\right )+e \left (3 x^4+6 x^5+3 x^6\right )} \, dx \end {gather*}
Verification is not applicable to the result.
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\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {216 e^3 x^2+e^2 \left (-864 x-432 x^2\right )+e \left (864+864 x+216 x^2\right )}{x^2+2 x^3+x^4+e^2 x^4+e \left (-2 x^3-2 x^4\right )}\right ) \left (-432 e^4 x^3+e^2 \left (-4320 x-5184 x^2-1296 x^3\right )+e \left (1728+4320 x+2592 x^2+432 x^3\right )+e^3 \left (2592 x^2+1296 x^3\right )\right )}{-x^3-3 x^4-3 x^5+\left (-1+e^3\right ) x^6+e^2 \left (-3 x^5-3 x^6\right )+e \left (3 x^4+6 x^5+3 x^6\right )} \, dx\\ &=\int \frac {432 \exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right ) \left (-4-10 (1-e) x-6 (1-e)^2 x^2-(1-e)^3 x^3\right )}{x^3 (1-(-1+e) x)^3} \, dx\\ &=432 \int \frac {\exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right ) \left (-4-10 (1-e) x-6 (1-e)^2 x^2-(1-e)^3 x^3\right )}{x^3 (1-(-1+e) x)^3} \, dx\\ &=432 \int \left (-\frac {4 \exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{x^3}-\frac {2 (-1+e) \exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{x^2}+\frac {(-1+e)^3 \exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{(1+(1-e) x)^3}+\frac {2 (-1+e)^3 \exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{(1+(1-e) x)^2}\right ) \, dx\\ &=-\left (1728 \int \frac {\exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{x^3} \, dx\right )+(864 (1-e)) \int \frac {\exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{x^2} \, dx-\left (432 (1-e)^3\right ) \int \frac {\exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{(1+(1-e) x)^3} \, dx-\left (864 (1-e)^3\right ) \int \frac {\exp \left (\frac {864 e+864 (1-e) e x+\left (1+216 e-432 e^2+216 e^3\right ) x^2+2 (1-e) x^3+(1-e)^2 x^4}{x^2 (-1+(-1+e) x)^2}\right )}{(1+(1-e) x)^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 26, normalized size = 1.24 \begin {gather*} e^{\frac {216 e (-2+(-1+e) x)^2}{x^2 (-1+(-1+e) x)^2}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.64, size = 63, normalized size = 3.00 \begin {gather*} e^{\left (\frac {216 \, {\left (x^{2} e^{3} - 2 \, {\left (x^{2} + 2 \, x\right )} e^{2} + {\left (x^{2} + 4 \, x + 4\right )} e\right )}}{x^{4} e^{2} + x^{4} + 2 \, x^{3} + x^{2} - 2 \, {\left (x^{4} + x^{3}\right )} e}\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 = 0.63, size = 67, normalized size = 3.19
method | result | size |
gosper | \({\mathrm e}^{\frac {216 \,{\mathrm e} \left (x^{2} {\mathrm e}^{2}-2 x^{2} {\mathrm e}-4 x \,{\mathrm e}+x^{2}+4 x +4\right )}{x^{2} \left (x^{2} {\mathrm e}^{2}-2 x^{2} {\mathrm e}-2 x \,{\mathrm e}+x^{2}+2 x +1\right )}}\) | \(67\) |
risch | \({\mathrm e}^{-\frac {216 \left (-2 x^{2} {\mathrm e}^{2}+x^{2} {\mathrm e}+x^{2} {\mathrm e}^{3}-4 \,{\mathrm e}^{2} x +4 x \,{\mathrm e}+4 \,{\mathrm e}\right )}{x^{2} \left (2 x^{2} {\mathrm e}-x^{2} {\mathrm e}^{2}+2 x \,{\mathrm e}-x^{2}-2 x -1\right )}}\) | \(72\) |
norman | \(\frac {x^{2} {\mathrm e}^{\frac {216 x^{2} {\mathrm e}^{3}+\left (-432 x^{2}-864 x \right ) {\mathrm e}^{2}+\left (216 x^{2}+864 x +864\right ) {\mathrm e}}{x^{4} {\mathrm e}^{2}+\left (-2 x^{4}-2 x^{3}\right ) {\mathrm e}+x^{4}+2 x^{3}+x^{2}}}+\left (-2 \,{\mathrm e}+2\right ) x^{3} {\mathrm e}^{\frac {216 x^{2} {\mathrm e}^{3}+\left (-432 x^{2}-864 x \right ) {\mathrm e}^{2}+\left (216 x^{2}+864 x +864\right ) {\mathrm e}}{x^{4} {\mathrm e}^{2}+\left (-2 x^{4}-2 x^{3}\right ) {\mathrm e}+x^{4}+2 x^{3}+x^{2}}}+\left ({\mathrm e}^{2}-2 \,{\mathrm e}+1\right ) x^{4} {\mathrm e}^{\frac {216 x^{2} {\mathrm e}^{3}+\left (-432 x^{2}-864 x \right ) {\mathrm e}^{2}+\left (216 x^{2}+864 x +864\right ) {\mathrm e}}{x^{4} {\mathrm e}^{2}+\left (-2 x^{4}-2 x^{3}\right ) {\mathrm e}+x^{4}+2 x^{3}+x^{2}}}}{x^{2} \left (x \,{\mathrm e}-x -1\right )^{2}}\) | \(270\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 2.80, size = 146, normalized size = 6.95 \begin {gather*} e^{\left (\frac {216 \, e^{3}}{x^{2} {\left (e^{2} - 2 \, e + 1\right )} - 2 \, x {\left (e - 1\right )} + 1} - \frac {864 \, e^{3}}{x {\left (e - 1\right )} - 1} - \frac {432 \, e^{2}}{x^{2} {\left (e^{2} - 2 \, e + 1\right )} - 2 \, x {\left (e - 1\right )} + 1} + \frac {1728 \, e^{2}}{x {\left (e - 1\right )} - 1} + \frac {864 \, e^{2}}{x} + \frac {216 \, e}{x^{2} {\left (e^{2} - 2 \, e + 1\right )} - 2 \, x {\left (e - 1\right )} + 1} - \frac {864 \, e}{x {\left (e - 1\right )} - 1} - \frac {864 \, e}{x} + \frac {864 \, e}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.44, size = 213, normalized size = 10.14 \begin {gather*} {\mathrm {e}}^{\frac {216\,\mathrm {e}}{2\,x-2\,x\,\mathrm {e}-2\,x^2\,\mathrm {e}+x^2\,{\mathrm {e}}^2+x^2+1}}\,{\mathrm {e}}^{\frac {216\,{\mathrm {e}}^3}{2\,x-2\,x\,\mathrm {e}-2\,x^2\,\mathrm {e}+x^2\,{\mathrm {e}}^2+x^2+1}}\,{\mathrm {e}}^{-\frac {432\,{\mathrm {e}}^2}{2\,x-2\,x\,\mathrm {e}-2\,x^2\,\mathrm {e}+x^2\,{\mathrm {e}}^2+x^2+1}}\,{\mathrm {e}}^{\frac {864\,\mathrm {e}}{x-2\,x^2\,\mathrm {e}-2\,x^3\,\mathrm {e}+x^3\,{\mathrm {e}}^2+2\,x^2+x^3}}\,{\mathrm {e}}^{-\frac {864\,{\mathrm {e}}^2}{x-2\,x^2\,\mathrm {e}-2\,x^3\,\mathrm {e}+x^3\,{\mathrm {e}}^2+2\,x^2+x^3}}\,{\mathrm {e}}^{\frac {864\,\mathrm {e}}{x^4\,{\mathrm {e}}^2-2\,x^4\,\mathrm {e}-2\,x^3\,\mathrm {e}+x^2+2\,x^3+x^4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 2.66, size = 70, normalized size = 3.33 \begin {gather*} e^{\frac {216 x^{2} e^{3} + \left (- 432 x^{2} - 864 x\right ) e^{2} + e \left (216 x^{2} + 864 x + 864\right )}{x^{4} + x^{4} e^{2} + 2 x^{3} + x^{2} + e \left (- 2 x^{4} - 2 x^{3}\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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