Optimal. Leaf size=30 \[ \frac {1}{16} e^{x^2+\frac {x}{\left (-e^{4 (12-e)}+x\right )^2}} x^2 \]
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Rubi [F] time = 10.34, 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 {x^2-2 e^{-48+4 e} x^3+e^{-96+8 e} \left (x+x^4\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}\right ) \left (-2 x-2 x^3+e^{-48+4 e} \left (6 x^2+6 x^4\right )+e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )+e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{-16+48 e^{-48+4 e} x-48 e^{-96+8 e} x^2+16 e^{-144+12 e} x^3} \, 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 {x \left (e^{-96+8 e}+x-2 e^{-48+4 e} x^2+e^{-96+8 e} x^3\right )}{1-2 e^{-48+4 e} x+e^{-96+8 e} x^2}\right ) \left (2 x+2 x^3-e^{-48+4 e} \left (6 x^2+6 x^4\right )-e^{-96+8 e} \left (-x^2-6 x^3-6 x^5\right )-e^{-144+12 e} \left (-x^3+2 x^4+2 x^6\right )\right )}{16-48 e^{-48+4 e} x+48 e^{-96+8 e} x^2-16 e^{-12 (12-e)} x^3} \, dx\\ &=\int \frac {\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \left (2 e^{144} \left (1+x^2\right )-6 e^{96+4 e} x \left (1+x^2\right )-e^{12 e} x^2 \left (-1+2 x+2 x^3\right )+e^{8 (6+e)} x \left (1+6 x+6 x^3\right )\right )}{16 \left (e^{48}-e^{4 e} x\right )^3} \, dx\\ &=\frac {1}{16} \int \frac {\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \left (2 e^{144} \left (1+x^2\right )-6 e^{96+4 e} x \left (1+x^2\right )-e^{12 e} x^2 \left (-1+2 x+2 x^3\right )+e^{8 (6+e)} x \left (1+6 x+6 x^3\right )\right )}{\left (e^{48}-e^{4 e} x\right )^3} \, dx\\ &=\frac {1}{16} \int \left (-\exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )+2 \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x+2 \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x^3+\frac {2 \exp \left (144+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^3}-\frac {5 \exp \left (96+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^2}+\frac {4 \exp \left (48+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{e^{48}-e^{4 e} x}\right ) \, dx\\ &=-\left (\frac {1}{16} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) \, dx\right )+\frac {1}{8} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x \, dx+\frac {1}{8} \int \exp \left (\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right ) x^3 \, dx+\frac {1}{8} \int \frac {\exp \left (144+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^3} \, dx+\frac {1}{4} \int \frac {\exp \left (48+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{e^{48}-e^{4 e} x} \, dx-\frac {5}{16} \int \frac {\exp \left (96+\frac {x \left (e^{8 e}+e^{96} x-2 e^{48+4 e} x^2+e^{8 e} x^3\right )}{\left (e^{48}-e^{4 e} x\right )^2}\right )}{\left (e^{48}-e^{4 e} x\right )^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 7.35, size = 54, normalized size = 1.80 \begin {gather*} \frac {1}{16} e^{\frac {x \left (e^{96} x-2 e^{48+4 e} x^2+e^{8 e} \left (1+x^3\right )\right )}{\left (e^{48}-e^{4 e} x\right )^2}} x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.46, size = 65, normalized size = 2.17 \begin {gather*} \frac {1}{16} \, x^{2} e^{\left (-\frac {2 \, x^{3} e^{\left (4 \, e - 48\right )} - x^{2} - {\left (x^{4} + x\right )} e^{\left (8 \, e - 96\right )}}{x^{2} e^{\left (8 \, e - 96\right )} - 2 \, x e^{\left (4 \, e - 48\right )} + 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 2.47, size = 68, normalized size = 2.27 \begin {gather*} \frac {1}{16} \, x^{2} e^{\left (\frac {x^{4} e^{\left (8 \, e - 96\right )} - 2 \, x^{3} e^{\left (4 \, e - 48\right )} + x^{2} + x e^{\left (8 \, e - 96\right )}}{x^{2} e^{\left (8 \, e - 96\right )} - 2 \, x e^{\left (4 \, e - 48\right )} + 1}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.40, size = 66, normalized size = 2.20
method | result | size |
risch | \(\frac {x^{2} {\mathrm e}^{\frac {x \left ({\mathrm e}^{8 \,{\mathrm e}-96} x^{3}-2 x^{2} {\mathrm e}^{4 \,{\mathrm e}-48}+{\mathrm e}^{8 \,{\mathrm e}-96}+x \right )}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}\) | \(66\) |
gosper | \(\frac {x^{2} {\mathrm e}^{\frac {x \left ({\mathrm e}^{8 \,{\mathrm e}-96} x^{3}-2 x^{2} {\mathrm e}^{4 \,{\mathrm e}-48}+{\mathrm e}^{8 \,{\mathrm e}-96}+x \right )}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}\) | \(72\) |
norman | \(\frac {\frac {x^{2} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}-\frac {x^{3} {\mathrm e}^{4 \,{\mathrm e}} {\mathrm e}^{-48} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{8}+\frac {{\mathrm e}^{8 \,{\mathrm e}} {\mathrm e}^{-96} x^{4} {\mathrm e}^{\frac {\left (x^{4}+x \right ) {\mathrm e}^{8 \,{\mathrm e}-96}-2 x^{3} {\mathrm e}^{4 \,{\mathrm e}-48}+x^{2}}{x^{2} {\mathrm e}^{8 \,{\mathrm e}-96}-2 x \,{\mathrm e}^{4 \,{\mathrm e}-48}+1}}}{16}}{\left (x \,{\mathrm e}^{4 \,{\mathrm e}-48}-1\right )^{2}}\) | \(227\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.72, size = 62, normalized size = 2.07 \begin {gather*} \frac {1}{16} \, x^{2} e^{\left (x^{2} + \frac {e^{\left (4 \, e\right )}}{x e^{\left (4 \, e\right )} - e^{48}} + \frac {e^{\left (4 \, e + 48\right )}}{x^{2} e^{\left (8 \, e\right )} - 2 \, x e^{\left (4 \, e + 48\right )} + e^{96}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F(-1)] time = 0.00, size = -1, normalized size = -0.03 \begin {gather*} \text {Hanged} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.79, size = 61, normalized size = 2.03 \begin {gather*} \frac {x^{2} e^{\frac {- \frac {2 x^{3}}{e^{48 - 4 e}} + x^{2} + \frac {x^{4} + x}{e^{96 - 8 e}}}{\frac {x^{2}}{e^{96 - 8 e}} - \frac {2 x}{e^{48 - 4 e}} + 1}}}{16} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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