Optimal. Leaf size=30 \[ e^{\left (\left (4-\frac {25}{3 \left (1-3 e^{10/x}\right )}\right )^2-e x\right )^2} \]
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Rubi [F] time = 76.78, 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 {28561-3042 e x+81 e^2 x^2+e^{30/x} \left (2426112-11664 e x-8748 e^2 x^2\right )+e^{10/x} \left (316368+1404 e x-972 e^2 x^2\right )+e^{20/x} \left (1314144+50382 e x+4374 e^2 x^2\right )+e^{40/x} \left (1679616-209952 e x+6561 e^2 x^2\right )}{81-972 e^{10/x}+4374 e^{20/x}-8748 e^{30/x}+6561 e^{40/x}}\right ) \left (1014 e x^2-54 e^2 x^3+e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )+e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )+e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )+e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )+e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{-27 x^2+405 e^{10/x} x^2-2430 e^{20/x} x^2+7290 e^{30/x} x^2-10935 e^{40/x} x^2+6561 e^{50/x} 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 \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-1014 e x^2+54 e^2 x^3-e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )-e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )-e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )-e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )-e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{27 \left (1-3 e^{10/x}\right )^5 x^2} \, dx\\ &=\frac {1}{27} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-1014 e x^2+54 e^2 x^3-e^{50/x} \left (-209952 e x^2+13122 e^2 x^3\right )-e^{20/x} \left (18252000-4860 e^2 x^3+e \left (378000 x-15390 x^2\right )\right )-e^{10/x} \left (2197000+810 e^2 x^3+e \left (-117000 x-3510 x^2\right )\right )-e^{30/x} \left (50544000+14580 e^2 x^3+e \left (891000 x+54270 x^2\right )\right )-e^{40/x} \left (46656000-21870 e^2 x^3+e \left (-2916000 x+58320 x^2\right )\right )\right )}{\left (1-3 e^{10/x}\right )^5 x^2} \, dx\\ &=\frac {1}{27} \int \left (\frac {15625000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{3 \left (-1+3 e^{10/x}\right )^5 x^2}+\frac {38125000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{3 \left (-1+3 e^{10/x}\right )^4 x^2}-\frac {75000 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-148+e x)}{\left (-1+3 e^{10/x}\right )^3 x^2}+54 \exp \left (1+\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-16+e x)-\frac {3600 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-160+10 e x+e x^2\right )}{\left (-1+3 e^{10/x}\right ) x^2}-\frac {750 \exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-5568+148 e x+5 e x^2\right )}{\left (-1+3 e^{10/x}\right )^2 x^2}\right ) \, dx\\ &=2 \int \exp \left (1+\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-16+e x) \, dx-\frac {250}{9} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-5568+148 e x+5 e x^2\right )}{\left (-1+3 e^{10/x}\right )^2 x^2} \, dx-\frac {400}{3} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) \left (-160+10 e x+e x^2\right )}{\left (-1+3 e^{10/x}\right ) x^2} \, dx-\frac {25000}{9} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right ) (-148+e x)}{\left (-1+3 e^{10/x}\right )^3 x^2} \, dx+\frac {15625000}{81} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{\left (-1+3 e^{10/x}\right )^5 x^2} \, dx+\frac {38125000}{81} \int \frac {\exp \left (\frac {\left (-169-936 e^{10/x}-1296 e^{20/x}+9 e x-54 e^{1+\frac {10}{x}} x+81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (-1+3 e^{10/x}\right )^4}\right )}{\left (-1+3 e^{10/x}\right )^4 x^2} \, dx\\ &=\text {Rest of rules removed due to large latex content} \end {aligned} \end {gather*}
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Mathematica [B] time = 0.50, size = 69, normalized size = 2.30 \begin {gather*} e^{\frac {\left (169+936 e^{10/x}+1296 e^{20/x}-9 e x+54 e^{1+\frac {10}{x}} x-81 e^{1+\frac {20}{x}} x\right )^2}{81 \left (1-3 e^{10/x}\right )^4}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.69, size = 140, normalized size = 4.67 \begin {gather*} e^{\left (\frac {81 \, x^{2} e^{2} - 3042 \, x e + 6561 \, {\left (x^{2} e^{2} - 32 \, x e + 256\right )} e^{\frac {40}{x}} - 2916 \, {\left (3 \, x^{2} e^{2} + 4 \, x e - 832\right )} e^{\frac {30}{x}} + 162 \, {\left (27 \, x^{2} e^{2} + 311 \, x e + 8112\right )} e^{\frac {20}{x}} - 36 \, {\left (27 \, x^{2} e^{2} - 39 \, x e - 8788\right )} e^{\frac {10}{x}} + 28561}{81 \, {\left (81 \, e^{\frac {40}{x}} - 108 \, e^{\frac {30}{x}} + 54 \, e^{\frac {20}{x}} - 12 \, e^{\frac {10}{x}} + 1\right )}}\right )} \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 {2 \, {\left (27 \, x^{3} e^{2} - 507 \, x^{2} e - 6561 \, {\left (x^{3} e^{2} - 16 \, x^{2} e\right )} e^{\frac {50}{x}} + 3645 \, {\left (3 \, x^{3} e^{2} - 8 \, {\left (x^{2} - 50 \, x\right )} e - 6400\right )} e^{\frac {40}{x}} - 405 \, {\left (18 \, x^{3} e^{2} + {\left (67 \, x^{2} + 1100 \, x\right )} e + 62400\right )} e^{\frac {30}{x}} + 135 \, {\left (18 \, x^{3} e^{2} + {\left (57 \, x^{2} - 1400 \, x\right )} e - 67600\right )} e^{\frac {20}{x}} - 5 \, {\left (81 \, x^{3} e^{2} - 117 \, {\left (3 \, x^{2} + 100 \, x\right )} e + 219700\right )} e^{\frac {10}{x}}\right )} e^{\left (\frac {81 \, x^{2} e^{2} - 3042 \, x e + 6561 \, {\left (x^{2} e^{2} - 32 \, x e + 256\right )} e^{\frac {40}{x}} - 2916 \, {\left (3 \, x^{2} e^{2} + 4 \, x e - 832\right )} e^{\frac {30}{x}} + 162 \, {\left (27 \, x^{2} e^{2} + 311 \, x e + 8112\right )} e^{\frac {20}{x}} - 36 \, {\left (27 \, x^{2} e^{2} - 39 \, x e - 8788\right )} e^{\frac {10}{x}} + 28561}{81 \, {\left (81 \, e^{\frac {40}{x}} - 108 \, e^{\frac {30}{x}} + 54 \, e^{\frac {20}{x}} - 12 \, e^{\frac {10}{x}} + 1\right )}}\right )}}{27 \, {\left (243 \, x^{2} e^{\frac {50}{x}} - 405 \, x^{2} e^{\frac {40}{x}} + 270 \, x^{2} e^{\frac {30}{x}} - 90 \, x^{2} e^{\frac {20}{x}} + 15 \, x^{2} e^{\frac {10}{x}} - x^{2}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 3.39, size = 186, normalized size = 6.20
method | result | size |
risch | \({\mathrm e}^{\frac {-6561 x^{2} {\mathrm e}^{\frac {40+2 x}{x}}+8748 x^{2} {\mathrm e}^{\frac {2 x +30}{x}}-4374 x^{2} {\mathrm e}^{\frac {2 x +20}{x}}+972 x^{2} {\mathrm e}^{\frac {2 x +10}{x}}-81 x^{2} {\mathrm e}^{2}+209952 x \,{\mathrm e}^{\frac {40+x}{x}}+11664 x \,{\mathrm e}^{\frac {30+x}{x}}-50382 x \,{\mathrm e}^{\frac {20+x}{x}}-1404 x \,{\mathrm e}^{\frac {x +10}{x}}+3042 x \,{\mathrm e}-1679616 \,{\mathrm e}^{\frac {40}{x}}-2426112 \,{\mathrm e}^{\frac {30}{x}}-1314144 \,{\mathrm e}^{\frac {20}{x}}-316368 \,{\mathrm e}^{\frac {10}{x}}-28561}{-6561 \,{\mathrm e}^{\frac {40}{x}}+8748 \,{\mathrm e}^{\frac {30}{x}}-4374 \,{\mathrm e}^{\frac {20}{x}}+972 \,{\mathrm e}^{\frac {10}{x}}-81}}\) | \(186\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [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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mupad [B] time = 9.22, size = 697, normalized size = 23.23 \begin {gather*} {\mathrm {e}}^{\frac {16224\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {20736\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {29952\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {35152\,{\mathrm {e}}^{10/x}}{486\,{\mathrm {e}}^{20/x}-108\,{\mathrm {e}}^{10/x}-972\,{\mathrm {e}}^{30/x}+729\,{\mathrm {e}}^{40/x}+9}}\,{\mathrm {e}}^{-\frac {12\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{10/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {54\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {81\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {108\,x^2\,{\mathrm {e}}^2\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {338\,x\,\mathrm {e}}{486\,{\mathrm {e}}^{20/x}-108\,{\mathrm {e}}^{10/x}-972\,{\mathrm {e}}^{30/x}+729\,{\mathrm {e}}^{40/x}+9}}\,{\mathrm {e}}^{\frac {28561}{4374\,{\mathrm {e}}^{20/x}-972\,{\mathrm {e}}^{10/x}-8748\,{\mathrm {e}}^{30/x}+6561\,{\mathrm {e}}^{40/x}+81}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^2}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {144\,x\,\mathrm {e}\,{\mathrm {e}}^{30/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{\frac {52\,x\,\mathrm {e}\,{\mathrm {e}}^{10/x}}{162\,{\mathrm {e}}^{20/x}-36\,{\mathrm {e}}^{10/x}-324\,{\mathrm {e}}^{30/x}+243\,{\mathrm {e}}^{40/x}+3}}\,{\mathrm {e}}^{\frac {622\,x\,\mathrm {e}\,{\mathrm {e}}^{20/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}}\,{\mathrm {e}}^{-\frac {2592\,x\,\mathrm {e}\,{\mathrm {e}}^{40/x}}{54\,{\mathrm {e}}^{20/x}-12\,{\mathrm {e}}^{10/x}-108\,{\mathrm {e}}^{30/x}+81\,{\mathrm {e}}^{40/x}+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 3.64, size = 134, normalized size = 4.47 \begin {gather*} e^{\frac {81 x^{2} e^{2} - 3042 e x + \left (- 8748 x^{2} e^{2} - 11664 e x + 2426112\right ) e^{\frac {30}{x}} + \left (- 972 x^{2} e^{2} + 1404 e x + 316368\right ) e^{\frac {10}{x}} + \left (4374 x^{2} e^{2} + 50382 e x + 1314144\right ) e^{\frac {20}{x}} + \left (6561 x^{2} e^{2} - 209952 e x + 1679616\right ) e^{\frac {40}{x}} + 28561}{6561 e^{\frac {40}{x}} - 8748 e^{\frac {30}{x}} + 4374 e^{\frac {20}{x}} - 972 e^{\frac {10}{x}} + 81}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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