Optimal. Leaf size=30 \[ \left (\frac {e^{-2+2 x}}{x^2}+9 x^2 \left (-3+e^5+x+x^2\right )^2\right )^2 \]
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Rubi [B] time = 0.41, antiderivative size = 193, normalized size of antiderivative = 6.43, number of steps used = 22, number of rules used = 7, integrand size = 223, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {6, 14, 2197, 2196, 2194, 2176, 1588} \begin {gather*} 18 e^{2 x-2} x^4+\frac {e^{4 x-4}}{x^4}+36 e^{2 x-2} x^3-54 e^{2 x-2} x^2-36 \left (1-e^5\right ) e^{2 x-2} x^2+81 \left (-x^2-x-e^5+3\right )^4 x^4+54 e^{2 x-2} x+36 \left (1-e^5\right ) e^{2 x-2} x-18 \left (11-4 e^5\right ) e^{2 x-2} x-27 e^{2 x-2}+18 \left (6-5 e^5+e^{10}\right ) e^{2 x-2}-18 \left (1-e^5\right ) e^{2 x-2}+9 \left (11-4 e^5\right ) e^{2 x-2} \end {gather*}
Antiderivative was successfully verified.
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Rule 6
Rule 14
Rule 1588
Rule 2176
Rule 2194
Rule 2196
Rule 2197
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\left (26244+324 e^{20}\right ) x^8-43740 x^9-26244 x^{10}+54432 x^{11}+12312 x^{12}-23328 x^{13}-4860 x^{14}+3564 x^{15}+972 x^{16}+e^{-4+4 x} (-4+4 x)+e^{15} \left (-3888 x^8+1620 x^9+1944 x^{10}\right )+e^{10} \left (17496 x^8-14580 x^9-14580 x^{10}+6804 x^{11}+3888 x^{12}\right )+e^5 \left (-34992 x^8+43740 x^9+34992 x^{10}-38556 x^{11}-15552 x^{12}+8748 x^{13}+3240 x^{14}\right )+e^{-2+2 x} \left (216 x^5+36 e^{10} x^5-396 x^6-72 x^7+144 x^8+36 x^9+e^5 \left (-180 x^5+144 x^6+72 x^7\right )\right )}{x^5} \, dx\\ &=\int \left (\frac {4 e^{-4+4 x} (-1+x)}{x^5}+36 e^{-2+2 x} \left (-3+e^5+x+x^2\right ) \left (-2+e^5+3 x+x^2\right )+324 x^3 \left (-3+e^5+x+x^2\right )^3 \left (-3+e^5+2 x+3 x^2\right )\right ) \, dx\\ &=4 \int \frac {e^{-4+4 x} (-1+x)}{x^5} \, dx+36 \int e^{-2+2 x} \left (-3+e^5+x+x^2\right ) \left (-2+e^5+3 x+x^2\right ) \, dx+324 \int x^3 \left (-3+e^5+x+x^2\right )^3 \left (-3+e^5+2 x+3 x^2\right ) \, dx\\ &=\frac {e^{-4+4 x}}{x^4}+81 x^4 \left (3-e^5-x-x^2\right )^4+36 \int \left (6 e^{-2+2 x} \left (1+\frac {1}{6} e^5 \left (-5+e^5\right )\right )+e^{-2+2 x} \left (-11+4 e^5\right ) x+2 e^{-2+2 x} \left (-1+e^5\right ) x^2+4 e^{-2+2 x} x^3+e^{-2+2 x} x^4\right ) \, dx\\ &=\frac {e^{-4+4 x}}{x^4}+81 x^4 \left (3-e^5-x-x^2\right )^4+36 \int e^{-2+2 x} x^4 \, dx+144 \int e^{-2+2 x} x^3 \, dx-\left (36 \left (11-4 e^5\right )\right ) \int e^{-2+2 x} x \, dx-\left (72 \left (1-e^5\right )\right ) \int e^{-2+2 x} x^2 \, dx+\left (36 \left (6-5 e^5+e^{10}\right )\right ) \int e^{-2+2 x} \, dx\\ &=18 e^{-2+2 x} \left (6-5 e^5+e^{10}\right )+\frac {e^{-4+4 x}}{x^4}-18 e^{-2+2 x} \left (11-4 e^5\right ) x-36 e^{-2+2 x} \left (1-e^5\right ) x^2+72 e^{-2+2 x} x^3+18 e^{-2+2 x} x^4+81 x^4 \left (3-e^5-x-x^2\right )^4-72 \int e^{-2+2 x} x^3 \, dx-216 \int e^{-2+2 x} x^2 \, dx+\left (18 \left (11-4 e^5\right )\right ) \int e^{-2+2 x} \, dx+\left (72 \left (1-e^5\right )\right ) \int e^{-2+2 x} x \, dx\\ &=9 e^{-2+2 x} \left (11-4 e^5\right )+18 e^{-2+2 x} \left (6-5 e^5+e^{10}\right )+\frac {e^{-4+4 x}}{x^4}-18 e^{-2+2 x} \left (11-4 e^5\right ) x+36 e^{-2+2 x} \left (1-e^5\right ) x-108 e^{-2+2 x} x^2-36 e^{-2+2 x} \left (1-e^5\right ) x^2+36 e^{-2+2 x} x^3+18 e^{-2+2 x} x^4+81 x^4 \left (3-e^5-x-x^2\right )^4+108 \int e^{-2+2 x} x^2 \, dx+216 \int e^{-2+2 x} x \, dx-\left (36 \left (1-e^5\right )\right ) \int e^{-2+2 x} \, dx\\ &=9 e^{-2+2 x} \left (11-4 e^5\right )-18 e^{-2+2 x} \left (1-e^5\right )+18 e^{-2+2 x} \left (6-5 e^5+e^{10}\right )+\frac {e^{-4+4 x}}{x^4}+108 e^{-2+2 x} x-18 e^{-2+2 x} \left (11-4 e^5\right ) x+36 e^{-2+2 x} \left (1-e^5\right ) x-54 e^{-2+2 x} x^2-36 e^{-2+2 x} \left (1-e^5\right ) x^2+36 e^{-2+2 x} x^3+18 e^{-2+2 x} x^4+81 x^4 \left (3-e^5-x-x^2\right )^4-108 \int e^{-2+2 x} \, dx-108 \int e^{-2+2 x} x \, dx\\ &=-54 e^{-2+2 x}+9 e^{-2+2 x} \left (11-4 e^5\right )-18 e^{-2+2 x} \left (1-e^5\right )+18 e^{-2+2 x} \left (6-5 e^5+e^{10}\right )+\frac {e^{-4+4 x}}{x^4}+54 e^{-2+2 x} x-18 e^{-2+2 x} \left (11-4 e^5\right ) x+36 e^{-2+2 x} \left (1-e^5\right ) x-54 e^{-2+2 x} x^2-36 e^{-2+2 x} \left (1-e^5\right ) x^2+36 e^{-2+2 x} x^3+18 e^{-2+2 x} x^4+81 x^4 \left (3-e^5-x-x^2\right )^4+54 \int e^{-2+2 x} \, dx\\ &=-27 e^{-2+2 x}+9 e^{-2+2 x} \left (11-4 e^5\right )-18 e^{-2+2 x} \left (1-e^5\right )+18 e^{-2+2 x} \left (6-5 e^5+e^{10}\right )+\frac {e^{-4+4 x}}{x^4}+54 e^{-2+2 x} x-18 e^{-2+2 x} \left (11-4 e^5\right ) x+36 e^{-2+2 x} \left (1-e^5\right ) x-54 e^{-2+2 x} x^2-36 e^{-2+2 x} \left (1-e^5\right ) x^2+36 e^{-2+2 x} x^3+18 e^{-2+2 x} x^4+81 x^4 \left (3-e^5-x-x^2\right )^4\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 53, normalized size = 1.77 \begin {gather*} \frac {\left (e^{2 x}+9 e^{12} x^4+18 e^7 x^4 \left (-3+x+x^2\right )+9 e^2 x^4 \left (-3+x+x^2\right )^2\right )^2}{e^4 x^4} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 199, normalized size = 6.63 \begin {gather*} \frac {81 \, x^{16} + 324 \, x^{15} - 486 \, x^{14} - 2592 \, x^{13} + 1539 \, x^{12} + 7776 \, x^{11} - 4374 \, x^{10} - 8748 \, x^{9} + 81 \, x^{8} e^{20} + 6561 \, x^{8} + 324 \, {\left (x^{10} + x^{9} - 3 \, x^{8}\right )} e^{15} + 486 \, {\left (x^{12} + 2 \, x^{11} - 5 \, x^{10} - 6 \, x^{9} + 9 \, x^{8}\right )} e^{10} + 324 \, {\left (x^{14} + 3 \, x^{13} - 6 \, x^{12} - 17 \, x^{11} + 18 \, x^{10} + 27 \, x^{9} - 27 \, x^{8}\right )} e^{5} + 18 \, {\left (x^{8} + 2 \, x^{7} - 5 \, x^{6} - 6 \, x^{5} + x^{4} e^{10} + 9 \, x^{4} + 2 \, {\left (x^{6} + x^{5} - 3 \, x^{4}\right )} e^{5}\right )} e^{\left (2 \, x - 2\right )} + e^{\left (4 \, x - 4\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.39, size = 287, normalized size = 9.57 \begin {gather*} \frac {{\left (81 \, x^{16} e^{6} + 324 \, x^{15} e^{6} + 324 \, x^{14} e^{11} - 486 \, x^{14} e^{6} + 972 \, x^{13} e^{11} - 2592 \, x^{13} e^{6} + 486 \, x^{12} e^{16} - 1944 \, x^{12} e^{11} + 1539 \, x^{12} e^{6} + 972 \, x^{11} e^{16} - 5508 \, x^{11} e^{11} + 7776 \, x^{11} e^{6} + 324 \, x^{10} e^{21} - 2430 \, x^{10} e^{16} + 5832 \, x^{10} e^{11} - 4374 \, x^{10} e^{6} + 324 \, x^{9} e^{21} - 2916 \, x^{9} e^{16} + 8748 \, x^{9} e^{11} - 8748 \, x^{9} e^{6} + 81 \, x^{8} e^{26} - 972 \, x^{8} e^{21} + 4374 \, x^{8} e^{16} - 8748 \, x^{8} e^{11} + 6561 \, x^{8} e^{6} + 18 \, x^{8} e^{\left (2 \, x + 4\right )} + 36 \, x^{7} e^{\left (2 \, x + 4\right )} + 36 \, x^{6} e^{\left (2 \, x + 9\right )} - 90 \, x^{6} e^{\left (2 \, x + 4\right )} + 36 \, x^{5} e^{\left (2 \, x + 9\right )} - 108 \, x^{5} e^{\left (2 \, x + 4\right )} + 18 \, x^{4} e^{\left (2 \, x + 14\right )} - 108 \, x^{4} e^{\left (2 \, x + 9\right )} + 162 \, x^{4} e^{\left (2 \, x + 4\right )} + e^{\left (4 \, x + 2\right )}\right )} e^{\left (-6\right )}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [B] time = 0.40, size = 216, normalized size = 7.20
method | result | size |
risch | \(324 x^{11}+81 x^{12}+7776 x^{7}+1539 x^{8}-486 x^{10}-2592 x^{9}-4374 x^{6}-8748 x^{5}+6561 x^{4}-5508 x^{7} {\mathrm e}^{5}+8748 x^{5} {\mathrm e}^{5}-1944 x^{8} {\mathrm e}^{5}-8748 x^{4} {\mathrm e}^{5}+5832 x^{6} {\mathrm e}^{5}+324 \,{\mathrm e}^{5} x^{10}+972 \,{\mathrm e}^{5} x^{9}+324 x^{6} {\mathrm e}^{15}-2430 x^{6} {\mathrm e}^{10}+324 x^{5} {\mathrm e}^{15}-2916 x^{5} {\mathrm e}^{10}-972 x^{4} {\mathrm e}^{15}+4374 x^{4} {\mathrm e}^{10}+81 x^{4} {\mathrm e}^{20}+486 x^{8} {\mathrm e}^{10}+972 x^{7} {\mathrm e}^{10}+\left (18 x^{4}+36 x^{2} {\mathrm e}^{5}+36 x^{3}+18 \,{\mathrm e}^{10}+36 x \,{\mathrm e}^{5}-90 x^{2}-108 \,{\mathrm e}^{5}-108 x +162\right ) {\mathrm e}^{2 x -2}+\frac {{\mathrm e}^{4 x -4}}{x^{4}}\) | \(216\) |
derivativedivides | \(648-648 x -\frac {188244 \,{\mathrm e}^{5}}{x}+648 \left (x -1\right )^{2}+\frac {282204 \,{\mathrm e}^{5}}{x^{2}}-\frac {184032 \,{\mathrm e}^{5}}{x^{3}}-4536 \left (x -1\right )^{4}+324 \left (x -1\right ) {\mathrm e}^{20}+\frac {151632 \,{\mathrm e}^{15}}{x}+1620 \left (x -1\right ) {\mathrm e}^{5}+18 \,{\mathrm e}^{2 x -2}+\frac {{\mathrm e}^{4 x -4}}{x^{4}}-972 \left (x -1\right ) {\mathrm e}^{10}-\frac {7047 \,{\mathrm e}^{10}}{x^{4}}-\frac {16524 \,{\mathrm e}^{10}}{x}-\frac {29403 \,{\mathrm e}^{15}}{x^{4}}+486 \,{\mathrm e}^{10} \left (x -1\right )^{8}+324 \,{\mathrm e}^{15} \left (x -1\right )^{6}+4860 \,{\mathrm e}^{10} \left (x -1\right )^{7}+81 \,{\mathrm e}^{20} \left (x -1\right )^{4}+2268 \,{\mathrm e}^{15} \left (x -1\right )^{5}+17982 \,{\mathrm e}^{10} \left (x -1\right )^{6}+324 \,{\mathrm e}^{20} \left (x -1\right )^{3}+5508 \,{\mathrm e}^{15} \left (x -1\right )^{4}+30132 \,{\mathrm e}^{10} \left (x -1\right )^{5}+486 \,{\mathrm e}^{20} \left (x -1\right )^{2}+5832 \,{\mathrm e}^{15} \left (x -1\right )^{3}+21384 \,{\mathrm e}^{10} \left (x -1\right )^{4}+18 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{4}+2268 \,{\mathrm e}^{15} \left (x -1\right )^{2}+972 \,{\mathrm e}^{10} \left (x -1\right )^{3}+108 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{3}-324 \,{\mathrm e}^{15} \left (x -1\right )-5346 \,{\mathrm e}^{10} \left (x -1\right )^{2}+126 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{2}-108 \,{\mathrm e}^{2 x -2} \left (x -1\right )-\frac {2916 \,{\mathrm e}^{20}}{x^{4}}-15552 \,{\mathrm e}^{10} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )-60264 \,{\mathrm e}^{10} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )-16524 \,{\mathrm e}^{10} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {18468 \,{\mathrm e}^{10}}{x^{3}}-\frac {5346 \,{\mathrm e}^{10}}{x^{2}}+2916 \,{\mathrm e}^{15} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+36936 \,{\mathrm e}^{15} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )+151632 \,{\mathrm e}^{15} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {127980 \,{\mathrm e}^{15}}{x^{3}}-\frac {208980 \,{\mathrm e}^{15}}{x^{2}}+2592 \,{\mathrm e}^{20} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+9072 \,{\mathrm e}^{20} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )+18144 \,{\mathrm e}^{20} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {12960 \,{\mathrm e}^{20}}{x^{3}}-\frac {22680 \,{\mathrm e}^{20}}{x^{2}}+\frac {18144 \,{\mathrm e}^{20}}{x}+1872 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2}}{2 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+360 \,{\mathrm e}^{10} \left (\frac {{\mathrm e}^{2 x -2}}{2 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+36 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}\right )+36 \,{\mathrm e}^{10} \left (-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}\right )+468 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+3600 \,{\mathrm e}^{5} \left (-\frac {5 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {2 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}+\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+3780 \,{\mathrm e}^{5} \left (\frac {7 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+2196 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2}}{2}-\frac {3 \,{\mathrm e}^{2 x -2}}{2 x^{3}}+\frac {7 \,{\mathrm e}^{2 x -2}}{2 x^{2}}-\frac {3 \,{\mathrm e}^{2 x -2}}{x}-{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+648 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2} \left (x -1\right )}{2}-\frac {11 \,{\mathrm e}^{2 x -2}}{4}+\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {17 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {26 \,{\mathrm e}^{2 x -2}}{3 x}+\frac {7 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+72 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2} \left (x -1\right )^{2}}{2}-3 \,{\mathrm e}^{2 x -2} \left (x -1\right )+9 \,{\mathrm e}^{2 x -2}-\frac {13 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {25 \,{\mathrm e}^{2 x -2}}{3 x^{2}}-\frac {55 \,{\mathrm e}^{2 x -2}}{3 x}-\frac {5 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+180 \,{\mathrm e}^{10} \left (-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+360 \,{\mathrm e}^{10} \left (-\frac {5 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {2 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}+\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+180 \,{\mathrm e}^{10} \left (\frac {7 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+36 \,{\mathrm e}^{10} \left (\frac {{\mathrm e}^{2 x -2}}{2}-\frac {3 \,{\mathrm e}^{2 x -2}}{2 x^{3}}+\frac {7 \,{\mathrm e}^{2 x -2}}{2 x^{2}}-\frac {3 \,{\mathrm e}^{2 x -2}}{x}-{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )-324 \,{\mathrm e}^{5} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )-188244 \,{\mathrm e}^{5} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+11988 \,{\mathrm e}^{5} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+\frac {43983 \,{\mathrm e}^{5}}{x^{4}}+324 \,{\mathrm e}^{5} \left (x -1\right )^{10}+4212 \,{\mathrm e}^{5} \left (x -1\right )^{9}+21384 \,{\mathrm e}^{5} \left (x -1\right )^{8}+52812 \,{\mathrm e}^{5} \left (x -1\right )^{7}+62532 \,{\mathrm e}^{5} \left (x -1\right )^{6}+23328 \,{\mathrm e}^{5} \left (x -1\right )^{5}-15876 \,{\mathrm e}^{5} \left (x -1\right )^{4}-11988 \,{\mathrm e}^{5} \left (x -1\right )^{3}+1944 \,{\mathrm e}^{5} \left (x -1\right )^{2}+81 \left (x -1\right )^{12}+1296 \left (x -1\right )^{11}+8424 \left (x -1\right )^{10}+28188 \left (x -1\right )^{9}+49896 \left (x -1\right )^{8}+39528 \left (x -1\right )^{7}-2106 \left (x -1\right )^{6}-20736 \left (x -1\right )^{5}+4860 \left (x -1\right )^{3}\) | \(1654\) |
default | \(648-648 x -\frac {188244 \,{\mathrm e}^{5}}{x}+648 \left (x -1\right )^{2}+\frac {282204 \,{\mathrm e}^{5}}{x^{2}}-\frac {184032 \,{\mathrm e}^{5}}{x^{3}}-4536 \left (x -1\right )^{4}+324 \left (x -1\right ) {\mathrm e}^{20}+\frac {151632 \,{\mathrm e}^{15}}{x}+1620 \left (x -1\right ) {\mathrm e}^{5}+18 \,{\mathrm e}^{2 x -2}+\frac {{\mathrm e}^{4 x -4}}{x^{4}}-972 \left (x -1\right ) {\mathrm e}^{10}-\frac {7047 \,{\mathrm e}^{10}}{x^{4}}-\frac {16524 \,{\mathrm e}^{10}}{x}-\frac {29403 \,{\mathrm e}^{15}}{x^{4}}+486 \,{\mathrm e}^{10} \left (x -1\right )^{8}+324 \,{\mathrm e}^{15} \left (x -1\right )^{6}+4860 \,{\mathrm e}^{10} \left (x -1\right )^{7}+81 \,{\mathrm e}^{20} \left (x -1\right )^{4}+2268 \,{\mathrm e}^{15} \left (x -1\right )^{5}+17982 \,{\mathrm e}^{10} \left (x -1\right )^{6}+324 \,{\mathrm e}^{20} \left (x -1\right )^{3}+5508 \,{\mathrm e}^{15} \left (x -1\right )^{4}+30132 \,{\mathrm e}^{10} \left (x -1\right )^{5}+486 \,{\mathrm e}^{20} \left (x -1\right )^{2}+5832 \,{\mathrm e}^{15} \left (x -1\right )^{3}+21384 \,{\mathrm e}^{10} \left (x -1\right )^{4}+18 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{4}+2268 \,{\mathrm e}^{15} \left (x -1\right )^{2}+972 \,{\mathrm e}^{10} \left (x -1\right )^{3}+108 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{3}-324 \,{\mathrm e}^{15} \left (x -1\right )-5346 \,{\mathrm e}^{10} \left (x -1\right )^{2}+126 \,{\mathrm e}^{2 x -2} \left (x -1\right )^{2}-108 \,{\mathrm e}^{2 x -2} \left (x -1\right )-\frac {2916 \,{\mathrm e}^{20}}{x^{4}}-15552 \,{\mathrm e}^{10} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )-60264 \,{\mathrm e}^{10} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )-16524 \,{\mathrm e}^{10} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {18468 \,{\mathrm e}^{10}}{x^{3}}-\frac {5346 \,{\mathrm e}^{10}}{x^{2}}+2916 \,{\mathrm e}^{15} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+36936 \,{\mathrm e}^{15} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )+151632 \,{\mathrm e}^{15} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {127980 \,{\mathrm e}^{15}}{x^{3}}-\frac {208980 \,{\mathrm e}^{15}}{x^{2}}+2592 \,{\mathrm e}^{20} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+9072 \,{\mathrm e}^{20} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )+18144 \,{\mathrm e}^{20} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+\frac {12960 \,{\mathrm e}^{20}}{x^{3}}-\frac {22680 \,{\mathrm e}^{20}}{x^{2}}+\frac {18144 \,{\mathrm e}^{20}}{x}+1872 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2}}{2 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+360 \,{\mathrm e}^{10} \left (\frac {{\mathrm e}^{2 x -2}}{2 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+36 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}\right )+36 \,{\mathrm e}^{10} \left (-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}\right )+468 \,{\mathrm e}^{5} \left (-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+3600 \,{\mathrm e}^{5} \left (-\frac {5 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {2 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}+\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+3780 \,{\mathrm e}^{5} \left (\frac {7 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+2196 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2}}{2}-\frac {3 \,{\mathrm e}^{2 x -2}}{2 x^{3}}+\frac {7 \,{\mathrm e}^{2 x -2}}{2 x^{2}}-\frac {3 \,{\mathrm e}^{2 x -2}}{x}-{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+648 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2} \left (x -1\right )}{2}-\frac {11 \,{\mathrm e}^{2 x -2}}{4}+\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {17 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {26 \,{\mathrm e}^{2 x -2}}{3 x}+\frac {7 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+72 \,{\mathrm e}^{5} \left (\frac {{\mathrm e}^{2 x -2} \left (x -1\right )^{2}}{2}-3 \,{\mathrm e}^{2 x -2} \left (x -1\right )+9 \,{\mathrm e}^{2 x -2}-\frac {13 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {25 \,{\mathrm e}^{2 x -2}}{3 x^{2}}-\frac {55 \,{\mathrm e}^{2 x -2}}{3 x}-\frac {5 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+180 \,{\mathrm e}^{10} \left (-\frac {{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {{\mathrm e}^{2 x -2}}{6 x^{2}}-\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+360 \,{\mathrm e}^{10} \left (-\frac {5 \,{\mathrm e}^{2 x -2}}{6 x^{3}}+\frac {2 \,{\mathrm e}^{2 x -2}}{3 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}+\frac {2 \,{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+180 \,{\mathrm e}^{10} \left (\frac {7 \,{\mathrm e}^{2 x -2}}{6 x^{3}}-\frac {11 \,{\mathrm e}^{2 x -2}}{6 x^{2}}+\frac {{\mathrm e}^{2 x -2}}{3 x}-\frac {{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )}{3}-\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )+36 \,{\mathrm e}^{10} \left (\frac {{\mathrm e}^{2 x -2}}{2}-\frac {3 \,{\mathrm e}^{2 x -2}}{2 x^{3}}+\frac {7 \,{\mathrm e}^{2 x -2}}{2 x^{2}}-\frac {3 \,{\mathrm e}^{2 x -2}}{x}-{\mathrm e}^{-2} \expIntegralEi \left (1, -2 x \right )+\frac {{\mathrm e}^{2 x -2}}{4 x^{4}}\right )-324 \,{\mathrm e}^{5} \left (\frac {2}{3 x^{3}}-\frac {1}{4 x^{4}}-\frac {1}{2 x^{2}}\right )-188244 \,{\mathrm e}^{5} \left (-\frac {1}{x^{3}}+\frac {1}{4 x^{4}}+\frac {3}{2 x^{2}}-\frac {1}{x}\right )+11988 \,{\mathrm e}^{5} \left (-\frac {1}{3 x^{3}}+\frac {1}{4 x^{4}}\right )+\frac {43983 \,{\mathrm e}^{5}}{x^{4}}+324 \,{\mathrm e}^{5} \left (x -1\right )^{10}+4212 \,{\mathrm e}^{5} \left (x -1\right )^{9}+21384 \,{\mathrm e}^{5} \left (x -1\right )^{8}+52812 \,{\mathrm e}^{5} \left (x -1\right )^{7}+62532 \,{\mathrm e}^{5} \left (x -1\right )^{6}+23328 \,{\mathrm e}^{5} \left (x -1\right )^{5}-15876 \,{\mathrm e}^{5} \left (x -1\right )^{4}-11988 \,{\mathrm e}^{5} \left (x -1\right )^{3}+1944 \,{\mathrm e}^{5} \left (x -1\right )^{2}+81 \left (x -1\right )^{12}+1296 \left (x -1\right )^{11}+8424 \left (x -1\right )^{10}+28188 \left (x -1\right )^{9}+49896 \left (x -1\right )^{8}+39528 \left (x -1\right )^{7}-2106 \left (x -1\right )^{6}-20736 \left (x -1\right )^{5}+4860 \left (x -1\right )^{3}\) | \(1654\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [C] time = 0.93, size = 319, normalized size = 10.63 \begin {gather*} 81 \, x^{12} + 324 \, x^{11} + 324 \, x^{10} e^{5} - 486 \, x^{10} + 972 \, x^{9} e^{5} - 2592 \, x^{9} + 486 \, x^{8} e^{10} - 1944 \, x^{8} e^{5} + 1539 \, x^{8} + 972 \, x^{7} e^{10} - 5508 \, x^{7} e^{5} + 7776 \, x^{7} + 324 \, x^{6} e^{15} - 2430 \, x^{6} e^{10} + 5832 \, x^{6} e^{5} - 4374 \, x^{6} + 324 \, x^{5} e^{15} - 2916 \, x^{5} e^{10} + 8748 \, x^{5} e^{5} - 8748 \, x^{5} + 81 \, x^{4} e^{20} - 972 \, x^{4} e^{15} + 4374 \, x^{4} e^{10} - 8748 \, x^{4} e^{5} + 6561 \, x^{4} + 18 \, {\left (2 \, x^{2} e^{3} - 2 \, x e^{3} + e^{3}\right )} e^{\left (2 \, x\right )} + 36 \, {\left (2 \, x e^{3} - e^{3}\right )} e^{\left (2 \, x\right )} + 9 \, {\left (2 \, x^{4} - 4 \, x^{3} + 6 \, x^{2} - 6 \, x + 3\right )} e^{\left (2 \, x - 2\right )} + 18 \, {\left (4 \, x^{3} - 6 \, x^{2} + 6 \, x - 3\right )} e^{\left (2 \, x - 2\right )} - 18 \, {\left (2 \, x^{2} - 2 \, x + 1\right )} e^{\left (2 \, x - 2\right )} - 99 \, {\left (2 \, x - 1\right )} e^{\left (2 \, x - 2\right )} + 256 \, e^{\left (-4\right )} \Gamma \left (-3, -4 \, x\right ) + 1024 \, e^{\left (-4\right )} \Gamma \left (-4, -4 \, x\right ) + 18 \, e^{\left (2 \, x + 8\right )} - 90 \, e^{\left (2 \, x + 3\right )} + 108 \, e^{\left (2 \, x - 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.94, size = 152, normalized size = 5.07 \begin {gather*} x^8\,\left (486\,{\mathrm {e}}^{10}-1944\,{\mathrm {e}}^5+1539\right )+x^7\,\left (972\,{\mathrm {e}}^{10}-5508\,{\mathrm {e}}^5+7776\right )+x^{10}\,\left (324\,{\mathrm {e}}^5-486\right )+x^9\,\left (972\,{\mathrm {e}}^5-2592\right )+81\,x^4\,{\left ({\mathrm {e}}^5-3\right )}^4+324\,x^5\,{\left ({\mathrm {e}}^5-3\right )}^3+{\mathrm {e}}^{2\,x-2}\,\left (18\,x^4+36\,x^3+\left (36\,{\mathrm {e}}^5-90\right )\,x^2+\left (36\,{\mathrm {e}}^5-108\right )\,x+18\,{\left ({\mathrm {e}}^5-3\right )}^2\right )+\frac {{\mathrm {e}}^{4\,x-4}}{x^4}+324\,x^{11}+81\,x^{12}+162\,x^6\,\left (2\,{\mathrm {e}}^5-3\right )\,{\left ({\mathrm {e}}^5-3\right )}^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.32, size = 202, normalized size = 6.73 \begin {gather*} 81 x^{12} + 324 x^{11} + x^{10} \left (-486 + 324 e^{5}\right ) + x^{9} \left (-2592 + 972 e^{5}\right ) + x^{8} \left (- 1944 e^{5} + 1539 + 486 e^{10}\right ) + x^{7} \left (- 5508 e^{5} + 7776 + 972 e^{10}\right ) + x^{6} \left (- 2430 e^{10} - 4374 + 5832 e^{5} + 324 e^{15}\right ) + x^{5} \left (- 2916 e^{10} - 8748 + 8748 e^{5} + 324 e^{15}\right ) + x^{4} \left (- 972 e^{15} - 8748 e^{5} + 6561 + 4374 e^{10} + 81 e^{20}\right ) + \frac {\left (18 x^{8} + 36 x^{7} - 90 x^{6} + 36 x^{6} e^{5} - 108 x^{5} + 36 x^{5} e^{5} - 108 x^{4} e^{5} + 162 x^{4} + 18 x^{4} e^{10}\right ) e^{2 x - 2} + e^{4 x - 4}}{x^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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