Integrand size = 289, antiderivative size = 27 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=x \left (5+\frac {x^{12}}{6561 \left (-e^{-x}-x+x^2\right )^4}\right ) \]
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\[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {32805-164025 e^x (-1+x) x+328050 e^{2 x} (-1+x)^2 x^2-328050 e^{3 x} (-1+x)^3 x^3+e^{4 x} x^4 \left (164025-656100 x+984150 x^2-656100 x^3+164025 x^4+13 x^8+4 x^9\right )-e^{5 x} x^5 \left (-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9\right )}{6561 \left (1-e^x (-1+x) x\right )^5} \, dx \\ & = \frac {\int \frac {32805-164025 e^x (-1+x) x+328050 e^{2 x} (-1+x)^2 x^2-328050 e^{3 x} (-1+x)^3 x^3+e^{4 x} x^4 \left (164025-656100 x+984150 x^2-656100 x^3+164025 x^4+13 x^8+4 x^9\right )-e^{5 x} x^5 \left (-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9\right )}{\left (1-e^x (-1+x) x\right )^5} \, dx}{6561} \\ & = \frac {\int \left (-\frac {4 x^8 \left (-1+x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^5}-\frac {x^8 \left (-7+11 x+16 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^4}-\frac {4 x^8 \left (3+x+6 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^3}-\frac {2 x^8 \left (19-7 x+8 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^2}-\frac {4 x^8 \left (8-4 x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )}+\frac {-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9}{(-1+x)^5}\right ) \, dx}{6561} \\ & = -\frac {\int \frac {x^8 \left (-7+11 x+16 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^4} \, dx}{6561}+\frac {\int \frac {-32805+164025 x-328050 x^2+328050 x^3-164025 x^4+32805 x^5-9 x^8+5 x^9}{(-1+x)^5} \, dx}{6561}-\frac {2 \int \frac {x^8 \left (19-7 x+8 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^2} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (-1+x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^5} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (3+x+6 x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^3} \, dx}{6561}-\frac {4 \int \frac {x^8 \left (8-4 x+x^2\right )}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )} \, dx}{6561} \\ & = \frac {\int \left (32840-\frac {4}{(-1+x)^5}-\frac {27}{(-1+x)^4}-\frac {72}{(-1+x)^3}-\frac {84}{(-1+x)^2}+40 x+30 x^2+16 x^3+5 x^4\right ) \, dx}{6561}-\frac {\int \left (\frac {2541}{\left (-1-e^x x+e^x x^2\right )^4}+\frac {20}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^4}+\frac {203}{(-1+x)^4 \left (-1-e^x x+e^x x^2\right )^4}+\frac {920}{(-1+x)^3 \left (-1-e^x x+e^x x^2\right )^4}+\frac {2452}{(-1+x)^2 \left (-1-e^x x+e^x x^2\right )^4}+\frac {4256}{(-1+x) \left (-1-e^x x+e^x x^2\right )^4}+\frac {1400 x}{\left (-1-e^x x+e^x x^2\right )^4}+\frac {690 x^2}{\left (-1-e^x x+e^x x^2\right )^4}+\frac {288 x^3}{\left (-1-e^x x+e^x x^2\right )^4}+\frac {91 x^4}{\left (-1-e^x x+e^x x^2\right )^4}+\frac {16 x^5}{\left (-1-e^x x+e^x x^2\right )^4}\right ) \, dx}{6561}-\frac {2 \int \left (\frac {1183}{\left (-1-e^x x+e^x x^2\right )^2}+\frac {20}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^2}+\frac {169}{(-1+x)^4 \left (-1-e^x x+e^x x^2\right )^2}+\frac {640}{(-1+x)^3 \left (-1-e^x x+e^x x^2\right )^2}+\frac {1436}{(-1+x)^2 \left (-1-e^x x+e^x x^2\right )^2}+\frac {2128}{(-1+x) \left (-1-e^x x+e^x x^2\right )^2}+\frac {600 x}{\left (-1-e^x x+e^x x^2\right )^2}+\frac {270 x^2}{\left (-1-e^x x+e^x x^2\right )^2}+\frac {104 x^3}{\left (-1-e^x x+e^x x^2\right )^2}+\frac {33 x^4}{\left (-1-e^x x+e^x x^2\right )^2}+\frac {8 x^5}{\left (-1-e^x x+e^x x^2\right )^2}\right ) \, dx}{6561}-\frac {4 \int \left (\frac {161}{\left (-1-e^x x+e^x x^2\right )^5}+\frac {1}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^5}+\frac {11}{(-1+x)^4 \left (-1-e^x x+e^x x^2\right )^5}+\frac {53}{(-1+x)^3 \left (-1-e^x x+e^x x^2\right )^5}+\frac {148}{(-1+x)^2 \left (-1-e^x x+e^x x^2\right )^5}+\frac {266}{(-1+x) \left (-1-e^x x+e^x x^2\right )^5}+\frac {90 x}{\left (-1-e^x x+e^x x^2\right )^5}+\frac {45 x^2}{\left (-1-e^x x+e^x x^2\right )^5}+\frac {19 x^3}{\left (-1-e^x x+e^x x^2\right )^5}+\frac {6 x^4}{\left (-1-e^x x+e^x x^2\right )^5}+\frac {x^5}{\left (-1-e^x x+e^x x^2\right )^5}\right ) \, dx}{6561}-\frac {4 \int \left (\frac {931}{\left (-1-e^x x+e^x x^2\right )^3}+\frac {10}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )^3}+\frac {93}{(-1+x)^4 \left (-1-e^x x+e^x x^2\right )^3}+\frac {390}{(-1+x)^3 \left (-1-e^x x+e^x x^2\right )^3}+\frac {972}{(-1+x)^2 \left (-1-e^x x+e^x x^2\right )^3}+\frac {1596}{(-1+x) \left (-1-e^x x+e^x x^2\right )^3}+\frac {500 x}{\left (-1-e^x x+e^x x^2\right )^3}+\frac {240 x^2}{\left (-1-e^x x+e^x x^2\right )^3}+\frac {98 x^3}{\left (-1-e^x x+e^x x^2\right )^3}+\frac {31 x^4}{\left (-1-e^x x+e^x x^2\right )^3}+\frac {6 x^5}{\left (-1-e^x x+e^x x^2\right )^3}\right ) \, dx}{6561}-\frac {4 \int \left (\frac {126}{-1-e^x x+e^x x^2}+\frac {5}{(-1+x)^5 \left (-1-e^x x+e^x x^2\right )}+\frac {38}{(-1+x)^4 \left (-1-e^x x+e^x x^2\right )}+\frac {125}{(-1+x)^3 \left (-1-e^x x+e^x x^2\right )}+\frac {232}{(-1+x)^2 \left (-1-e^x x+e^x x^2\right )}+\frac {266}{(-1+x) \left (-1-e^x x+e^x x^2\right )}+\frac {50 x}{-1-e^x x+e^x x^2}+\frac {15 x^2}{-1-e^x x+e^x x^2}+\frac {3 x^3}{-1-e^x x+e^x x^2}+\frac {x^4}{-1-e^x x+e^x x^2}+\frac {x^5}{-1-e^x x+e^x x^2}\right ) \, dx}{6561} \\ & = \text {Too large to display} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(109\) vs. \(2(27)=54\).
Time = 10.23 (sec) , antiderivative size = 109, normalized size of antiderivative = 4.04 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\frac {32840 x+20 x^2+10 x^3+4 x^4+x^5+\frac {-56+189 x-216 x^2+84 x^3}{(-1+x)^4}+\frac {x^9 \left (-1+4 e^x (-1+x) x-6 e^{2 x} (-1+x)^2 x^2+4 e^{3 x} (-1+x)^3 x^3\right )}{(-1+x)^4 \left (-1+e^x (-1+x) x\right )^4}}{6561} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(167\) vs. \(2(26)=52\).
Time = 0.76 (sec) , antiderivative size = 168, normalized size of antiderivative = 6.22
method | result | size |
risch | \(\frac {x^{5}}{6561}+\frac {4 x^{4}}{6561}+\frac {10 x^{3}}{6561}+\frac {20 x^{2}}{6561}+\frac {32840 x}{6561}+\frac {\frac {28}{2187} x^{3}-\frac {8}{243} x^{2}+\frac {7}{243} x -\frac {56}{6561}}{x^{4}-4 x^{3}+6 x^{2}-4 x +1}+\frac {x^{9} \left (4 \,{\mathrm e}^{3 x} x^{6}-12 \,{\mathrm e}^{3 x} x^{5}+12 \,{\mathrm e}^{3 x} x^{4}-6 \,{\mathrm e}^{2 x} x^{4}-4 x^{3} {\mathrm e}^{3 x}+12 \,{\mathrm e}^{2 x} x^{3}-6 \,{\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{x} x^{2}-4 \,{\mathrm e}^{x} x -1\right )}{6561 \left (x^{2}-2 x +1\right )^{2} \left ({\mathrm e}^{x} x^{2}-{\mathrm e}^{x} x -1\right )^{4}}\) | \(168\) |
parallelrisch | \(\frac {131220 x -524880 x^{7} {\mathrm e}^{3 x}+524880 \,{\mathrm e}^{3 x} x^{4}-1574640 \,{\mathrm e}^{3 x} x^{5}-524880 x^{6} {\mathrm e}^{4 x}+1574640 \,{\mathrm e}^{3 x} x^{6}-1574640 \,{\mathrm e}^{2 x} x^{4}+787320 x^{5} {\mathrm e}^{2 x}+524880 \,{\mathrm e}^{x} x^{2}-524880 \,{\mathrm e}^{x} x^{3}-524880 x^{8} {\mathrm e}^{4 x}+131220 x^{5} {\mathrm e}^{4 x}+787320 \,{\mathrm e}^{2 x} x^{3}+4 \,{\mathrm e}^{4 x} x^{13}+787320 \,{\mathrm e}^{4 x} x^{7}+131220 \,{\mathrm e}^{4 x} x^{9}}{26244 x^{8} {\mathrm e}^{4 x}-104976 \,{\mathrm e}^{4 x} x^{7}+157464 x^{6} {\mathrm e}^{4 x}-104976 \,{\mathrm e}^{3 x} x^{6}-104976 x^{5} {\mathrm e}^{4 x}+314928 \,{\mathrm e}^{3 x} x^{5}+26244 x^{4} {\mathrm e}^{4 x}-314928 \,{\mathrm e}^{3 x} x^{4}+157464 \,{\mathrm e}^{2 x} x^{4}+104976 x^{3} {\mathrm e}^{3 x}-314928 \,{\mathrm e}^{2 x} x^{3}+157464 \,{\mathrm e}^{2 x} x^{2}-104976 \,{\mathrm e}^{x} x^{2}+104976 \,{\mathrm e}^{x} x +26244}\) | \(260\) |
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Leaf count of result is larger than twice the leaf count of optimal. 208 vs. \(2 (24) = 48\).
Time = 0.28 (sec) , antiderivative size = 208, normalized size of antiderivative = 7.70 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\frac {{\left (x^{13} + 32805 \, x^{9} - 131276 \, x^{8} + 197054 \, x^{7} - 131556 \, x^{6} + 33029 \, x^{5} - 56 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (32805 \, x^{7} - 98471 \, x^{6} + 98583 \, x^{5} - 32973 \, x^{4} + 56 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (32805 \, x^{5} - 65666 \, x^{4} + 32917 \, x^{3} - 56 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (32805 \, x^{3} - 32861 \, x^{2} + 56 \, x\right )} e^{x} + 32805 \, x - 56}{6561 \, {\left ({\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{2} - x\right )} e^{x} + 1\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 318 vs. \(2 (22) = 44\).
Time = 0.53 (sec) , antiderivative size = 318, normalized size of antiderivative = 11.78 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\frac {x^{5}}{6561} + \frac {4 x^{4}}{6561} + \frac {10 x^{3}}{6561} + \frac {20 x^{2}}{6561} + \frac {32840 x}{6561} + \frac {84 x^{3} - 216 x^{2} + 189 x - 56}{6561 x^{4} - 26244 x^{3} + 39366 x^{2} - 26244 x + 6561} + \frac {- x^{9} + \left (4 x^{11} - 4 x^{10}\right ) e^{x} + \left (- 6 x^{13} + 12 x^{12} - 6 x^{11}\right ) e^{2 x} + \left (4 x^{15} - 12 x^{14} + 12 x^{13} - 4 x^{12}\right ) e^{3 x}}{6561 x^{4} - 26244 x^{3} + 39366 x^{2} - 26244 x + \left (- 26244 x^{6} + 131220 x^{5} - 262440 x^{4} + 262440 x^{3} - 131220 x^{2} + 26244 x\right ) e^{x} + \left (39366 x^{8} - 236196 x^{7} + 590490 x^{6} - 787320 x^{5} + 590490 x^{4} - 236196 x^{3} + 39366 x^{2}\right ) e^{2 x} + \left (- 26244 x^{10} + 183708 x^{9} - 551124 x^{8} + 918540 x^{7} - 918540 x^{6} + 551124 x^{5} - 183708 x^{4} + 26244 x^{3}\right ) e^{3 x} + \left (6561 x^{12} - 52488 x^{11} + 183708 x^{10} - 367416 x^{9} + 459270 x^{8} - 367416 x^{7} + 183708 x^{6} - 52488 x^{5} + 6561 x^{4}\right ) e^{4 x} + 6561} \]
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Leaf count of result is larger than twice the leaf count of optimal. 208 vs. \(2 (24) = 48\).
Time = 0.41 (sec) , antiderivative size = 208, normalized size of antiderivative = 7.70 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\frac {{\left (x^{13} + 32805 \, x^{9} - 131276 \, x^{8} + 197054 \, x^{7} - 131556 \, x^{6} + 33029 \, x^{5} - 56 \, x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (32805 \, x^{7} - 98471 \, x^{6} + 98583 \, x^{5} - 32973 \, x^{4} + 56 \, x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (32805 \, x^{5} - 65666 \, x^{4} + 32917 \, x^{3} - 56 \, x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (32805 \, x^{3} - 32861 \, x^{2} + 56 \, x\right )} e^{x} + 32805 \, x - 56}{6561 \, {\left ({\left (x^{8} - 4 \, x^{7} + 6 \, x^{6} - 4 \, x^{5} + x^{4}\right )} e^{\left (4 \, x\right )} - 4 \, {\left (x^{6} - 3 \, x^{5} + 3 \, x^{4} - x^{3}\right )} e^{\left (3 \, x\right )} + 6 \, {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{\left (2 \, x\right )} - 4 \, {\left (x^{2} - x\right )} e^{x} + 1\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 291 vs. \(2 (24) = 48\).
Time = 0.37 (sec) , antiderivative size = 291, normalized size of antiderivative = 10.78 \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\frac {x^{13} e^{\left (4 \, x\right )} + 32805 \, x^{9} e^{\left (4 \, x\right )} - 131276 \, x^{8} e^{\left (4 \, x\right )} + 197054 \, x^{7} e^{\left (4 \, x\right )} - 131220 \, x^{7} e^{\left (3 \, x\right )} - 131556 \, x^{6} e^{\left (4 \, x\right )} + 393884 \, x^{6} e^{\left (3 \, x\right )} + 33029 \, x^{5} e^{\left (4 \, x\right )} - 394332 \, x^{5} e^{\left (3 \, x\right )} + 196830 \, x^{5} e^{\left (2 \, x\right )} - 56 \, x^{4} e^{\left (4 \, x\right )} + 131892 \, x^{4} e^{\left (3 \, x\right )} - 393996 \, x^{4} e^{\left (2 \, x\right )} - 224 \, x^{3} e^{\left (3 \, x\right )} + 197502 \, x^{3} e^{\left (2 \, x\right )} - 131220 \, x^{3} e^{x} - 336 \, x^{2} e^{\left (2 \, x\right )} + 131444 \, x^{2} e^{x} - 224 \, x e^{x} + 32805 \, x - 56}{6561 \, {\left (x^{8} e^{\left (4 \, x\right )} - 4 \, x^{7} e^{\left (4 \, x\right )} + 6 \, x^{6} e^{\left (4 \, x\right )} - 4 \, x^{6} e^{\left (3 \, x\right )} - 4 \, x^{5} e^{\left (4 \, x\right )} + 12 \, x^{5} e^{\left (3 \, x\right )} + x^{4} e^{\left (4 \, x\right )} - 12 \, x^{4} e^{\left (3 \, x\right )} + 6 \, x^{4} e^{\left (2 \, x\right )} + 4 \, x^{3} e^{\left (3 \, x\right )} - 12 \, x^{3} e^{\left (2 \, x\right )} + 6 \, x^{2} e^{\left (2 \, x\right )} - 4 \, x^{2} e^{x} + 4 \, x e^{x} + 1\right )}} \]
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Timed out. \[ \int \frac {-32805+e^x \left (-164025 x+164025 x^2\right )+e^{2 x} \left (-328050 x^2+656100 x^3-328050 x^4\right )+e^{3 x} \left (-328050 x^3+984150 x^4-984150 x^5+328050 x^6\right )+e^{4 x} \left (-164025 x^4+656100 x^5-984150 x^6+656100 x^7-164025 x^8-13 x^{12}-4 x^{13}\right )+e^{5 x} \left (-32805 x^5+164025 x^6-328050 x^7+328050 x^8-164025 x^9+32805 x^{10}-9 x^{13}+5 x^{14}\right )}{-6561+e^x \left (-32805 x+32805 x^2\right )+e^{2 x} \left (-65610 x^2+131220 x^3-65610 x^4\right )+e^{3 x} \left (-65610 x^3+196830 x^4-196830 x^5+65610 x^6\right )+e^{4 x} \left (-32805 x^4+131220 x^5-196830 x^6+131220 x^7-32805 x^8\right )+e^{5 x} \left (-6561 x^5+32805 x^6-65610 x^7+65610 x^8-32805 x^9+6561 x^{10}\right )} \, dx=\int \frac {{\mathrm {e}}^{4\,x}\,\left (4\,x^{13}+13\,x^{12}+164025\,x^8-656100\,x^7+984150\,x^6-656100\,x^5+164025\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (328050\,x^4-656100\,x^3+328050\,x^2\right )+{\mathrm {e}}^x\,\left (164025\,x-164025\,x^2\right )+{\mathrm {e}}^{5\,x}\,\left (-5\,x^{14}+9\,x^{13}-32805\,x^{10}+164025\,x^9-328050\,x^8+328050\,x^7-164025\,x^6+32805\,x^5\right )+{\mathrm {e}}^{3\,x}\,\left (-328050\,x^6+984150\,x^5-984150\,x^4+328050\,x^3\right )+32805}{{\mathrm {e}}^{4\,x}\,\left (32805\,x^8-131220\,x^7+196830\,x^6-131220\,x^5+32805\,x^4\right )+{\mathrm {e}}^{5\,x}\,\left (-6561\,x^{10}+32805\,x^9-65610\,x^8+65610\,x^7-32805\,x^6+6561\,x^5\right )+{\mathrm {e}}^{2\,x}\,\left (65610\,x^4-131220\,x^3+65610\,x^2\right )+{\mathrm {e}}^x\,\left (32805\,x-32805\,x^2\right )+{\mathrm {e}}^{3\,x}\,\left (-65610\,x^6+196830\,x^5-196830\,x^4+65610\,x^3\right )+6561} \,d x \]
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