Integrand size = 728, antiderivative size = 34 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\frac {4 e^x}{e^3-(9-x)^2-\frac {4}{\left (e^x+x-x^2\right )^2}} \]
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Timed out. \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Leaf count is larger than twice the leaf count of optimal. \(102\) vs. \(2(34)=68\).
Time = 9.81 (sec) , antiderivative size = 102, normalized size of antiderivative = 3.00 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=-\frac {4 e^x \left (e^x+x-x^2\right )^2}{4-e^{3+2 x}+e^{2 x} (-9+x)^2+2 e^{3+x} (-1+x) x-2 e^x (-9+x)^2 (-1+x) x+81 x^2-e^3 (-1+x)^2 x^2-180 x^3+118 x^4-20 x^5+x^6} \]
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Leaf count of result is larger than twice the leaf count of optimal. \(238\) vs. \(2(31)=62\).
Time = 3.30 (sec) , antiderivative size = 239, normalized size of antiderivative = 7.03
method | result | size |
parallelrisch | \(-\frac {-32+8 \,{\mathrm e}^{3} {\mathrm e}^{2 x}+12 \,{\mathrm e}^{x} x^{4}+8 x^{4} {\mathrm e}^{3}+1580 \,{\mathrm e}^{x} x^{2}-16 x^{3} {\mathrm e}^{3}+8 x^{2} {\mathrm e}^{3}+136 x \,{\mathrm e}^{2 x}-296 \,{\mathrm e}^{x} x^{3}-1296 \,{\mathrm e}^{x} x +16 x \,{\mathrm e}^{3} {\mathrm e}^{x}-16 x^{2} {\mathrm e}^{3} {\mathrm e}^{x}-4 \,{\mathrm e}^{3 x}-944 x^{4}+1440 x^{3}-648 x^{2}-648 \,{\mathrm e}^{2 x}-8 x^{6}+160 x^{5}}{-x^{6}+2 \,{\mathrm e}^{x} x^{4}+x^{4} {\mathrm e}^{3}+20 x^{5}-{\mathrm e}^{2 x} x^{2}-2 x^{2} {\mathrm e}^{3} {\mathrm e}^{x}-38 \,{\mathrm e}^{x} x^{3}-2 x^{3} {\mathrm e}^{3}-118 x^{4}+{\mathrm e}^{3} {\mathrm e}^{2 x}+18 x \,{\mathrm e}^{2 x}+2 x \,{\mathrm e}^{3} {\mathrm e}^{x}+198 \,{\mathrm e}^{x} x^{2}+x^{2} {\mathrm e}^{3}+180 x^{3}-81 \,{\mathrm e}^{2 x}-162 \,{\mathrm e}^{x} x -81 x^{2}-4}\) | \(239\) |
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Leaf count of result is larger than twice the leaf count of optimal. 130 vs. \(2 (31) = 62\).
Time = 0.28 (sec) , antiderivative size = 130, normalized size of antiderivative = 3.82 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\frac {4 \, {\left (2 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )}}{x^{6} - 20 \, x^{5} + 118 \, x^{4} - 180 \, x^{3} + 81 \, x^{2} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{3} + {\left (x^{2} - 18 \, x - e^{3} + 81\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} - 19 \, x^{3} + 99 \, x^{2} - {\left (x^{2} - x\right )} e^{3} - 81 \, x\right )} e^{x} + 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 257 vs. \(2 (24) = 48\).
Time = 1.39 (sec) , antiderivative size = 257, normalized size of antiderivative = 7.56 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\frac {16 e^{x}}{x^{8} - 38 x^{7} - 2 x^{6} e^{3} + 559 x^{6} - 3924 x^{5} + 40 x^{5} e^{3} - 236 x^{4} e^{3} + x^{4} e^{6} + 12879 x^{4} - 16038 x^{3} - 2 x^{3} e^{6} + 360 x^{3} e^{3} - 162 x^{2} e^{3} + x^{2} e^{6} + 6565 x^{2} - 72 x + \left (x^{4} - 36 x^{3} - 2 x^{2} e^{3} + 486 x^{2} - 2916 x + 36 x e^{3} - 162 e^{3} + e^{6} + 6561\right ) e^{2 x} + \left (- 2 x^{6} + 74 x^{5} - 1044 x^{4} + 4 x^{4} e^{3} - 76 x^{3} e^{3} + 6804 x^{3} - 18954 x^{2} - 2 x^{2} e^{6} + 396 x^{2} e^{3} - 324 x e^{3} + 2 x e^{6} + 13122 x\right ) e^{x} - 4 e^{3} + 324} - \frac {4 e^{x}}{x^{2} - 18 x - e^{3} + 81} \]
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Leaf count of result is larger than twice the leaf count of optimal. 122 vs. \(2 (31) = 62\).
Time = 0.61 (sec) , antiderivative size = 122, normalized size of antiderivative = 3.59 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\frac {4 \, {\left (2 \, {\left (x^{2} - x\right )} e^{\left (2 \, x\right )} - {\left (x^{4} - 2 \, x^{3} + x^{2}\right )} e^{x} - e^{\left (3 \, x\right )}\right )}}{x^{6} - 20 \, x^{5} - x^{4} {\left (e^{3} - 118\right )} + 2 \, x^{3} {\left (e^{3} - 90\right )} - x^{2} {\left (e^{3} - 81\right )} + {\left (x^{2} - 18 \, x - e^{3} + 81\right )} e^{\left (2 \, x\right )} - 2 \, {\left (x^{4} - 19 \, x^{3} - x^{2} {\left (e^{3} - 99\right )} + x {\left (e^{3} - 81\right )}\right )} e^{x} + 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 161 vs. \(2 (31) = 62\).
Time = 9.71 (sec) , antiderivative size = 161, normalized size of antiderivative = 4.74 \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=-\frac {8 \, {\left (x^{4} e^{x} - 2 \, x^{3} e^{x} - 2 \, x^{2} e^{\left (2 \, x\right )} + x^{2} e^{x} + 2 \, x e^{\left (2 \, x\right )} + e^{\left (3 \, x\right )}\right )}}{x^{6} - 20 \, x^{5} - x^{4} e^{3} - 2 \, x^{4} e^{x} + 118 \, x^{4} + 2 \, x^{3} e^{3} + 38 \, x^{3} e^{x} - 180 \, x^{3} - x^{2} e^{3} + x^{2} e^{\left (2 \, x\right )} + 2 \, x^{2} e^{\left (x + 3\right )} - 198 \, x^{2} e^{x} + 81 \, x^{2} - 18 \, x e^{\left (2 \, x\right )} - 2 \, x e^{\left (x + 3\right )} + 162 \, x e^{x} + 81 \, e^{\left (2 \, x\right )} - e^{\left (2 \, x + 3\right )} + 4} \]
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Timed out. \[ \int \frac {e^{5 x} \left (-396+4 e^3+80 x-4 x^2\right )+e^{4 x} \left (-1584 x+1904 x^2-336 x^3+16 x^4+e^3 \left (16 x-16 x^2\right )\right )+e^{3 x} \left (-48-2376 x^2+5232 x^3-3360 x^4+528 x^5-24 x^6+e^3 \left (24 x^2-48 x^3+24 x^4\right )\right )+e^{2 x} \left (-32+64 x^2-1584 x^3+5072 x^4-5728 x^5+2592 x^6-368 x^7+16 x^8+e^3 \left (16 x^3-48 x^4+48 x^5-16 x^6\right )\right )+e^x \left (-32 x+80 x^2-32 x^3-412 x^4+1664 x^5-2700 x^6+2080 x^7-740 x^8+96 x^9-4 x^{10}+e^3 \left (4 x^4-16 x^5+24 x^6-16 x^7+4 x^8\right )\right )}{16+648 x^2-1440 x^3+7505 x^4-29320 x^5+51524 x^6-45720 x^7+21286 x^8-5080 x^9+636 x^{10}-40 x^{11}+x^{12}+e^6 \left (x^4-4 x^5+6 x^6-4 x^7+x^8\right )+e^3 \left (-8 x^2+16 x^3-170 x^4+684 x^5-1118 x^6+872 x^7-318 x^8+44 x^9-2 x^{10}\right )+e^{4 x} \left (6561+e^6-2916 x+486 x^2-36 x^3+x^4+e^3 \left (-162+36 x-2 x^2\right )\right )+e^{3 x} \left (26244 x-37908 x^2+13608 x^3-2088 x^4+148 x^5-4 x^6+e^6 \left (4 x-4 x^2\right )+e^3 \left (-648 x+792 x^2-152 x^3+8 x^4\right )\right )+e^{2 x} \left (648-144 x+39374 x^2-96228 x^3+77274 x^4-23544 x^5+3354 x^6-228 x^7+6 x^8+e^6 \left (6 x^2-12 x^3+6 x^4\right )+e^3 \left (-8-972 x^2+2160 x^3-1416 x^4+240 x^5-12 x^6\right )\right )+e^x \left (1296 x-1584 x^2+26548 x^3-90412 x^4+115668 x^5-67212 x^6+17932 x^7-2388 x^8+156 x^9-4 x^{10}+e^6 \left (4 x^3-12 x^4+12 x^5-4 x^6\right )+e^3 \left (-16 x+16 x^2-648 x^3+2088 x^4-2384 x^5+1104 x^6-168 x^7+8 x^8\right )\right )} \, dx=\int \frac {{\mathrm {e}}^{2\,x}\,\left (64\,x^2-1584\,x^3+5072\,x^4-5728\,x^5+2592\,x^6-368\,x^7+16\,x^8+{\mathrm {e}}^3\,\left (-16\,x^6+48\,x^5-48\,x^4+16\,x^3\right )-32\right )-{\mathrm {e}}^x\,\left (32\,x-{\mathrm {e}}^3\,\left (4\,x^8-16\,x^7+24\,x^6-16\,x^5+4\,x^4\right )-80\,x^2+32\,x^3+412\,x^4-1664\,x^5+2700\,x^6-2080\,x^7+740\,x^8-96\,x^9+4\,x^{10}\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^3\,\left (16\,x-16\,x^2\right )-1584\,x+1904\,x^2-336\,x^3+16\,x^4\right )+{\mathrm {e}}^{5\,x}\,\left (-4\,x^2+80\,x+4\,{\mathrm {e}}^3-396\right )-{\mathrm {e}}^{3\,x}\,\left (2376\,x^2-{\mathrm {e}}^3\,\left (24\,x^4-48\,x^3+24\,x^2\right )-5232\,x^3+3360\,x^4-528\,x^5+24\,x^6+48\right )}{{\mathrm {e}}^{2\,x}\,\left ({\mathrm {e}}^6\,\left (6\,x^4-12\,x^3+6\,x^2\right )-{\mathrm {e}}^3\,\left (12\,x^6-240\,x^5+1416\,x^4-2160\,x^3+972\,x^2+8\right )-144\,x+39374\,x^2-96228\,x^3+77274\,x^4-23544\,x^5+3354\,x^6-228\,x^7+6\,x^8+648\right )-{\mathrm {e}}^3\,\left (2\,x^{10}-44\,x^9+318\,x^8-872\,x^7+1118\,x^6-684\,x^5+170\,x^4-16\,x^3+8\,x^2\right )+{\mathrm {e}}^6\,\left (x^8-4\,x^7+6\,x^6-4\,x^5+x^4\right )+{\mathrm {e}}^{4\,x}\,\left ({\mathrm {e}}^6-2916\,x-{\mathrm {e}}^3\,\left (2\,x^2-36\,x+162\right )+486\,x^2-36\,x^3+x^4+6561\right )+{\mathrm {e}}^{3\,x}\,\left (26244\,x+{\mathrm {e}}^6\,\left (4\,x-4\,x^2\right )-{\mathrm {e}}^3\,\left (-8\,x^4+152\,x^3-792\,x^2+648\,x\right )-37908\,x^2+13608\,x^3-2088\,x^4+148\,x^5-4\,x^6\right )+648\,x^2-1440\,x^3+7505\,x^4-29320\,x^5+51524\,x^6-45720\,x^7+21286\,x^8-5080\,x^9+636\,x^{10}-40\,x^{11}+x^{12}+{\mathrm {e}}^x\,\left (1296\,x-{\mathrm {e}}^3\,\left (-8\,x^8+168\,x^7-1104\,x^6+2384\,x^5-2088\,x^4+648\,x^3-16\,x^2+16\,x\right )-1584\,x^2+26548\,x^3-90412\,x^4+115668\,x^5-67212\,x^6+17932\,x^7-2388\,x^8+156\,x^9-4\,x^{10}+{\mathrm {e}}^6\,\left (-4\,x^6+12\,x^5-12\,x^4+4\,x^3\right )\right )+16} \,d x \]
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