Integrand size = 1066, antiderivative size = 30 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\frac {x^2}{\left (5+e^{-3-\frac {3}{3+x}} x (2+x) \left (x+\log ^2(x)\right )\right )^4} \]
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Timed out. \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Time = 0.28 (sec) , antiderivative size = 47, normalized size of antiderivative = 1.57 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\frac {e^{12 \left (1+\frac {1}{3+x}\right )} x^2}{\left (5 e^{3+\frac {3}{3+x}}+x^2 (2+x)+x (2+x) \log ^2(x)\right )^4} \]
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Time = 0.26 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.83
\[\frac {x^{2} {\mathrm e}^{\frac {12 x +48}{3+x}}}{\left (x^{2} \ln \left (x \right )^{2}+x^{3}+2 x \ln \left (x \right )^{2}+2 x^{2}+5 \,{\mathrm e}^{\frac {3 x +12}{3+x}}\right )^{4}}\]
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Leaf count of result is larger than twice the leaf count of optimal. 424 vs. \(2 (29) = 58\).
Time = 0.27 (sec) , antiderivative size = 424, normalized size of antiderivative = 14.13 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\frac {x^{2} e^{\left (\frac {12 \, {\left (x + 4\right )}}{x + 3}\right )}}{x^{12} + 8 \, x^{11} + 24 \, x^{10} + 32 \, x^{9} + {\left (x^{8} + 8 \, x^{7} + 24 \, x^{6} + 32 \, x^{5} + 16 \, x^{4}\right )} \log \left (x\right )^{8} + 16 \, x^{8} + 4 \, {\left (x^{9} + 8 \, x^{8} + 24 \, x^{7} + 32 \, x^{6} + 16 \, x^{5} + 5 \, {\left (x^{6} + 6 \, x^{5} + 12 \, x^{4} + 8 \, x^{3}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \left (x\right )^{6} + 6 \, {\left (x^{10} + 8 \, x^{9} + 24 \, x^{8} + 32 \, x^{7} + 16 \, x^{6} + 25 \, {\left (x^{4} + 4 \, x^{3} + 4 \, x^{2}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 10 \, {\left (x^{7} + 6 \, x^{6} + 12 \, x^{5} + 8 \, x^{4}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{11} + 8 \, x^{10} + 24 \, x^{9} + 32 \, x^{8} + 16 \, x^{7} + 125 \, {\left (x^{2} + 2 \, x\right )} e^{\left (\frac {9 \, {\left (x + 4\right )}}{x + 3}\right )} + 75 \, {\left (x^{5} + 4 \, x^{4} + 4 \, x^{3}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 15 \, {\left (x^{8} + 6 \, x^{7} + 12 \, x^{6} + 8 \, x^{5}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )}\right )} \log \left (x\right )^{2} + 500 \, {\left (x^{3} + 2 \, x^{2}\right )} e^{\left (\frac {9 \, {\left (x + 4\right )}}{x + 3}\right )} + 150 \, {\left (x^{6} + 4 \, x^{5} + 4 \, x^{4}\right )} e^{\left (\frac {6 \, {\left (x + 4\right )}}{x + 3}\right )} + 20 \, {\left (x^{9} + 6 \, x^{8} + 12 \, x^{7} + 8 \, x^{6}\right )} e^{\left (\frac {3 \, {\left (x + 4\right )}}{x + 3}\right )} + 625 \, e^{\left (\frac {12 \, {\left (x + 4\right )}}{x + 3}\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1035 vs. \(2 (27) = 54\).
Time = 8.02 (sec) , antiderivative size = 1035, normalized size of antiderivative = 34.50 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\text {Too large to display} \]
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Leaf count of result is larger than twice the leaf count of optimal. 435 vs. \(2 (29) = 58\).
Time = 3.86 (sec) , antiderivative size = 435, normalized size of antiderivative = 14.50 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\frac {x^{2} e^{\left (\frac {12}{x + 3} + 12\right )}}{x^{12} + 8 \, x^{11} + 24 \, x^{10} + 32 \, x^{9} + {\left (x^{8} + 8 \, x^{7} + 24 \, x^{6} + 32 \, x^{5} + 16 \, x^{4}\right )} \log \left (x\right )^{8} + 16 \, x^{8} + 4 \, {\left (x^{9} + 8 \, x^{8} + 24 \, x^{7} + 32 \, x^{6} + 16 \, x^{5}\right )} \log \left (x\right )^{6} + 6 \, {\left (x^{10} + 8 \, x^{9} + 24 \, x^{8} + 32 \, x^{7} + 16 \, x^{6}\right )} \log \left (x\right )^{4} + 4 \, {\left (x^{11} + 8 \, x^{10} + 24 \, x^{9} + 32 \, x^{8} + 16 \, x^{7}\right )} \log \left (x\right )^{2} + 500 \, {\left (x^{3} e^{9} + 2 \, x^{2} e^{9} + {\left (x^{2} e^{9} + 2 \, x e^{9}\right )} \log \left (x\right )^{2}\right )} e^{\left (\frac {9}{x + 3}\right )} + 150 \, {\left (x^{6} e^{6} + 4 \, x^{5} e^{6} + 4 \, x^{4} e^{6} + {\left (x^{4} e^{6} + 4 \, x^{3} e^{6} + 4 \, x^{2} e^{6}\right )} \log \left (x\right )^{4} + 2 \, {\left (x^{5} e^{6} + 4 \, x^{4} e^{6} + 4 \, x^{3} e^{6}\right )} \log \left (x\right )^{2}\right )} e^{\left (\frac {6}{x + 3}\right )} + 20 \, {\left (x^{9} e^{3} + 6 \, x^{8} e^{3} + 12 \, x^{7} e^{3} + 8 \, x^{6} e^{3} + {\left (x^{6} e^{3} + 6 \, x^{5} e^{3} + 12 \, x^{4} e^{3} + 8 \, x^{3} e^{3}\right )} \log \left (x\right )^{6} + 3 \, {\left (x^{7} e^{3} + 6 \, x^{6} e^{3} + 12 \, x^{5} e^{3} + 8 \, x^{4} e^{3}\right )} \log \left (x\right )^{4} + 3 \, {\left (x^{8} e^{3} + 6 \, x^{7} e^{3} + 12 \, x^{6} e^{3} + 8 \, x^{5} e^{3}\right )} \log \left (x\right )^{2}\right )} e^{\left (\frac {3}{x + 3}\right )} + 625 \, e^{\left (\frac {12}{x + 3} + 12\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 775 vs. \(2 (29) = 58\).
Time = 2.06 (sec) , antiderivative size = 775, normalized size of antiderivative = 25.83 \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\frac {x^{2} e^{\left (-\frac {4 \, x}{x + 3} + 16\right )}}{x^{8} \log \left (x\right )^{8} + 4 \, x^{9} \log \left (x\right )^{6} + 8 \, x^{7} \log \left (x\right )^{8} + 6 \, x^{10} \log \left (x\right )^{4} + 32 \, x^{8} \log \left (x\right )^{6} + 24 \, x^{6} \log \left (x\right )^{8} + 4 \, x^{11} \log \left (x\right )^{2} + 48 \, x^{9} \log \left (x\right )^{4} + 96 \, x^{7} \log \left (x\right )^{6} + 20 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{6} + 32 \, x^{5} \log \left (x\right )^{8} + x^{12} + 32 \, x^{10} \log \left (x\right )^{2} + 144 \, x^{8} \log \left (x\right )^{4} + 60 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{4} + 128 \, x^{6} \log \left (x\right )^{6} + 120 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{6} + 16 \, x^{4} \log \left (x\right )^{8} + 8 \, x^{11} + 96 \, x^{9} \log \left (x\right )^{2} + 60 \, x^{8} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{2} + 192 \, x^{7} \log \left (x\right )^{4} + 360 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{4} + 64 \, x^{5} \log \left (x\right )^{6} + 240 \, x^{4} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{6} + 24 \, x^{10} + 20 \, x^{9} e^{\left (-\frac {x}{x + 3} + 4\right )} + 128 \, x^{8} \log \left (x\right )^{2} + 360 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{2} + 96 \, x^{6} \log \left (x\right )^{4} + 720 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{4} + 160 \, x^{3} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{6} + 32 \, x^{9} + 120 \, x^{8} e^{\left (-\frac {x}{x + 3} + 4\right )} + 64 \, x^{7} \log \left (x\right )^{2} + 720 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{2} + 480 \, x^{4} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{4} + 150 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{4} + 16 \, x^{8} + 240 \, x^{7} e^{\left (-\frac {x}{x + 3} + 4\right )} + 480 \, x^{5} e^{\left (-\frac {x}{x + 3} + 4\right )} \log \left (x\right )^{2} + 300 \, x^{5} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{2} + 600 \, x^{3} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{4} + 160 \, x^{6} e^{\left (-\frac {x}{x + 3} + 4\right )} + 150 \, x^{6} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 1200 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{2} + 600 \, x^{2} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{4} + 600 \, x^{5} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 1200 \, x^{3} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} \log \left (x\right )^{2} + 600 \, x^{4} e^{\left (-\frac {2 \, x}{x + 3} + 8\right )} + 500 \, x^{2} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} \log \left (x\right )^{2} + 500 \, x^{3} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} + 1000 \, x e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} \log \left (x\right )^{2} + 1000 \, x^{2} e^{\left (-\frac {3 \, x}{x + 3} + 12\right )} + 625 \, e^{\left (-\frac {4 \, x}{x + 3} + 16\right )}} \]
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Timed out. \[ \int \frac {e^{\frac {5 (12+3 x)}{3+x}} \left (90 x+60 x^2+10 x^3\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-108 x^3-186 x^4-84 x^5-10 x^6\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (-144 x^2-168 x^3-64 x^4-8 x^5\right ) \log (x)+e^{\frac {4 (12+3 x)}{3+x}} \left (-36 x^2-102 x^3-52 x^4-6 x^5\right ) \log ^2(x)}{288 x^{10}+912 x^{11}+1232 x^{12}+920 x^{13}+410 x^{14}+109 x^{15}+16 x^{16}+x^{17}+e^{\frac {5 (12+3 x)}{3+x}} \left (28125+18750 x+3125 x^2\right )+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x^2+65625 x^3+25000 x^4+3125 x^5\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^4+75000 x^5+46250 x^6+12500 x^7+1250 x^8\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^6+39000 x^7+33500 x^8+14250 x^9+3000 x^{10}+250 x^{11}\right )+e^{\frac {12+3 x}{3+x}} \left (3600 x^8+9600 x^9+10600 x^{10}+6200 x^{11}+2025 x^{12}+350 x^{13}+25 x^{14}\right )+\left (1440 x^9+4560 x^{10}+6160 x^{11}+4600 x^{12}+2050 x^{13}+545 x^{14}+80 x^{15}+5 x^{16}+e^{\frac {4 (12+3 x)}{3+x}} \left (56250 x+65625 x^2+25000 x^3+3125 x^4\right )+e^{\frac {3 (12+3 x)}{3+x}} \left (90000 x^3+150000 x^4+92500 x^5+25000 x^6+2500 x^7\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^5+117000 x^6+100500 x^7+42750 x^8+9000 x^9+750 x^{10}\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^7+38400 x^8+42400 x^9+24800 x^{10}+8100 x^{11}+1400 x^{12}+100 x^{13}\right )\right ) \log ^2(x)+\left (2880 x^8+9120 x^9+12320 x^{10}+9200 x^{11}+4100 x^{12}+1090 x^{13}+160 x^{14}+10 x^{15}+e^{\frac {3 (12+3 x)}{3+x}} \left (45000 x^2+75000 x^3+46250 x^4+12500 x^5+1250 x^6\right )+e^{\frac {2 (12+3 x)}{3+x}} \left (54000 x^4+117000 x^5+100500 x^6+42750 x^7+9000 x^8+750 x^9\right )+e^{\frac {12+3 x}{3+x}} \left (21600 x^6+57600 x^7+63600 x^8+37200 x^9+12150 x^{10}+2100 x^{11}+150 x^{12}\right )\right ) \log ^4(x)+\left (2880 x^7+9120 x^8+12320 x^9+9200 x^{10}+4100 x^{11}+1090 x^{12}+160 x^{13}+10 x^{14}+e^{\frac {2 (12+3 x)}{3+x}} \left (18000 x^3+39000 x^4+33500 x^5+14250 x^6+3000 x^7+250 x^8\right )+e^{\frac {12+3 x}{3+x}} \left (14400 x^5+38400 x^6+42400 x^7+24800 x^8+8100 x^9+1400 x^{10}+100 x^{11}\right )\right ) \log ^6(x)+\left (1440 x^6+4560 x^7+6160 x^8+4600 x^9+2050 x^{10}+545 x^{11}+80 x^{12}+5 x^{13}+e^{\frac {12+3 x}{3+x}} \left (3600 x^4+9600 x^5+10600 x^6+6200 x^7+2025 x^8+350 x^9+25 x^{10}\right )\right ) \log ^8(x)+\left (288 x^5+912 x^6+1232 x^7+920 x^8+410 x^9+109 x^{10}+16 x^{11}+x^{12}\right ) \log ^{10}(x)} \, dx=\int -\frac {{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (6\,x^5+52\,x^4+102\,x^3+36\,x^2\right )\,{\ln \left (x\right )}^2+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (8\,x^5+64\,x^4+168\,x^3+144\,x^2\right )\,\ln \left (x\right )-{\mathrm {e}}^{\frac {5\,\left (3\,x+12\right )}{x+3}}\,\left (10\,x^3+60\,x^2+90\,x\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (10\,x^6+84\,x^5+186\,x^4+108\,x^3\right )}{{\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (1250\,x^8+12500\,x^7+46250\,x^6+75000\,x^5+45000\,x^4\right )+{\ln \left (x\right )}^8\,\left ({\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (25\,x^{10}+350\,x^9+2025\,x^8+6200\,x^7+10600\,x^6+9600\,x^5+3600\,x^4\right )+1440\,x^6+4560\,x^7+6160\,x^8+4600\,x^9+2050\,x^{10}+545\,x^{11}+80\,x^{12}+5\,x^{13}\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (250\,x^{11}+3000\,x^{10}+14250\,x^9+33500\,x^8+39000\,x^7+18000\,x^6\right )+{\ln \left (x\right )}^{10}\,\left (x^{12}+16\,x^{11}+109\,x^{10}+410\,x^9+920\,x^8+1232\,x^7+912\,x^6+288\,x^5\right )+{\ln \left (x\right )}^6\,\left ({\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (250\,x^8+3000\,x^7+14250\,x^6+33500\,x^5+39000\,x^4+18000\,x^3\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (100\,x^{11}+1400\,x^{10}+8100\,x^9+24800\,x^8+42400\,x^7+38400\,x^6+14400\,x^5\right )+2880\,x^7+9120\,x^8+12320\,x^9+9200\,x^{10}+4100\,x^{11}+1090\,x^{12}+160\,x^{13}+10\,x^{14}\right )+{\ln \left (x\right )}^4\,\left ({\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (1250\,x^6+12500\,x^5+46250\,x^4+75000\,x^3+45000\,x^2\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (750\,x^9+9000\,x^8+42750\,x^7+100500\,x^6+117000\,x^5+54000\,x^4\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (150\,x^{12}+2100\,x^{11}+12150\,x^{10}+37200\,x^9+63600\,x^8+57600\,x^7+21600\,x^6\right )+2880\,x^8+9120\,x^9+12320\,x^{10}+9200\,x^{11}+4100\,x^{12}+1090\,x^{13}+160\,x^{14}+10\,x^{15}\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (25\,x^{14}+350\,x^{13}+2025\,x^{12}+6200\,x^{11}+10600\,x^{10}+9600\,x^9+3600\,x^8\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^5+25000\,x^4+65625\,x^3+56250\,x^2\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^{\frac {3\,\left (3\,x+12\right )}{x+3}}\,\left (2500\,x^7+25000\,x^6+92500\,x^5+150000\,x^4+90000\,x^3\right )+{\mathrm {e}}^{\frac {2\,\left (3\,x+12\right )}{x+3}}\,\left (750\,x^{10}+9000\,x^9+42750\,x^8+100500\,x^7+117000\,x^6+54000\,x^5\right )+{\mathrm {e}}^{\frac {4\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^4+25000\,x^3+65625\,x^2+56250\,x\right )+{\mathrm {e}}^{\frac {3\,x+12}{x+3}}\,\left (100\,x^{13}+1400\,x^{12}+8100\,x^{11}+24800\,x^{10}+42400\,x^9+38400\,x^8+14400\,x^7\right )+1440\,x^9+4560\,x^{10}+6160\,x^{11}+4600\,x^{12}+2050\,x^{13}+545\,x^{14}+80\,x^{15}+5\,x^{16}\right )+288\,x^{10}+912\,x^{11}+1232\,x^{12}+920\,x^{13}+410\,x^{14}+109\,x^{15}+16\,x^{16}+x^{17}+{\mathrm {e}}^{\frac {5\,\left (3\,x+12\right )}{x+3}}\,\left (3125\,x^2+18750\,x+28125\right )} \,d x \]
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