Integrand size = 943, antiderivative size = 32 \[ \text {the integral} =\frac {16 \left (5+\frac {5}{x}\right )^8 \left (-2+x-e^{2 x} (-x+\log (x))\right )^4}{x} \]
Leaf count is larger than twice the leaf count of optimal. \(218\) vs. \(2(32)=64\).
Time = 0.50 (sec) , antiderivative size = 218, normalized size of antiderivative = 6.81 \[ \text {the integral} =\frac {6250000 \left (16+96 x+216 x^2+184 x^3-63 x^4-216 x^5-84 x^6+72 x^7+54 x^8-12 x^{10}+x^{12}+4 e^{2 x} (-2+x)^3 x (1+x)^8+6 e^{4 x} (-2+x)^2 x^2 (1+x)^8+4 e^{6 x} (-2+x) x^3 (1+x)^8+e^{8 x} x^4 (1+x)^8-4 e^{2 x} (1+x)^8 \left (-2+x+e^{2 x} x\right )^3 \log (x)+6 e^{4 x} (1+x)^8 \left (-2+x+e^{2 x} x\right )^2 \log ^2(x)-4 e^{6 x} (1+x)^8 \left (-2+x+e^{2 x} x\right ) \log ^3(x)+e^{8 x} (1+x)^8 \log ^4(x)\right )}{x^9} \]
Integrate[(-900000000 - 4800000000*x - 9450000000*x^2 - 6900000000*x^3 + 1 968750000*x^4 + 5400000000*x^5 + 1575000000*x^6 - 900000000*x^7 - 33750000 0*x^8 - 75000000*x^10 + 18750000*x^12 + E^(2*x)*(200000000 + 2900000000*x + 12050000000*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 1 0800000000*x^6 - 150000000*x^7 + 4650000000*x^8 + 500000000*x^9 - 14500000 00*x^10 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13) + E^(8*x)*(-250 00000*x^3 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^ 7 + 962500000*x^8 + 2800000000*x^9 + 2775000000*x^10 + 1475000000*x^11 + 4 18750000*x^12 + 50000000*x^13) + E^(4*x)*(-300000000*x - 3150000000*x^2 - 11775000000*x^3 - 19987500000*x^4 - 12150000000*x^5 + 8550000000*x^6 + 157 50000000*x^7 + 3375000000*x^8 - 6300000000*x^9 - 3900000000*x^10 + 2250000 00*x^11 + 712500000*x^12 + 150000000*x^13) + E^(6*x)*(150000000*x^2 + 1425 000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000 *x^7 - 11550000000*x^8 - 7200000000*x^9 - 150000000*x^10 + 2025000000*x^11 + 975000000*x^12 + 150000000*x^13) + (E^(6*x)*(-300000000*x - 3300000000* x^2 - 13050000000*x^3 - 23850000000*x^4 - 16200000000*x^5 + 12600000000*x^ 6 + 31500000000*x^7 + 20700000000*x^8 + 900000000*x^9 - 5700000000*x^10 - 2850000000*x^11 - 450000000*x^12) + E^(4*x)*(300000000 + 4500000000*x + 19 575000000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 10800000000*x^5 - 2835 0000000*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 22500000 0*x^10 - 1350000000*x^11 - 300000000*x^12) + E^(8*x)*(75000000*x^2 + 75000 0000*x^3 + 2900000000*x^4 + 5400000000*x^5 + 3850000000*x^6 - 3500000000*x ^7 - 10500000000*x^8 - 10600000000*x^9 - 5725000000*x^10 - 1650000000*x^11 - 200000000*x^12) + E^(2*x)*(-1800000000 - 10000000000*x - 20850000000*x^ 2 - 17150000000*x^3 + 1950000000*x^4 + 10800000000*x^5 + 2100000000*x^6 - 3900000000*x^7 - 900000000*x^8 + 1200000000*x^9 + 350000000*x^10 - 1500000 00*x^11 - 50000000*x^12))*Log[x] + (E^(4*x)*(-1350000000 - 7800000000*x - 17062500000*x^2 - 14850000000*x^3 + 2250000000*x^4 + 12600000000*x^5 + 472 5000000*x^6 - 4500000000*x^7 - 3600000000*x^8 + 637500000*x^10 + 150000000 *x^11) + E^(8*x)*(-75000000*x - 862500000*x^2 - 3600000000*x^3 - 705000000 0*x^4 - 5250000000*x^5 + 4725000000*x^6 + 14700000000*x^7 + 15150000000*x^ 8 + 8325000000*x^9 + 2437500000*x^10 + 300000000*x^11) + E^(6*x)*(15000000 0 + 2325000000*x + 10575000000*x^2 + 21150000000*x^3 + 16200000000*x^4 - 9 450000000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 53250 00000*x^9 + 2775000000*x^10 + 450000000*x^11))*Log[x]^2 + (E^(8*x)*(250000 00 + 400000000*x + 1900000000*x^2 + 4000000000*x^3 + 3150000000*x^4 - 2800 000000*x^5 - 9100000000*x^6 - 9600000000*x^7 - 5375000000*x^8 - 1600000000 *x^9 - 200000000*x^10) + E^(6*x)*(-450000000 - 2700000000*x - 6150000000*x ^2 - 5400000000*x^3 + 2100000000*x^4 + 8400000000*x^5 + 6300000000*x^6 + 6 00000000*x^7 - 1650000000*x^8 - 900000000*x^9 - 150000000*x^10))*Log[x]^3 + E^(8*x)*(-56250000 - 350000000*x - 825000000*x^2 - 700000000*x^3 + 61250 0000*x^4 + 2100000000*x^5 + 2275000000*x^6 + 1300000000*x^7 + 393750000*x^ 8 + 50000000*x^9)*Log[x]^4)/x^10,x]
(6250000*(16 + 96*x + 216*x^2 + 184*x^3 - 63*x^4 - 216*x^5 - 84*x^6 + 72*x ^7 + 54*x^8 - 12*x^10 + x^12 + 4*E^(2*x)*(-2 + x)^3*x*(1 + x)^8 + 6*E^(4*x )*(-2 + x)^2*x^2*(1 + x)^8 + 4*E^(6*x)*(-2 + x)*x^3*(1 + x)^8 + E^(8*x)*x^ 4*(1 + x)^8 - 4*E^(2*x)*(1 + x)^8*(-2 + x + E^(2*x)*x)^3*Log[x] + 6*E^(4*x )*(1 + x)^8*(-2 + x + E^(2*x)*x)^2*Log[x]^2 - 4*E^(6*x)*(1 + x)^8*(-2 + x + E^(2*x)*x)*Log[x]^3 + E^(8*x)*(1 + x)^8*Log[x]^4))/x^9
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {18750000 x^{12}-75000000 x^{10}-337500000 x^8-900000000 x^7+1575000000 x^6+5400000000 x^5+1968750000 x^4-6900000000 x^3-9450000000 x^2-4800000000 x+e^{8 x} \left (50000000 x^9+393750000 x^8+1300000000 x^7+2275000000 x^6+2100000000 x^5+612500000 x^4-700000000 x^3-825000000 x^2-350000000 x-56250000\right ) \log ^4(x)+\left (e^{8 x} \left (-200000000 x^{10}-1600000000 x^9-5375000000 x^8-9600000000 x^7-9100000000 x^6-2800000000 x^5+3150000000 x^4+4000000000 x^3+1900000000 x^2+400000000 x+25000000\right )+e^{6 x} \left (-150000000 x^{10}-900000000 x^9-1650000000 x^8+600000000 x^7+6300000000 x^6+8400000000 x^5+2100000000 x^4-5400000000 x^3-6150000000 x^2-2700000000 x-450000000\right )\right ) \log ^3(x)+\left (e^{4 x} \left (150000000 x^{11}+637500000 x^{10}-3600000000 x^8-4500000000 x^7+4725000000 x^6+12600000000 x^5+2250000000 x^4-14850000000 x^3-17062500000 x^2-7800000000 x-1350000000\right )+e^{8 x} \left (300000000 x^{11}+2437500000 x^{10}+8325000000 x^9+15150000000 x^8+14700000000 x^7+4725000000 x^6-5250000000 x^5-7050000000 x^4-3600000000 x^3-862500000 x^2-75000000 x\right )+e^{6 x} \left (450000000 x^{11}+2775000000 x^{10}+5325000000 x^9-1350000000 x^8-19800000000 x^7-28350000000 x^6-9450000000 x^5+16200000000 x^4+21150000000 x^3+10575000000 x^2+2325000000 x+150000000\right )\right ) \log ^2(x)+e^{2 x} \left (50000000 x^{13}+175000000 x^{12}-325000000 x^{11}-1450000000 x^{10}+500000000 x^9+4650000000 x^8-150000000 x^7-10800000000 x^6-5250000000 x^5+14375000000 x^4+21475000000 x^3+12050000000 x^2+2900000000 x+200000000\right )+e^{8 x} \left (50000000 x^{13}+418750000 x^{12}+1475000000 x^{11}+2775000000 x^{10}+2800000000 x^9+962500000 x^8-1050000000 x^7-1525000000 x^6-850000000 x^5-231250000 x^4-25000000 x^3\right )+e^{4 x} \left (150000000 x^{13}+712500000 x^{12}+225000000 x^{11}-3900000000 x^{10}-6300000000 x^9+3375000000 x^8+15750000000 x^7+8550000000 x^6-12150000000 x^5-19987500000 x^4-11775000000 x^3-3150000000 x^2-300000000 x\right )+e^{6 x} \left (150000000 x^{13}+975000000 x^{12}+2025000000 x^{11}-150000000 x^{10}-7200000000 x^9-11550000000 x^8-5250000000 x^7+5400000000 x^6+8850000000 x^5+5175000000 x^4+1425000000 x^3+150000000 x^2\right )+\left (e^{6 x} \left (-450000000 x^{12}-2850000000 x^{11}-5700000000 x^{10}+900000000 x^9+20700000000 x^8+31500000000 x^7+12600000000 x^6-16200000000 x^5-23850000000 x^4-13050000000 x^3-3300000000 x^2-300000000 x\right )+e^{4 x} \left (-300000000 x^{12}-1350000000 x^{11}-225000000 x^{10}+7500000000 x^9+10800000000 x^8-8100000000 x^7-28350000000 x^6-10800000000 x^5+27000000000 x^4+37050000000 x^3+19575000000 x^2+4500000000 x+300000000\right )+e^{8 x} \left (-200000000 x^{12}-1650000000 x^{11}-5725000000 x^{10}-10600000000 x^9-10500000000 x^8-3500000000 x^7+3850000000 x^6+5400000000 x^5+2900000000 x^4+750000000 x^3+75000000 x^2\right )+e^{2 x} \left (-50000000 x^{12}-150000000 x^{11}+350000000 x^{10}+1200000000 x^9-900000000 x^8-3900000000 x^7+2100000000 x^6+10800000000 x^5+1950000000 x^4-17150000000 x^3-20850000000 x^2-10000000000 x-1800000000\right )\right ) \log (x)-900000000}{x^{10}} \, dx\) |
| \(\Big \downarrow \) 2010 |
| \(\displaystyle \int \left (\frac {18750000 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}+\frac {6250000 e^{8 x} (x+1)^7 (x-\log (x))^3 \left (8 x^3+11 x^2-8 x^2 \log (x)-9 x-7 x \log (x)+9 \log (x)-4\right )}{x^{10}}+\frac {75000000 e^{6 x} (x-1) (x+1)^7 (x-\log (x))^2 \left (2 x^3+x^2-2 x^2 \log (x)-7 x+6 \log (x)-2\right )}{x^{10}}+\frac {25000000 e^{2 x} (x-2)^2 (x+1)^7 \left (2 x^4+x^3-2 x^3 \log (x)-10 x^2+17 x+8 x \log (x)-18 \log (x)+2\right )}{x^{10}}+\frac {37500000 e^{4 x} (x-2) (x+1)^7 \left (4 x^5-x^4-8 x^4 \log (x)-17 x^3+4 x^3 \log ^2(x)+4 x^3 \log (x)+16 x^2-3 x^2 \log ^2(x)+30 x^2 \log (x)+4 x-13 x \log ^2(x)+18 \log ^2(x)-34 x \log (x)-4 \log (x)\right )}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {6250000 (x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (-3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)-e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 6250000 \int -\frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )-e^{2 x} \left (-8 x^3-11 x^2+9 x+4\right )+e^{2 x} \left (-8 x^2-7 x+9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )-e^{2 x} \left (-8 x^3-11 x^2+9 x+4\right )+e^{2 x} \left (-8 x^2-7 x+9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -6250000 \int \left (-\frac {3 (x-2)^3 \left (x^2-x+6\right ) (x+1)^7}{x^{10}}-\frac {e^{8 x} (x-\log (x))^3 \left (8 x^3-8 \log (x) x^2+11 x^2-7 \log (x) x-9 x+9 \log (x)-4\right ) (x+1)^7}{x^{10}}-\frac {12 e^{6 x} (x-1) (x-\log (x))^2 \left (2 x^3-2 \log (x) x^2+x^2-7 x+6 \log (x)-2\right ) (x+1)^7}{x^{10}}-\frac {4 e^{2 x} (x-2)^2 \left (2 x^4-2 \log (x) x^3+x^3-10 x^2+8 \log (x) x+17 x-18 \log (x)+2\right ) (x+1)^7}{x^{10}}-\frac {6 e^{4 x} (x-2) \left (4 x^5-8 \log (x) x^4-x^4+4 \log ^2(x) x^3+4 \log (x) x^3-17 x^3-3 \log ^2(x) x^2+30 \log (x) x^2+16 x^2-13 \log ^2(x) x-34 \log (x) x+4 x+18 \log ^2(x)-4 \log (x)\right ) (x+1)^7}{x^{10}}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -6250000 \int \frac {(x+1)^7 \left (-e^{2 x} x-x+e^{2 x} \log (x)+2\right )^3 \left (3 \left (x^2-x+6\right )+e^{2 x} \left (8 x^3+11 x^2-9 x-4\right )-e^{2 x} \left (8 x^2+7 x-9\right ) \log (x)\right )}{x^{10}}dx\) |
Int[(-900000000 - 4800000000*x - 9450000000*x^2 - 6900000000*x^3 + 1968750 000*x^4 + 5400000000*x^5 + 1575000000*x^6 - 900000000*x^7 - 337500000*x^8 - 75000000*x^10 + 18750000*x^12 + E^(2*x)*(200000000 + 2900000000*x + 1205 0000000*x^2 + 21475000000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 1080000 0000*x^6 - 150000000*x^7 + 4650000000*x^8 + 500000000*x^9 - 1450000000*x^1 0 - 325000000*x^11 + 175000000*x^12 + 50000000*x^13) + E^(8*x)*(-25000000* x^3 - 231250000*x^4 - 850000000*x^5 - 1525000000*x^6 - 1050000000*x^7 + 96 2500000*x^8 + 2800000000*x^9 + 2775000000*x^10 + 1475000000*x^11 + 4187500 00*x^12 + 50000000*x^13) + E^(4*x)*(-300000000*x - 3150000000*x^2 - 117750 00000*x^3 - 19987500000*x^4 - 12150000000*x^5 + 8550000000*x^6 + 157500000 00*x^7 + 3375000000*x^8 - 6300000000*x^9 - 3900000000*x^10 + 225000000*x^1 1 + 712500000*x^12 + 150000000*x^13) + E^(6*x)*(150000000*x^2 + 1425000000 *x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 5250000000*x^7 - 11550000000*x^8 - 7200000000*x^9 - 150000000*x^10 + 2025000000*x^11 + 975 000000*x^12 + 150000000*x^13) + (E^(6*x)*(-300000000*x - 3300000000*x^2 - 13050000000*x^3 - 23850000000*x^4 - 16200000000*x^5 + 12600000000*x^6 + 31 500000000*x^7 + 20700000000*x^8 + 900000000*x^9 - 5700000000*x^10 - 285000 0000*x^11 - 450000000*x^12) + E^(4*x)*(300000000 + 4500000000*x + 19575000 000*x^2 + 37050000000*x^3 + 27000000000*x^4 - 10800000000*x^5 - 2835000000 0*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*x^11 - 300000000*x^12) + E^(8*x)*(75000000*x^2 + 750000000*x ^3 + 2900000000*x^4 + 5400000000*x^5 + 3850000000*x^6 - 3500000000*x^7 - 1 0500000000*x^8 - 10600000000*x^9 - 5725000000*x^10 - 1650000000*x^11 - 200 000000*x^12) + E^(2*x)*(-1800000000 - 10000000000*x - 20850000000*x^2 - 17 150000000*x^3 + 1950000000*x^4 + 10800000000*x^5 + 2100000000*x^6 - 390000 0000*x^7 - 900000000*x^8 + 1200000000*x^9 + 350000000*x^10 - 150000000*x^1 1 - 50000000*x^12))*Log[x] + (E^(4*x)*(-1350000000 - 7800000000*x - 170625 00000*x^2 - 14850000000*x^3 + 2250000000*x^4 + 12600000000*x^5 + 472500000 0*x^6 - 4500000000*x^7 - 3600000000*x^8 + 637500000*x^10 + 150000000*x^11) + E^(8*x)*(-75000000*x - 862500000*x^2 - 3600000000*x^3 - 7050000000*x^4 - 5250000000*x^5 + 4725000000*x^6 + 14700000000*x^7 + 15150000000*x^8 + 83 25000000*x^9 + 2437500000*x^10 + 300000000*x^11) + E^(6*x)*(150000000 + 23 25000000*x + 10575000000*x^2 + 21150000000*x^3 + 16200000000*x^4 - 9450000 000*x^5 - 28350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000* x^9 + 2775000000*x^10 + 450000000*x^11))*Log[x]^2 + (E^(8*x)*(25000000 + 4 00000000*x + 1900000000*x^2 + 4000000000*x^3 + 3150000000*x^4 - 2800000000 *x^5 - 9100000000*x^6 - 9600000000*x^7 - 5375000000*x^8 - 1600000000*x^9 - 200000000*x^10) + E^(6*x)*(-450000000 - 2700000000*x - 6150000000*x^2 - 5 400000000*x^3 + 2100000000*x^4 + 8400000000*x^5 + 6300000000*x^6 + 6000000 00*x^7 - 1650000000*x^8 - 900000000*x^9 - 150000000*x^10))*Log[x]^3 + E^(8 *x)*(-56250000 - 350000000*x - 825000000*x^2 - 700000000*x^3 + 612500000*x ^4 + 2100000000*x^5 + 2275000000*x^6 + 1300000000*x^7 + 393750000*x^8 + 50 000000*x^9)*Log[x]^4)/x^10,x]
3.2.4.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Int[(u_)*((c_.)*(x_))^(m_.), x_Symbol] :> Int[ExpandIntegrand[(c*x)^m*u, x] , x] /; FreeQ[{c, m}, x] && SumQ[u] && !LinearQ[u, x] && !MatchQ[u, (a_) + (b_.)*(v_) /; FreeQ[{a, b}, x] && InverseFunctionQ[v]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Leaf count of result is larger than twice the leaf count of optimal. \(1092\) vs. \(2(31)=62\).
Time = 1.39 (sec) , antiderivative size = 1093, normalized size of antiderivative = 34.16
| method | result | size |
| risch | \(\text {Expression too large to display}\) | \(1093\) |
| parallelrisch | \(\text {Expression too large to display}\) | \(1510\) |
int(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+2100000000* x^5+612500000*x^4-700000000*x^3-825000000*x^2-350000000*x-56250000)*exp(x) ^8*ln(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-9600000000*x^7- 9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000000*x^2 +400000000*x+25000000)*exp(x)^8+(-150000000*x^10-900000000*x^9-1650000000* x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-5400000000* x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*ln(x)^3+((300000000*x ^11+2437500000*x^10+8325000000*x^9+15150000000*x^8+14700000000*x^7+4725000 000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-862500000*x^2-7500000 0*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-1350000000*x^ 8-19800000000*x^7-28350000000*x^6-9450000000*x^5+16200000000*x^4+211500000 00*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(150000000*x^11+63 7500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000000*x^5+ 2250000000*x^4-14850000000*x^3-17062500000*x^2-7800000000*x-1350000000)*ex p(x)^4)*ln(x)^2+((-200000000*x^12-1650000000*x^11-5725000000*x^10-10600000 000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000*x^5+29000 00000*x^4+750000000*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2850000000 *x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+31500000000*x^7+126000 00000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000000*x^2-3 00000000*x)*exp(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x^10+75000 00000*x^9+10800000000*x^8-8100000000*x^7-28350000000*x^6-10800000000*x^5+2 7000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+300000000)*exp (x)^4+(-50000000*x^12-150000000*x^11+350000000*x^10+1200000000*x^9-9000000 00*x^8-3900000000*x^7+2100000000*x^6+10800000000*x^5+1950000000*x^4-171500 00000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*ln(x)+(50000 000*x^13+418750000*x^12+1475000000*x^11+2775000000*x^10+2800000000*x^9+962 500000*x^8-1050000000*x^7-1525000000*x^6-850000000*x^5-231250000*x^4-25000 000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11-150000000 *x^10-7200000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x^6+8850000 000*x^5+5175000000*x^4+1425000000*x^3+150000000*x^2)*exp(x)^6+(150000000*x ^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9+337500000 0*x^8+15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000*x^4-11775 000000*x^3-3150000000*x^2-300000000*x)*exp(x)^4+(50000000*x^13+175000000*x ^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8-150000000* x^7-10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x^3+1205000 0000*x^2+2900000000*x+200000000)*exp(x)^2+18750000*x^12-75000000*x^10-3375 00000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000*x^4-69000 00000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x,method=_RETURNVERB OSE)
6250000*(x^8+8*x^7+28*x^6+56*x^5+70*x^4+56*x^3+28*x^2+8*x+1)/x^9*exp(8*x)* ln(x)^4-25000000*exp(6*x)*(exp(2*x)*x^9+8*exp(2*x)*x^8+x^9+28*exp(2*x)*x^7 +6*x^8+56*exp(2*x)*x^6+12*x^7+70*x^5*exp(2*x)+56*exp(2*x)*x^4-42*x^5+28*ex p(2*x)*x^3-84*x^4+8*exp(2*x)*x^2-84*x^3+x*exp(2*x)-48*x^2-15*x-2)/x^9*ln(x )^3+37500000*exp(4*x)*(4+28*x-96*exp(2*x)*x^3+8*x^3*exp(4*x)-168*x^5*exp(2 *x)-30*exp(2*x)*x^2-4*x*exp(2*x)+x^2*exp(4*x)+x^10+4*x^9-24*x^7+84*x^4+120 *x^3+81*x^2-42*x^6+70*x^6*exp(4*x)+2*exp(2*x)*x^10+12*exp(2*x)*x^9+8*exp(4 *x)*x^9+56*exp(4*x)*x^7+28*x^8*exp(4*x)+56*x^5*exp(4*x)+exp(4*x)*x^10+24*e xp(2*x)*x^8-84*exp(2*x)*x^6-168*exp(2*x)*x^4+28*x^4*exp(4*x))/x^9*ln(x)^2- 25000000*exp(2*x)*(-8-52*x+70*exp(6*x)*x^7+56*exp(6*x)*x^6+243*exp(2*x)*x^ 3-45*x^3*exp(4*x)+252*x^5*exp(2*x)+84*exp(2*x)*x^2+12*x*exp(2*x)+x^11-6*x^ 2*exp(4*x)+2*x^10-8*x^9+6*x^7-24*x^8-48*x^4-159*x^3-134*x^2+84*x^6+84*x^5- 252*x^6*exp(4*x)+8*exp(6*x)*x^4+exp(6*x)*x^3+12*exp(2*x)*x^10+3*exp(2*x)*x ^11+36*exp(4*x)*x^9-126*exp(4*x)*x^7-252*x^5*exp(4*x)+18*exp(4*x)*x^10+exp (6*x)*x^11+3*exp(4*x)*x^11-72*exp(2*x)*x^8-126*exp(2*x)*x^7+360*exp(2*x)*x ^4+28*exp(6*x)*x^5+8*exp(6*x)*x^10+28*exp(6*x)*x^9-144*x^4*exp(4*x)+56*exp (6*x)*x^8)/x^9*ln(x)+6250000*(16+96*x-336*exp(6*x)*x^7+28*exp(8*x)*x^6-336 *exp(6*x)*x^6-536*exp(2*x)*x^3+168*x^3*exp(4*x)-192*x^5*exp(2*x)-208*exp(2 *x)*x^2-32*x*exp(2*x)+x^12+24*x^2*exp(4*x)-12*x^10+72*x^7+54*x^8-63*x^4+18 4*x^3+216*x^2-84*x^6-216*x^5+8*exp(8*x)*x^5+exp(8*x)*x^4+504*x^6*exp(4*...
Leaf count of result is larger than twice the leaf count of optimal. 758 vs. \(2 (28) = 56\).
Time = 0.30 (sec) , antiderivative size = 758, normalized size of antiderivative = 23.69 \[ \text {the integral} =\text {Too large to display} \]
integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+21000 00000*x^5+612500000*x^4-700000000*x^3-825000000*x^2-350000000*x-56250000)* exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-96000000 00*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000 000*x^2+400000000*x+25000000)*exp(x)^8+(-150000000*x^10-900000000*x^9-1650 000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-5400 000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300 000000*x^11+2437500000*x^10+8325000000*x^9+15150000000*x^8+14700000000*x^7 +4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-862500000*x^2 -75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-13500 00000*x^8-19800000000*x^7-28350000000*x^6-9450000000*x^5+16200000000*x^4+2 1150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(150000000 *x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000 000*x^5+2250000000*x^4-14850000000*x^3-17062500000*x^2-7800000000*x-135000 0000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-5725000000*x^10 -10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000* x^5+2900000000*x^4+750000000*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2 850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+31500000000*x ^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000 000*x^2-300000000*x)*exp(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x ^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-28350000000*x^6-10800000 000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+30000 0000)*exp(x)^4+(-50000000*x^12-150000000*x^11+350000000*x^10+1200000000*x^ 9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*x^5+1950000000*x ^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log (x)+(50000000*x^13+418750000*x^12+1475000000*x^11+2775000000*x^10+28000000 00*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-850000000*x^5-231250000 *x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11 -150000000*x^10-7200000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x ^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000000*x^2)*exp(x)^6+(1 50000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9 +3375000000*x^8+15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000 *x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp(x)^4+(50000000*x^13+1 75000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8- 150000000*x^7-10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x ^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^2+18750000*x^12-75000000 *x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000 *x^4-6900000000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorit hm=\
6250000*(x^12 - 12*x^10 + 54*x^8 + 72*x^7 - 84*x^6 + (x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8*x + 1)*e^(8*x)*log(x)^4 - 216*x^5 - 63*x^4 - 4*((x^9 + 8*x^8 + 28*x^7 + 56*x^6 + 70*x^5 + 56*x^4 + 28*x^3 + 8*x^2 + x)*e^(8*x) + (x^9 + 6*x^8 + 12*x^7 - 42*x^5 - 84*x^4 - 84*x^3 - 4 8*x^2 - 15*x - 2)*e^(6*x))*log(x)^3 + 184*x^3 + 6*((x^10 + 8*x^9 + 28*x^8 + 56*x^7 + 70*x^6 + 56*x^5 + 28*x^4 + 8*x^3 + x^2)*e^(8*x) + 2*(x^10 + 6*x ^9 + 12*x^8 - 42*x^6 - 84*x^5 - 84*x^4 - 48*x^3 - 15*x^2 - 2*x)*e^(6*x) + (x^10 + 4*x^9 - 24*x^7 - 42*x^6 + 84*x^4 + 120*x^3 + 81*x^2 + 28*x + 4)*e^ (4*x))*log(x)^2 + 216*x^2 + (x^12 + 8*x^11 + 28*x^10 + 56*x^9 + 70*x^8 + 5 6*x^7 + 28*x^6 + 8*x^5 + x^4)*e^(8*x) + 4*(x^12 + 6*x^11 + 12*x^10 - 42*x^ 8 - 84*x^7 - 84*x^6 - 48*x^5 - 15*x^4 - 2*x^3)*e^(6*x) + 6*(x^12 + 4*x^11 - 24*x^9 - 42*x^8 + 84*x^6 + 120*x^5 + 81*x^4 + 28*x^3 + 4*x^2)*e^(4*x) + 4*(x^12 + 2*x^11 - 8*x^10 - 24*x^9 + 6*x^8 + 84*x^7 + 84*x^6 - 48*x^5 - 15 9*x^4 - 134*x^3 - 52*x^2 - 8*x)*e^(2*x) - 4*((x^11 + 8*x^10 + 28*x^9 + 56* x^8 + 70*x^7 + 56*x^6 + 28*x^5 + 8*x^4 + x^3)*e^(8*x) + 3*(x^11 + 6*x^10 + 12*x^9 - 42*x^7 - 84*x^6 - 84*x^5 - 48*x^4 - 15*x^3 - 2*x^2)*e^(6*x) + 3* (x^11 + 4*x^10 - 24*x^8 - 42*x^7 + 84*x^5 + 120*x^4 + 81*x^3 + 28*x^2 + 4* x)*e^(4*x) + (x^11 + 2*x^10 - 8*x^9 - 24*x^8 + 6*x^7 + 84*x^6 + 84*x^5 - 4 8*x^4 - 159*x^3 - 134*x^2 - 52*x - 8)*e^(2*x))*log(x) + 96*x + 16)/x^9
Leaf count of result is larger than twice the leaf count of optimal. 1156 vs. \(2 (24) = 48\).
Time = 1.26 (sec) , antiderivative size = 1156, normalized size of antiderivative = 36.12 \[ \text {the integral} =\text {Too large to display} \]
integrate(((50000000*x**9+393750000*x**8+1300000000*x**7+2275000000*x**6+2 100000000*x**5+612500000*x**4-700000000*x**3-825000000*x**2-350000000*x-56 250000)*exp(x)**8*ln(x)**4+((-200000000*x**10-1600000000*x**9-5375000000*x **8-9600000000*x**7-9100000000*x**6-2800000000*x**5+3150000000*x**4+400000 0000*x**3+1900000000*x**2+400000000*x+25000000)*exp(x)**8+(-150000000*x**1 0-900000000*x**9-1650000000*x**8+600000000*x**7+6300000000*x**6+8400000000 *x**5+2100000000*x**4-5400000000*x**3-6150000000*x**2-2700000000*x-4500000 00)*exp(x)**6)*ln(x)**3+((300000000*x**11+2437500000*x**10+8325000000*x**9 +15150000000*x**8+14700000000*x**7+4725000000*x**6-5250000000*x**5-7050000 000*x**4-3600000000*x**3-862500000*x**2-75000000*x)*exp(x)**8+(450000000*x **11+2775000000*x**10+5325000000*x**9-1350000000*x**8-19800000000*x**7-283 50000000*x**6-9450000000*x**5+16200000000*x**4+21150000000*x**3+1057500000 0*x**2+2325000000*x+150000000)*exp(x)**6+(150000000*x**11+637500000*x**10- 3600000000*x**8-4500000000*x**7+4725000000*x**6+12600000000*x**5+225000000 0*x**4-14850000000*x**3-17062500000*x**2-7800000000*x-1350000000)*exp(x)** 4)*ln(x)**2+((-200000000*x**12-1650000000*x**11-5725000000*x**10-106000000 00*x**9-10500000000*x**8-3500000000*x**7+3850000000*x**6+5400000000*x**5+2 900000000*x**4+750000000*x**3+75000000*x**2)*exp(x)**8+(-450000000*x**12-2 850000000*x**11-5700000000*x**10+900000000*x**9+20700000000*x**8+315000000 00*x**7+12600000000*x**6-16200000000*x**5-23850000000*x**4-13050000000*x** 3-3300000000*x**2-300000000*x)*exp(x)**6+(-300000000*x**12-1350000000*x**1 1-225000000*x**10+7500000000*x**9+10800000000*x**8-8100000000*x**7-2835000 0000*x**6-10800000000*x**5+27000000000*x**4+37050000000*x**3+19575000000*x **2+4500000000*x+300000000)*exp(x)**4+(-50000000*x**12-150000000*x**11+350 000000*x**10+1200000000*x**9-900000000*x**8-3900000000*x**7+2100000000*x** 6+10800000000*x**5+1950000000*x**4-17150000000*x**3-20850000000*x**2-10000 000000*x-1800000000)*exp(x)**2)*ln(x)+(50000000*x**13+418750000*x**12+1475 000000*x**11+2775000000*x**10+2800000000*x**9+962500000*x**8-1050000000*x* *7-1525000000*x**6-850000000*x**5-231250000*x**4-25000000*x**3)*exp(x)**8+ (150000000*x**13+975000000*x**12+2025000000*x**11-150000000*x**10-72000000 00*x**9-11550000000*x**8-5250000000*x**7+5400000000*x**6+8850000000*x**5+5 175000000*x**4+1425000000*x**3+150000000*x**2)*exp(x)**6+(150000000*x**13+ 712500000*x**12+225000000*x**11-3900000000*x**10-6300000000*x**9+337500000 0*x**8+15750000000*x**7+8550000000*x**6-12150000000*x**5-19987500000*x**4- 11775000000*x**3-3150000000*x**2-300000000*x)*exp(x)**4+(50000000*x**13+17 5000000*x**12-325000000*x**11-1450000000*x**10+500000000*x**9+4650000000*x **8-150000000*x**7-10800000000*x**6-5250000000*x**5+14375000000*x**4+21475 000000*x**3+12050000000*x**2+2900000000*x+200000000)*exp(x)**2+18750000*x* *12-75000000*x**10-337500000*x**8-900000000*x**7+1575000000*x**6+540000000 0*x**5+1968750000*x**4-6900000000*x**3-9450000000*x**2-4800000000*x-900000 000)/x**10,x)
6250000*x**3 - 75000000*x + (337500000*x**8 + 450000000*x**7 - 525000000*x **6 - 1350000000*x**5 - 393750000*x**4 + 1150000000*x**3 + 1350000000*x**2 + 600000000*x + 100000000)/x**9 + ((25000000*x**39 - 25000000*x**38*log(x ) + 50000000*x**38 - 50000000*x**37*log(x) - 200000000*x**37 + 200000000*x **36*log(x) - 600000000*x**36 + 600000000*x**35*log(x) + 150000000*x**35 - 150000000*x**34*log(x) + 2100000000*x**34 - 2100000000*x**33*log(x) + 210 0000000*x**33 - 2100000000*x**32*log(x) - 1200000000*x**32 + 1200000000*x* *31*log(x) - 3975000000*x**31 + 3975000000*x**30*log(x) - 3350000000*x**30 + 3350000000*x**29*log(x) - 1300000000*x**29 + 1300000000*x**28*log(x) - 200000000*x**28 + 200000000*x**27*log(x))*exp(2*x) + (37500000*x**39 - 750 00000*x**38*log(x) + 150000000*x**38 + 37500000*x**37*log(x)**2 - 30000000 0*x**37*log(x) + 150000000*x**36*log(x)**2 - 900000000*x**36 + 1800000000* x**35*log(x) - 1575000000*x**35 - 900000000*x**34*log(x)**2 + 3150000000*x **34*log(x) - 1575000000*x**33*log(x)**2 + 3150000000*x**33 - 6300000000*x **32*log(x) + 4500000000*x**32 + 3150000000*x**31*log(x)**2 - 9000000000*x **31*log(x) + 3037500000*x**31 + 4500000000*x**30*log(x)**2 - 6075000000*x **30*log(x) + 1050000000*x**30 + 3037500000*x**29*log(x)**2 - 2100000000*x **29*log(x) + 150000000*x**29 + 1050000000*x**28*log(x)**2 - 300000000*x** 28*log(x) + 150000000*x**27*log(x)**2)*exp(4*x) + (25000000*x**39 - 750000 00*x**38*log(x) + 150000000*x**38 + 75000000*x**37*log(x)**2 - 45000000...
\[ \text {the integral} =\text {Too large to display} \]
integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+21000 00000*x^5+612500000*x^4-700000000*x^3-825000000*x^2-350000000*x-56250000)* exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-96000000 00*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000 000*x^2+400000000*x+25000000)*exp(x)^8+(-150000000*x^10-900000000*x^9-1650 000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-5400 000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300 000000*x^11+2437500000*x^10+8325000000*x^9+15150000000*x^8+14700000000*x^7 +4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-862500000*x^2 -75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-13500 00000*x^8-19800000000*x^7-28350000000*x^6-9450000000*x^5+16200000000*x^4+2 1150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(150000000 *x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000 000*x^5+2250000000*x^4-14850000000*x^3-17062500000*x^2-7800000000*x-135000 0000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-5725000000*x^10 -10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000* x^5+2900000000*x^4+750000000*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2 850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+31500000000*x ^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000 000*x^2-300000000*x)*exp(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x ^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-28350000000*x^6-10800000 000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+30000 0000)*exp(x)^4+(-50000000*x^12-150000000*x^11+350000000*x^10+1200000000*x^ 9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*x^5+1950000000*x ^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log (x)+(50000000*x^13+418750000*x^12+1475000000*x^11+2775000000*x^10+28000000 00*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-850000000*x^5-231250000 *x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11 -150000000*x^10-7200000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x ^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000000*x^2)*exp(x)^6+(1 50000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9 +3375000000*x^8+15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000 *x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp(x)^4+(50000000*x^13+1 75000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8- 150000000*x^7-10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x ^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^2+18750000*x^12-75000000 *x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000 *x^4-6900000000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorit hm=\
6250000*x^3 + 390625/16*(256*x^3 - 96*x^2 + 24*x - 3)*e^(8*x) + 26171875/1 6*(32*x^2 - 8*x + 1)*e^(8*x) + 23046875*(8*x - 1)*e^(8*x) + 6250000/9*(36* x^3 - 18*x^2 + 6*x - 1)*e^(6*x) + 81250000/9*(18*x^2 - 6*x + 1)*e^(6*x) + 56250000*(6*x - 1)*e^(6*x) + 1171875*(32*x^3 - 24*x^2 + 12*x - 3)*e^(4*x) + 22265625*(8*x^2 - 4*x + 1)*e^(4*x) + 14062500*(4*x - 1)*e^(4*x) + 625000 0*(4*x^3 - 6*x^2 + 6*x - 3)*e^(2*x) + 43750000*(2*x^2 - 2*x + 1)*e^(2*x) - 81250000*(2*x - 1)*e^(2*x) + 175000000*e^(2*x)*log(x) - 75000000*x + 3375 00000/x + 450000000/x^2 - 525000000/x^3 - 1350000000/x^4 - 393750000/x^5 + 1150000000/x^6 + 1350000000/x^7 - 6250000*(4*(x^11 + 2*x^10 - x^9 - 24*x^ 8 + 6*x^7 + 84*x^6 + 84*x^5 - 48*x^4 - 159*x^3 - 134*x^2 - 52*x - 8)*e^(2* x)*log(x) - ((x^8 + 8*x^7 + 28*x^6 + 56*x^5 + 70*x^4 + 56*x^3 + 28*x^2 + 8 *x + 1)*log(x)^4 - 4*(x^9 + 8*x^8 + 28*x^7 + 56*x^6 + 70*x^5 + 56*x^4 + 28 *x^3 + 8*x^2 + x)*log(x)^3 + 6*(x^10 + 8*x^9 + 28*x^8 + 56*x^7 + 70*x^6 + 56*x^5 + 28*x^4 + 8*x^3 + x^2)*log(x)^2 - 4*(x^11 + 8*x^10 + 28*x^9 + 56*x ^8 + 70*x^7 + 56*x^6 + 28*x^5 + 8*x^4 + x^3)*log(x))*e^(8*x) + 4*((x^9 + 6 *x^8 + 12*x^7 - 42*x^5 - 84*x^4 - 84*x^3 - 48*x^2 - 15*x - 2)*log(x)^3 - 3 *(x^10 + 6*x^9 + 12*x^8 - 42*x^6 - 84*x^5 - 84*x^4 - 48*x^3 - 15*x^2 - 2*x )*log(x)^2 + 3*(x^11 + 6*x^10 + 12*x^9 - 42*x^7 - 84*x^6 - 84*x^5 - 48*x^4 - 15*x^3 - 2*x^2)*log(x))*e^(6*x) - 6*((x^10 + 4*x^9 - 24*x^7 - 42*x^6 + 84*x^4 + 120*x^3 + 81*x^2 + 28*x + 4)*log(x)^2 - 2*(x^11 + 4*x^10 - 24*...
Leaf count of result is larger than twice the leaf count of optimal. 1503 vs. \(2 (28) = 56\).
Time = 0.35 (sec) , antiderivative size = 1503, normalized size of antiderivative = 46.97 \[ \text {the integral} =\text {Too large to display} \]
integrate(((50000000*x^9+393750000*x^8+1300000000*x^7+2275000000*x^6+21000 00000*x^5+612500000*x^4-700000000*x^3-825000000*x^2-350000000*x-56250000)* exp(x)^8*log(x)^4+((-200000000*x^10-1600000000*x^9-5375000000*x^8-96000000 00*x^7-9100000000*x^6-2800000000*x^5+3150000000*x^4+4000000000*x^3+1900000 000*x^2+400000000*x+25000000)*exp(x)^8+(-150000000*x^10-900000000*x^9-1650 000000*x^8+600000000*x^7+6300000000*x^6+8400000000*x^5+2100000000*x^4-5400 000000*x^3-6150000000*x^2-2700000000*x-450000000)*exp(x)^6)*log(x)^3+((300 000000*x^11+2437500000*x^10+8325000000*x^9+15150000000*x^8+14700000000*x^7 +4725000000*x^6-5250000000*x^5-7050000000*x^4-3600000000*x^3-862500000*x^2 -75000000*x)*exp(x)^8+(450000000*x^11+2775000000*x^10+5325000000*x^9-13500 00000*x^8-19800000000*x^7-28350000000*x^6-9450000000*x^5+16200000000*x^4+2 1150000000*x^3+10575000000*x^2+2325000000*x+150000000)*exp(x)^6+(150000000 *x^11+637500000*x^10-3600000000*x^8-4500000000*x^7+4725000000*x^6+12600000 000*x^5+2250000000*x^4-14850000000*x^3-17062500000*x^2-7800000000*x-135000 0000)*exp(x)^4)*log(x)^2+((-200000000*x^12-1650000000*x^11-5725000000*x^10 -10600000000*x^9-10500000000*x^8-3500000000*x^7+3850000000*x^6+5400000000* x^5+2900000000*x^4+750000000*x^3+75000000*x^2)*exp(x)^8+(-450000000*x^12-2 850000000*x^11-5700000000*x^10+900000000*x^9+20700000000*x^8+31500000000*x ^7+12600000000*x^6-16200000000*x^5-23850000000*x^4-13050000000*x^3-3300000 000*x^2-300000000*x)*exp(x)^6+(-300000000*x^12-1350000000*x^11-225000000*x ^10+7500000000*x^9+10800000000*x^8-8100000000*x^7-28350000000*x^6-10800000 000*x^5+27000000000*x^4+37050000000*x^3+19575000000*x^2+4500000000*x+30000 0000)*exp(x)^4+(-50000000*x^12-150000000*x^11+350000000*x^10+1200000000*x^ 9-900000000*x^8-3900000000*x^7+2100000000*x^6+10800000000*x^5+1950000000*x ^4-17150000000*x^3-20850000000*x^2-10000000000*x-1800000000)*exp(x)^2)*log (x)+(50000000*x^13+418750000*x^12+1475000000*x^11+2775000000*x^10+28000000 00*x^9+962500000*x^8-1050000000*x^7-1525000000*x^6-850000000*x^5-231250000 *x^4-25000000*x^3)*exp(x)^8+(150000000*x^13+975000000*x^12+2025000000*x^11 -150000000*x^10-7200000000*x^9-11550000000*x^8-5250000000*x^7+5400000000*x ^6+8850000000*x^5+5175000000*x^4+1425000000*x^3+150000000*x^2)*exp(x)^6+(1 50000000*x^13+712500000*x^12+225000000*x^11-3900000000*x^10-6300000000*x^9 +3375000000*x^8+15750000000*x^7+8550000000*x^6-12150000000*x^5-19987500000 *x^4-11775000000*x^3-3150000000*x^2-300000000*x)*exp(x)^4+(50000000*x^13+1 75000000*x^12-325000000*x^11-1450000000*x^10+500000000*x^9+4650000000*x^8- 150000000*x^7-10800000000*x^6-5250000000*x^5+14375000000*x^4+21475000000*x ^3+12050000000*x^2+2900000000*x+200000000)*exp(x)^2+18750000*x^12-75000000 *x^10-337500000*x^8-900000000*x^7+1575000000*x^6+5400000000*x^5+1968750000 *x^4-6900000000*x^3-9450000000*x^2-4800000000*x-900000000)/x^10,x, algorit hm=\
6250000*(x^12*e^(8*x) + 4*x^12*e^(6*x) + 6*x^12*e^(4*x) + 4*x^12*e^(2*x) - 4*x^11*e^(8*x)*log(x) - 12*x^11*e^(6*x)*log(x) - 12*x^11*e^(4*x)*log(x) - 4*x^11*e^(2*x)*log(x) + 6*x^10*e^(8*x)*log(x)^2 + 12*x^10*e^(6*x)*log(x)^ 2 + 6*x^10*e^(4*x)*log(x)^2 - 4*x^9*e^(8*x)*log(x)^3 - 4*x^9*e^(6*x)*log(x )^3 + x^8*e^(8*x)*log(x)^4 + x^12 + 8*x^11*e^(8*x) + 24*x^11*e^(6*x) + 24* x^11*e^(4*x) + 8*x^11*e^(2*x) - 32*x^10*e^(8*x)*log(x) - 72*x^10*e^(6*x)*l og(x) - 48*x^10*e^(4*x)*log(x) - 8*x^10*e^(2*x)*log(x) + 48*x^9*e^(8*x)*lo g(x)^2 + 72*x^9*e^(6*x)*log(x)^2 + 24*x^9*e^(4*x)*log(x)^2 - 32*x^8*e^(8*x )*log(x)^3 - 24*x^8*e^(6*x)*log(x)^3 + 8*x^7*e^(8*x)*log(x)^4 + 28*x^10*e^ (8*x) + 48*x^10*e^(6*x) - 32*x^10*e^(2*x) - 112*x^9*e^(8*x)*log(x) - 144*x ^9*e^(6*x)*log(x) + 32*x^9*e^(2*x)*log(x) + 168*x^8*e^(8*x)*log(x)^2 + 144 *x^8*e^(6*x)*log(x)^2 - 112*x^7*e^(8*x)*log(x)^3 - 48*x^7*e^(6*x)*log(x)^3 + 28*x^6*e^(8*x)*log(x)^4 - 12*x^10 + 56*x^9*e^(8*x) - 144*x^9*e^(4*x) - 96*x^9*e^(2*x) - 224*x^8*e^(8*x)*log(x) + 288*x^8*e^(4*x)*log(x) + 96*x^8* e^(2*x)*log(x) + 336*x^7*e^(8*x)*log(x)^2 - 144*x^7*e^(4*x)*log(x)^2 - 224 *x^6*e^(8*x)*log(x)^3 + 56*x^5*e^(8*x)*log(x)^4 + 70*x^8*e^(8*x) - 168*x^8 *e^(6*x) - 252*x^8*e^(4*x) + 24*x^8*e^(2*x) - 280*x^7*e^(8*x)*log(x) + 504 *x^7*e^(6*x)*log(x) + 504*x^7*e^(4*x)*log(x) - 24*x^7*e^(2*x)*log(x) + 420 *x^6*e^(8*x)*log(x)^2 - 504*x^6*e^(6*x)*log(x)^2 - 252*x^6*e^(4*x)*log(x)^ 2 - 280*x^5*e^(8*x)*log(x)^3 + 168*x^5*e^(6*x)*log(x)^3 + 70*x^4*e^(8*x...
Timed out. \[ \text {the integral} =\text {Too large to display} \]
int(-(4800000000*x - exp(8*x)*(962500000*x^8 - 231250000*x^4 - 850000000*x ^5 - 1525000000*x^6 - 1050000000*x^7 - 25000000*x^3 + 2800000000*x^9 + 277 5000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + exp(4*x )*(300000000*x + 3150000000*x^2 + 11775000000*x^3 + 19987500000*x^4 + 1215 0000000*x^5 - 8550000000*x^6 - 15750000000*x^7 - 3375000000*x^8 + 63000000 00*x^9 + 3900000000*x^10 - 225000000*x^11 - 712500000*x^12 - 150000000*x^1 3) + log(x)*(exp(2*x)*(10000000000*x + 20850000000*x^2 + 17150000000*x^3 - 1950000000*x^4 - 10800000000*x^5 - 2100000000*x^6 + 3900000000*x^7 + 9000 00000*x^8 - 1200000000*x^9 - 350000000*x^10 + 150000000*x^11 + 50000000*x^ 12 + 1800000000) - exp(4*x)*(4500000000*x + 19575000000*x^2 + 37050000000* x^3 + 27000000000*x^4 - 10800000000*x^5 - 28350000000*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*x^11 - 3 00000000*x^12 + 300000000) + exp(6*x)*(300000000*x + 3300000000*x^2 + 1305 0000000*x^3 + 23850000000*x^4 + 16200000000*x^5 - 12600000000*x^6 - 315000 00000*x^7 - 20700000000*x^8 - 900000000*x^9 + 5700000000*x^10 + 2850000000 *x^11 + 450000000*x^12) + exp(8*x)*(3500000000*x^7 - 750000000*x^3 - 29000 00000*x^4 - 5400000000*x^5 - 3850000000*x^6 - 75000000*x^2 + 10500000000*x ^8 + 10600000000*x^9 + 5725000000*x^10 + 1650000000*x^11 + 200000000*x^12) ) + log(x)^3*(exp(8*x)*(2800000000*x^5 - 1900000000*x^2 - 4000000000*x^3 - 3150000000*x^4 - 400000000*x + 9100000000*x^6 + 9600000000*x^7 + 53750000 00*x^8 + 1600000000*x^9 + 200000000*x^10 - 25000000) + exp(6*x)*(270000000 0*x + 6150000000*x^2 + 5400000000*x^3 - 2100000000*x^4 - 8400000000*x^5 - 6300000000*x^6 - 600000000*x^7 + 1650000000*x^8 + 900000000*x^9 + 15000000 0*x^10 + 450000000)) - exp(2*x)*(2900000000*x + 12050000000*x^2 + 21475000 000*x^3 + 14375000000*x^4 - 5250000000*x^5 - 10800000000*x^6 - 150000000*x ^7 + 4650000000*x^8 + 500000000*x^9 - 1450000000*x^10 - 325000000*x^11 + 1 75000000*x^12 + 50000000*x^13 + 200000000) - exp(6*x)*(150000000*x^2 + 142 5000000*x^3 + 5175000000*x^4 + 8850000000*x^5 + 5400000000*x^6 - 525000000 0*x^7 - 11550000000*x^8 - 7200000000*x^9 - 150000000*x^10 + 2025000000*x^1 1 + 975000000*x^12 + 150000000*x^13) + 9450000000*x^2 + 6900000000*x^3 - 1 968750000*x^4 - 5400000000*x^5 - 1575000000*x^6 + 900000000*x^7 + 33750000 0*x^8 + 75000000*x^10 - 18750000*x^12 - log(x)^2*(exp(6*x)*(2325000000*x + 10575000000*x^2 + 21150000000*x^3 + 16200000000*x^4 - 9450000000*x^5 - 28 350000000*x^6 - 19800000000*x^7 - 1350000000*x^8 + 5325000000*x^9 + 277500 0000*x^10 + 450000000*x^11 + 150000000) + exp(8*x)*(4725000000*x^6 - 86250 0000*x^2 - 3600000000*x^3 - 7050000000*x^4 - 5250000000*x^5 - 75000000*x + 14700000000*x^7 + 15150000000*x^8 + 8325000000*x^9 + 2437500000*x^10 + 30 0000000*x^11) - exp(4*x)*(7800000000*x + 17062500000*x^2 + 14850000000*x^3 - 2250000000*x^4 - 12600000000*x^5 - 4725000000*x^6 + 4500000000*x^7 + 36 00000000*x^8 - 637500000*x^10 - 150000000*x^11 + 1350000000)) - exp(8*x)*l og(x)^4*(612500000*x^4 - 825000000*x^2 - 700000000*x^3 - 350000000*x + 210 0000000*x^5 + 2275000000*x^6 + 1300000000*x^7 + 393750000*x^8 + 50000000*x ^9 - 56250000) + 900000000)/x^10,x)
int(-(4800000000*x - exp(8*x)*(962500000*x^8 - 231250000*x^4 - 850000000*x ^5 - 1525000000*x^6 - 1050000000*x^7 - 25000000*x^3 + 2800000000*x^9 + 277 5000000*x^10 + 1475000000*x^11 + 418750000*x^12 + 50000000*x^13) + exp(4*x )*(300000000*x + 3150000000*x^2 + 11775000000*x^3 + 19987500000*x^4 + 1215 0000000*x^5 - 8550000000*x^6 - 15750000000*x^7 - 3375000000*x^8 + 63000000 00*x^9 + 3900000000*x^10 - 225000000*x^11 - 712500000*x^12 - 150000000*x^1 3) + log(x)*(exp(2*x)*(10000000000*x + 20850000000*x^2 + 17150000000*x^3 - 1950000000*x^4 - 10800000000*x^5 - 2100000000*x^6 + 3900000000*x^7 + 9000 00000*x^8 - 1200000000*x^9 - 350000000*x^10 + 150000000*x^11 + 50000000*x^ 12 + 1800000000) - exp(4*x)*(4500000000*x + 19575000000*x^2 + 37050000000* x^3 + 27000000000*x^4 - 10800000000*x^5 - 28350000000*x^6 - 8100000000*x^7 + 10800000000*x^8 + 7500000000*x^9 - 225000000*x^10 - 1350000000*x^11 - 3 00000000*x^12 + 300000000) + exp(6*x)*(300000000*x + 3300000000*x^2 + 1305 0000000*x^3 + 23850000000*x^4 + 16200000000*x^5 - 12600000000*x^6 - 315000 00000*x^7 - 20700000000*x^8 - 900000000*x^9 + 5700000000*x^10 + 2850000000 *x^11 + 450000000*x^12) + exp(8*x)*(3500000000*x^7 - 750000000*x^3 - 29000 00000*x^4 - 5400000000*x^5 - 3850000000*x^6 - 75000000*x^2 + 10500000000*x ^8 + 10600000000*x^9 + 5725000000*x^10 + 1650000000*x^11 + 200000000*x^12) ) + log(x)^3*(exp(8*x)*(2800000000*x^5 - 1900000000*x^2 - 4000000000*x^3 - 3150000000*x^4 - 400000000*x + 9100000000*x^6 + 9600000000*x^7 + 53750...