Integrand size = 253, antiderivative size = 35 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {e}{2 x \left (x+x \left (3+\frac {e^{2 x}}{x^2-\frac {5}{3+x}}\right )\right )^2} \] Output:
1/2*exp(1)/x/(x*(exp(x)^2/(x^2-5/(3+x))+3)+x)^2
Time = 4.58 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.26 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {e \left (-5+3 x^2+x^3\right )^2}{2 x^3 \left (e^{2 x} (3+x)+4 \left (-5+3 x^2+x^3\right )\right )^2} \] Input:
Integrate[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99*x^6 - 35*x^7 - 4*x^8) + E*(1500 - 2700*x^2 - 900*x^3 + 1620*x^4 + 10 80*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6 + 9600*x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128 *x^13 + E^(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 + 2400 *x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]
Output:
(E*(-5 + 3*x^2 + x^3)^2)/(2*x^3*(E^(2*x)*(3 + x) + 4*(-5 + 3*x^2 + x^3))^2 )
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.
| \(\displaystyle \int \frac {e^{2 x+1} \left (-4 x^8-35 x^7-99 x^6-41 x^5+287 x^4+450 x^3-10 x^2-425 x-225\right )+e \left (-12 x^9-108 x^8-324 x^7-144 x^6+1080 x^5+1620 x^4-900 x^3-2700 x^2+1500\right )}{128 x^{13}+1152 x^{12}+3456 x^{11}+1536 x^{10}-11520 x^9-17280 x^8+9600 x^7+28800 x^6-16000 x^4+e^{6 x} \left (2 x^7+18 x^6+54 x^5+54 x^4\right )+e^{4 x} \left (24 x^9+216 x^8+648 x^7+528 x^6-720 x^5-1080 x^4\right )+e^{2 x} \left (96 x^{11}+864 x^{10}+2592 x^9+1632 x^8-5760 x^7-8640 x^6+2400 x^5+7200 x^4\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e \left (-x^3-3 x^2+5\right ) \left (12 \left (x^3+3 x^2-5\right )^2+e^{2 x} \left (4 x^5+23 x^4+30 x^3-29 x^2-85 x-45\right )\right )}{2 x^4 \left (4 \left (x^3+3 x^2-5\right )+e^{2 x} (x+3)\right )^3}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{2} e \int \frac {\left (-x^3-3 x^2+5\right ) \left (12 \left (-x^3-3 x^2+5\right )^2-e^{2 x} \left (-4 x^5-23 x^4-30 x^3+29 x^2+85 x+45\right )\right )}{x^4 \left (e^{2 x} (x+3)-4 \left (-x^3-3 x^2+5\right )\right )^3}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{2} e \int \left (\frac {8 \left (x^3+3 x^2-5\right )^2 \left (2 x^4+10 x^3+6 x^2-28 x-35\right )}{x^3 (x+3) \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}-\frac {4 x^8+35 x^7+99 x^6+41 x^5-287 x^4-450 x^3+10 x^2+425 x+225}{x^4 (x+3) \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle \frac {1}{2} e \left (2640 \int \frac {1}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-\frac {7000}{3} \int \frac {1}{x^3 \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-\frac {9800}{9} \int \frac {1}{x^2 \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx+\frac {96200}{27} \int \frac {1}{x \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-1320 \int \frac {x}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-1752 \int \frac {x^2}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-240 \int \frac {x^3}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx+\frac {1000}{27} \int \frac {1}{(x+3) \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx+49 \int \frac {1}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx-\frac {350}{3} \int \frac {1}{x^3 \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx+\frac {320}{9} \int \frac {1}{x^2 \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx+\frac {3730}{27} \int \frac {1}{x \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx-30 \int \frac {x}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx-23 \int \frac {x^2}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx-4 \int \frac {x^3}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx+\frac {50}{27} \int \frac {1}{(x+3) \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx+16 \int \frac {x^6}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx+128 \int \frac {x^5}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx+288 \int \frac {x^4}{\left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^3}dx-75 \int \frac {1}{x^4 \left (4 x^3+12 x^2+e^{2 x} x+3 e^{2 x}-20\right )^2}dx\right )\) |
Input:
Int[(E^(1 + 2*x)*(-225 - 425*x - 10*x^2 + 450*x^3 + 287*x^4 - 41*x^5 - 99* x^6 - 35*x^7 - 4*x^8) + E*(1500 - 2700*x^2 - 900*x^3 + 1620*x^4 + 1080*x^5 - 144*x^6 - 324*x^7 - 108*x^8 - 12*x^9))/(-16000*x^4 + 28800*x^6 + 9600*x ^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 + E^(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) + E^(4*x)*(-1080*x^4 - 720*x^ 5 + 528*x^6 + 648*x^7 + 216*x^8 + 24*x^9) + E^(2*x)*(7200*x^4 + 2400*x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11)),x]
Output:
$Aborted
Time = 0.89 (sec) , antiderivative size = 59, normalized size of antiderivative = 1.69
| method | result | size |
| risch | \(\frac {{\mathrm e} \left (x^{6}+6 x^{5}+9 x^{4}-10 x^{3}-30 x^{2}+25\right )}{2 x^{3} \left (x \,{\mathrm e}^{2 x}+4 x^{3}+3 \,{\mathrm e}^{2 x}+12 x^{2}-20\right )^{2}}\) | \(59\) |
| parallelrisch | \(\frac {x^{6} {\mathrm e}+6 x^{5} {\mathrm e}+9 x^{4} {\mathrm e}-10 x^{3} {\mathrm e}-30 x^{2} {\mathrm e}+25 \,{\mathrm e}}{2 x^{3} \left (16 x^{6}+8 \,{\mathrm e}^{2 x} x^{4}+{\mathrm e}^{4 x} x^{2}+96 x^{5}+48 \,{\mathrm e}^{2 x} x^{3}+6 x \,{\mathrm e}^{4 x}+144 x^{4}+72 \,{\mathrm e}^{2 x} x^{2}+9 \,{\mathrm e}^{4 x}-160 x^{3}-40 x \,{\mathrm e}^{2 x}-480 x^{2}-120 \,{\mathrm e}^{2 x}+400\right )}\) | \(135\) |
Input:
int(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1) *exp(x)^2+(-12*x^9-108*x^8-324*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700* x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216*x^8+6 48*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632* x^8-5760*x^7-8640*x^6+2400*x^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456* x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x,method= _RETURNVERBOSE)
Output:
1/2*exp(1)*(x^6+6*x^5+9*x^4-10*x^3-30*x^2+25)/x^3/(x*exp(2*x)+4*x^3+3*exp( 2*x)+12*x^2-20)^2
Leaf count of result is larger than twice the leaf count of optimal. 118 vs. \(2 (33) = 66\).
Time = 0.09 (sec) , antiderivative size = 118, normalized size of antiderivative = 3.37 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {{\left (x^{6} + 6 \, x^{5} + 9 \, x^{4} - 10 \, x^{3} - 30 \, x^{2} + 25\right )} e^{3}}{2 \, {\left (16 \, {\left (x^{9} + 6 \, x^{8} + 9 \, x^{7} - 10 \, x^{6} - 30 \, x^{5} + 25 \, x^{3}\right )} e^{2} + {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3}\right )} e^{\left (4 \, x + 2\right )} + 8 \, {\left (x^{7} + 6 \, x^{6} + 9 \, x^{5} - 5 \, x^{4} - 15 \, x^{3}\right )} e^{\left (2 \, x + 2\right )}\right )}} \] Input:
integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)* exp(1)*exp(x)^2+(-12*x^9-108*x^8-324*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3 -2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216 *x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9 +1632*x^8-5760*x^7-8640*x^6+2400*x^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12 +3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x, algorithm="fricas")
Output:
1/2*(x^6 + 6*x^5 + 9*x^4 - 10*x^3 - 30*x^2 + 25)*e^3/(16*(x^9 + 6*x^8 + 9* x^7 - 10*x^6 - 30*x^5 + 25*x^3)*e^2 + (x^5 + 6*x^4 + 9*x^3)*e^(4*x + 2) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x + 2))
Leaf count of result is larger than twice the leaf count of optimal. 126 vs. \(2 (26) = 52\).
Time = 0.35 (sec) , antiderivative size = 126, normalized size of antiderivative = 3.60 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {e x^{6} + 6 e x^{5} + 9 e x^{4} - 10 e x^{3} - 30 e x^{2} + 25 e}{32 x^{9} + 192 x^{8} + 288 x^{7} - 320 x^{6} - 960 x^{5} + 800 x^{3} + \left (2 x^{5} + 12 x^{4} + 18 x^{3}\right ) e^{4 x} + \left (16 x^{7} + 96 x^{6} + 144 x^{5} - 80 x^{4} - 240 x^{3}\right ) e^{2 x}} \] Input:
integrate(((-4*x**8-35*x**7-99*x**6-41*x**5+287*x**4+450*x**3-10*x**2-425* x-225)*exp(1)*exp(x)**2+(-12*x**9-108*x**8-324*x**7-144*x**6+1080*x**5+162 0*x**4-900*x**3-2700*x**2+1500)*exp(1))/((2*x**7+18*x**6+54*x**5+54*x**4)* exp(x)**6+(24*x**9+216*x**8+648*x**7+528*x**6-720*x**5-1080*x**4)*exp(x)** 4+(96*x**11+864*x**10+2592*x**9+1632*x**8-5760*x**7-8640*x**6+2400*x**5+72 00*x**4)*exp(x)**2+128*x**13+1152*x**12+3456*x**11+1536*x**10-11520*x**9-1 7280*x**8+9600*x**7+28800*x**6-16000*x**4),x)
Output:
(E*x**6 + 6*E*x**5 + 9*E*x**4 - 10*E*x**3 - 30*E*x**2 + 25*E)/(32*x**9 + 1 92*x**8 + 288*x**7 - 320*x**6 - 960*x**5 + 800*x**3 + (2*x**5 + 12*x**4 + 18*x**3)*exp(4*x) + (16*x**7 + 96*x**6 + 144*x**5 - 80*x**4 - 240*x**3)*ex p(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 123 vs. \(2 (33) = 66\).
Time = 0.24 (sec) , antiderivative size = 123, normalized size of antiderivative = 3.51 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {x^{6} e + 6 \, x^{5} e + 9 \, x^{4} e - 10 \, x^{3} e - 30 \, x^{2} e + 25 \, e}{2 \, {\left (16 \, x^{9} + 96 \, x^{8} + 144 \, x^{7} - 160 \, x^{6} - 480 \, x^{5} + 400 \, x^{3} + {\left (x^{5} + 6 \, x^{4} + 9 \, x^{3}\right )} e^{\left (4 \, x\right )} + 8 \, {\left (x^{7} + 6 \, x^{6} + 9 \, x^{5} - 5 \, x^{4} - 15 \, x^{3}\right )} e^{\left (2 \, x\right )}\right )}} \] Input:
integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)* exp(1)*exp(x)^2+(-12*x^9-108*x^8-324*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3 -2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216 *x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9 +1632*x^8-5760*x^7-8640*x^6+2400*x^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12 +3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x, algorithm="maxima")
Output:
1/2*(x^6*e + 6*x^5*e + 9*x^4*e - 10*x^3*e - 30*x^2*e + 25*e)/(16*x^9 + 96* x^8 + 144*x^7 - 160*x^6 - 480*x^5 + 400*x^3 + (x^5 + 6*x^4 + 9*x^3)*e^(4*x ) + 8*(x^7 + 6*x^6 + 9*x^5 - 5*x^4 - 15*x^3)*e^(2*x))
Leaf count of result is larger than twice the leaf count of optimal. 364 vs. \(2 (33) = 66\).
Time = 0.23 (sec) , antiderivative size = 364, normalized size of antiderivative = 10.40 \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\frac {{\left (2 \, x + 1\right )}^{6} e^{3} + 6 \, {\left (2 \, x + 1\right )}^{5} e^{3} - 9 \, {\left (2 \, x + 1\right )}^{4} e^{3} - 124 \, {\left (2 \, x + 1\right )}^{3} e^{3} - 129 \, {\left (2 \, x + 1\right )}^{2} e^{3} + 630 \, {\left (2 \, x + 1\right )} e^{3} + 1225 \, e^{3}}{4 \, {\left ({\left (2 \, x + 1\right )}^{9} e^{2} + 3 \, {\left (2 \, x + 1\right )}^{8} e^{2} - 24 \, {\left (2 \, x + 1\right )}^{7} e^{2} + 2 \, {\left (2 \, x + 1\right )}^{7} e^{\left (2 \, x + 2\right )} - 80 \, {\left (2 \, x + 1\right )}^{6} e^{2} + 10 \, {\left (2 \, x + 1\right )}^{6} e^{\left (2 \, x + 2\right )} + 210 \, {\left (2 \, x + 1\right )}^{5} e^{2} + {\left (2 \, x + 1\right )}^{5} e^{\left (4 \, x + 2\right )} - 30 \, {\left (2 \, x + 1\right )}^{5} e^{\left (2 \, x + 2\right )} + 654 \, {\left (2 \, x + 1\right )}^{4} e^{2} + 7 \, {\left (2 \, x + 1\right )}^{4} e^{\left (4 \, x + 2\right )} - 150 \, {\left (2 \, x + 1\right )}^{4} e^{\left (2 \, x + 2\right )} - 928 \, {\left (2 \, x + 1\right )}^{3} e^{2} - 2 \, {\left (2 \, x + 1\right )}^{3} e^{\left (4 \, x + 2\right )} + 150 \, {\left (2 \, x + 1\right )}^{3} e^{\left (2 \, x + 2\right )} - 1656 \, {\left (2 \, x + 1\right )}^{2} e^{2} - 46 \, {\left (2 \, x + 1\right )}^{2} e^{\left (4 \, x + 2\right )} + 558 \, {\left (2 \, x + 1\right )}^{2} e^{\left (2 \, x + 2\right )} + 3045 \, {\left (2 \, x + 1\right )} e^{2} + 65 \, {\left (2 \, x + 1\right )} e^{\left (4 \, x + 2\right )} - 890 \, {\left (2 \, x + 1\right )} e^{\left (2 \, x + 2\right )} - 1225 \, e^{2} - 25 \, e^{\left (4 \, x + 2\right )} + 350 \, e^{\left (2 \, x + 2\right )}\right )}} \] Input:
integrate(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)* exp(1)*exp(x)^2+(-12*x^9-108*x^8-324*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3 -2700*x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216 *x^8+648*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9 +1632*x^8-5760*x^7-8640*x^6+2400*x^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12 +3456*x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x, algorithm="giac")
Output:
1/4*((2*x + 1)^6*e^3 + 6*(2*x + 1)^5*e^3 - 9*(2*x + 1)^4*e^3 - 124*(2*x + 1)^3*e^3 - 129*(2*x + 1)^2*e^3 + 630*(2*x + 1)*e^3 + 1225*e^3)/((2*x + 1)^ 9*e^2 + 3*(2*x + 1)^8*e^2 - 24*(2*x + 1)^7*e^2 + 2*(2*x + 1)^7*e^(2*x + 2) - 80*(2*x + 1)^6*e^2 + 10*(2*x + 1)^6*e^(2*x + 2) + 210*(2*x + 1)^5*e^2 + (2*x + 1)^5*e^(4*x + 2) - 30*(2*x + 1)^5*e^(2*x + 2) + 654*(2*x + 1)^4*e^ 2 + 7*(2*x + 1)^4*e^(4*x + 2) - 150*(2*x + 1)^4*e^(2*x + 2) - 928*(2*x + 1 )^3*e^2 - 2*(2*x + 1)^3*e^(4*x + 2) + 150*(2*x + 1)^3*e^(2*x + 2) - 1656*( 2*x + 1)^2*e^2 - 46*(2*x + 1)^2*e^(4*x + 2) + 558*(2*x + 1)^2*e^(2*x + 2) + 3045*(2*x + 1)*e^2 + 65*(2*x + 1)*e^(4*x + 2) - 890*(2*x + 1)*e^(2*x + 2 ) - 1225*e^2 - 25*e^(4*x + 2) + 350*e^(2*x + 2))
Timed out. \[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\int -\frac {\mathrm {e}\,\left (12\,x^9+108\,x^8+324\,x^7+144\,x^6-1080\,x^5-1620\,x^4+900\,x^3+2700\,x^2-1500\right )+{\mathrm {e}}^{2\,x}\,\mathrm {e}\,\left (4\,x^8+35\,x^7+99\,x^6+41\,x^5-287\,x^4-450\,x^3+10\,x^2+425\,x+225\right )}{{\mathrm {e}}^{4\,x}\,\left (24\,x^9+216\,x^8+648\,x^7+528\,x^6-720\,x^5-1080\,x^4\right )+{\mathrm {e}}^{2\,x}\,\left (96\,x^{11}+864\,x^{10}+2592\,x^9+1632\,x^8-5760\,x^7-8640\,x^6+2400\,x^5+7200\,x^4\right )+{\mathrm {e}}^{6\,x}\,\left (2\,x^7+18\,x^6+54\,x^5+54\,x^4\right )-16000\,x^4+28800\,x^6+9600\,x^7-17280\,x^8-11520\,x^9+1536\,x^{10}+3456\,x^{11}+1152\,x^{12}+128\,x^{13}} \,d x \] Input:
int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 - 72 0*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400 *x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + e xp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9600* x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 ),x)
Output:
int(-(exp(1)*(2700*x^2 + 900*x^3 - 1620*x^4 - 1080*x^5 + 144*x^6 + 324*x^7 + 108*x^8 + 12*x^9 - 1500) + exp(2*x)*exp(1)*(425*x + 10*x^2 - 450*x^3 - 287*x^4 + 41*x^5 + 99*x^6 + 35*x^7 + 4*x^8 + 225))/(exp(4*x)*(528*x^6 - 72 0*x^5 - 1080*x^4 + 648*x^7 + 216*x^8 + 24*x^9) + exp(2*x)*(7200*x^4 + 2400 *x^5 - 8640*x^6 - 5760*x^7 + 1632*x^8 + 2592*x^9 + 864*x^10 + 96*x^11) + e xp(6*x)*(54*x^4 + 54*x^5 + 18*x^6 + 2*x^7) - 16000*x^4 + 28800*x^6 + 9600* x^7 - 17280*x^8 - 11520*x^9 + 1536*x^10 + 3456*x^11 + 1152*x^12 + 128*x^13 ), x)
\[ \int \frac {e^{1+2 x} \left (-225-425 x-10 x^2+450 x^3+287 x^4-41 x^5-99 x^6-35 x^7-4 x^8\right )+e \left (1500-2700 x^2-900 x^3+1620 x^4+1080 x^5-144 x^6-324 x^7-108 x^8-12 x^9\right )}{-16000 x^4+28800 x^6+9600 x^7-17280 x^8-11520 x^9+1536 x^{10}+3456 x^{11}+1152 x^{12}+128 x^{13}+e^{6 x} \left (54 x^4+54 x^5+18 x^6+2 x^7\right )+e^{4 x} \left (-1080 x^4-720 x^5+528 x^6+648 x^7+216 x^8+24 x^9\right )+e^{2 x} \left (7200 x^4+2400 x^5-8640 x^6-5760 x^7+1632 x^8+2592 x^9+864 x^{10}+96 x^{11}\right )} \, dx=\text {too large to display} \] Input:
int(((-4*x^8-35*x^7-99*x^6-41*x^5+287*x^4+450*x^3-10*x^2-425*x-225)*exp(1) *exp(x)^2+(-12*x^9-108*x^8-324*x^7-144*x^6+1080*x^5+1620*x^4-900*x^3-2700* x^2+1500)*exp(1))/((2*x^7+18*x^6+54*x^5+54*x^4)*exp(x)^6+(24*x^9+216*x^8+6 48*x^7+528*x^6-720*x^5-1080*x^4)*exp(x)^4+(96*x^11+864*x^10+2592*x^9+1632* x^8-5760*x^7-8640*x^6+2400*x^5+7200*x^4)*exp(x)^2+128*x^13+1152*x^12+3456* x^11+1536*x^10-11520*x^9-17280*x^8+9600*x^7+28800*x^6-16000*x^4),x)
Output:
(e*( - 225*int(e**(2*x)/(e**(6*x)*x**7 + 9*e**(6*x)*x**6 + 27*e**(6*x)*x** 5 + 27*e**(6*x)*x**4 + 12*e**(4*x)*x**9 + 108*e**(4*x)*x**8 + 324*e**(4*x) *x**7 + 264*e**(4*x)*x**6 - 360*e**(4*x)*x**5 - 540*e**(4*x)*x**4 + 48*e** (2*x)*x**11 + 432*e**(2*x)*x**10 + 1296*e**(2*x)*x**9 + 816*e**(2*x)*x**8 - 2880*e**(2*x)*x**7 - 4320*e**(2*x)*x**6 + 1200*e**(2*x)*x**5 + 3600*e**( 2*x)*x**4 + 64*x**13 + 576*x**12 + 1728*x**11 + 768*x**10 - 5760*x**9 - 86 40*x**8 + 4800*x**7 + 14400*x**6 - 8000*x**4),x) - 425*int(e**(2*x)/(e**(6 *x)*x**6 + 9*e**(6*x)*x**5 + 27*e**(6*x)*x**4 + 27*e**(6*x)*x**3 + 12*e**( 4*x)*x**8 + 108*e**(4*x)*x**7 + 324*e**(4*x)*x**6 + 264*e**(4*x)*x**5 - 36 0*e**(4*x)*x**4 - 540*e**(4*x)*x**3 + 48*e**(2*x)*x**10 + 432*e**(2*x)*x** 9 + 1296*e**(2*x)*x**8 + 816*e**(2*x)*x**7 - 2880*e**(2*x)*x**6 - 4320*e** (2*x)*x**5 + 1200*e**(2*x)*x**4 + 3600*e**(2*x)*x**3 + 64*x**12 + 576*x**1 1 + 1728*x**10 + 768*x**9 - 5760*x**8 - 8640*x**7 + 4800*x**6 + 14400*x**5 - 8000*x**3),x) - 10*int(e**(2*x)/(e**(6*x)*x**5 + 9*e**(6*x)*x**4 + 27*e **(6*x)*x**3 + 27*e**(6*x)*x**2 + 12*e**(4*x)*x**7 + 108*e**(4*x)*x**6 + 3 24*e**(4*x)*x**5 + 264*e**(4*x)*x**4 - 360*e**(4*x)*x**3 - 540*e**(4*x)*x* *2 + 48*e**(2*x)*x**9 + 432*e**(2*x)*x**8 + 1296*e**(2*x)*x**7 + 816*e**(2 *x)*x**6 - 2880*e**(2*x)*x**5 - 4320*e**(2*x)*x**4 + 1200*e**(2*x)*x**3 + 3600*e**(2*x)*x**2 + 64*x**11 + 576*x**10 + 1728*x**9 + 768*x**8 - 5760*x* *7 - 8640*x**6 + 4800*x**5 + 14400*x**4 - 8000*x**2),x) + 450*int(e**(2...