Integrand size = 407, antiderivative size = 32 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=\left (-e^3+\frac {(5-\log (-2+x))^4}{e^5}+\log \left (-\frac {1}{x}+x^2\right )\right )^2 \]
Leaf count is larger than twice the leaf count of optimal. \(182\) vs. \(2(32)=64\).
Time = 0.23 (sec) , antiderivative size = 182, normalized size of antiderivative = 5.69 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=-\frac {2 \left (-500 \left (-625+e^8\right ) \log (2-x)+50 \left (-4375+3 e^8\right ) \log ^2(-2+x)-20 \left (-4375+e^8\right ) \log ^3(-2+x)+\left (-21875+e^8\right ) \log ^4(-2+x)+3500 \log ^5(-2+x)-350 \log ^6(-2+x)+20 \log ^7(-2+x)-\frac {1}{2} \log ^8(-2+x)-e^5 \left (-625+e^8\right ) \log (x)+e^5 \left (-625+e^8\right ) \log \left (1-x^3\right )-e^5 \log (-2+x) \left (-500+150 \log (-2+x)-20 \log ^2(-2+x)+\log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )-\frac {1}{2} e^{10} \log ^2\left (\frac {-1+x^3}{x}\right )\right )}{e^{10}} \]
Integrate[(625000*x - 625000*x^4 + E^13*(4 - 2*x + 8*x^3 - 4*x^4) + E^5*(- 2500 + 1250*x - 5000*x^3 + 2500*x^4 + E^3*(-1000*x + 1000*x^4)) + (-875000 *x + 875000*x^4 + E^5*(2000 - 1000*x + 4000*x^3 - 2000*x^4 + E^3*(600*x - 600*x^4)))*Log[-2 + x] + (525000*x - 525000*x^4 + E^5*(-600 + 300*x - 1200 *x^3 + 600*x^4 + E^3*(-120*x + 120*x^4)))*Log[-2 + x]^2 + (-175000*x + 175 000*x^4 + E^5*(80 - 40*x + 160*x^3 - 80*x^4 + E^3*(8*x - 8*x^4)))*Log[-2 + x]^3 + (35000*x - 35000*x^4 + E^5*(-4 + 2*x - 8*x^3 + 4*x^4))*Log[-2 + x] ^4 + (-4200*x + 4200*x^4)*Log[-2 + x]^5 + (280*x - 280*x^4)*Log[-2 + x]^6 + (-8*x + 8*x^4)*Log[-2 + x]^7 + (E^5*(1000*x - 1000*x^4) + E^10*(-4 + 2*x - 8*x^3 + 4*x^4) + E^5*(-600*x + 600*x^4)*Log[-2 + x] + E^5*(120*x - 120* x^4)*Log[-2 + x]^2 + E^5*(-8*x + 8*x^4)*Log[-2 + x]^3)*Log[(-1 + x^3)/x])/ (E^10*(2*x - x^2 - 2*x^4 + x^5)),x]
(-2*(-500*(-625 + E^8)*Log[2 - x] + 50*(-4375 + 3*E^8)*Log[-2 + x]^2 - 20* (-4375 + E^8)*Log[-2 + x]^3 + (-21875 + E^8)*Log[-2 + x]^4 + 3500*Log[-2 + x]^5 - 350*Log[-2 + x]^6 + 20*Log[-2 + x]^7 - Log[-2 + x]^8/2 - E^5*(-625 + E^8)*Log[x] + E^5*(-625 + E^8)*Log[1 - x^3] - E^5*Log[-2 + x]*(-500 + 1 50*Log[-2 + x] - 20*Log[-2 + x]^2 + Log[-2 + x]^3)*Log[(-1 + x^3)/x] - (E^ 10*Log[(-1 + x^3)/x]^2)/2))/E^10
Time = 12.23 (sec) , antiderivative size = 58, normalized size of antiderivative = 1.81, number of steps used = 6, number of rules used = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {27, 27, 2026, 2463, 7239, 7237}
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.
| \(\displaystyle \int \frac {-625000 x^4+\left (8 x^4-8 x\right ) \log ^7(x-2)+\left (280 x-280 x^4\right ) \log ^6(x-2)+\left (4200 x^4-4200 x\right ) \log ^5(x-2)+e^{13} \left (-4 x^4+8 x^3-2 x+4\right )+e^5 \left (2500 x^4+e^3 \left (1000 x^4-1000 x\right )-5000 x^3+1250 x-2500\right )+\left (-35000 x^4+e^5 \left (4 x^4-8 x^3+2 x-4\right )+35000 x\right ) \log ^4(x-2)+\left (175000 x^4+e^5 \left (-80 x^4+e^3 \left (8 x-8 x^4\right )+160 x^3-40 x+80\right )-175000 x\right ) \log ^3(x-2)+\left (-525000 x^4+e^5 \left (600 x^4+e^3 \left (120 x^4-120 x\right )-1200 x^3+300 x-600\right )+525000 x\right ) \log ^2(x-2)+\left (e^5 \left (1000 x-1000 x^4\right )+e^5 \left (8 x^4-8 x\right ) \log ^3(x-2)+e^5 \left (120 x-120 x^4\right ) \log ^2(x-2)+e^5 \left (600 x^4-600 x\right ) \log (x-2)+e^{10} \left (4 x^4-8 x^3+2 x-4\right )\right ) \log \left (\frac {x^3-1}{x}\right )+\left (875000 x^4+e^5 \left (-2000 x^4+e^3 \left (600 x-600 x^4\right )+4000 x^3-1000 x+2000\right )-875000 x\right ) \log (x-2)+625000 x}{e^{10} \left (x^5-2 x^4-x^2+2 x\right )} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {\int \frac {2 \left (-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )\right )}{x^5-2 x^4-x^2+2 x}dx}{e^{10}}\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {2 \int \frac {-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )}{x^5-2 x^4-x^2+2 x}dx}{e^{10}}\) |
| \(\Big \downarrow \) 2026 |
| \(\displaystyle \frac {2 \int \frac {-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )}{x \left (x^4-2 x^3-x+2\right )}dx}{e^{10}}\) |
| \(\Big \downarrow \) 2463 |
| \(\displaystyle \frac {2 \int \left (\frac {-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )}{7 (x-2) x}-\frac {-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )}{3 (x-1) x}+\frac {(4 x+5) \left (-4 \left (x-x^4\right ) \log ^7(x-2)+140 \left (x-x^4\right ) \log ^6(x-2)-2100 \left (x-x^4\right ) \log ^5(x-2)+\left (-17500 x^4+17500 x-e^5 \left (-2 x^4+4 x^3-x+2\right )\right ) \log ^4(x-2)-4 \left (-21875 x^4+21875 x-e^5 \left (-10 x^4+20 x^3-5 x+e^3 \left (x-x^4\right )+10\right )\right ) \log ^3(x-2)+30 \left (-8750 x^4+8750 x-e^5 \left (-10 x^4+20 x^3-5 x+2 e^3 \left (x-x^4\right )+10\right )\right ) \log ^2(x-2)-100 \left (-4375 x^4+4375 x-e^5 \left (-10 x^4+20 x^3-5 x+3 e^3 \left (x-x^4\right )+10\right )\right ) \log (x-2)-312500 x^4+312500 x+e^{13} \left (-2 x^4+4 x^3-x+2\right )-125 e^5 \left (-10 x^4+20 x^3-5 x+4 e^3 \left (x-x^4\right )+10\right )-\left (4 e^5 \left (x-x^4\right ) \log ^3(x-2)-60 e^5 \left (x-x^4\right ) \log ^2(x-2)+300 e^5 \left (x-x^4\right ) \log (x-2)+e^{10} \left (-2 x^4+4 x^3-x+2\right )-500 e^5 \left (x-x^4\right )\right ) \log \left (-\frac {1-x^3}{x}\right )\right )}{21 x \left (x^2+x+1\right )}\right )dx}{e^{10}}\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \frac {2 \int \frac {\left (-4 x \left (x^3-1\right ) \log ^3(x-2)+60 x \left (x^3-1\right ) \log ^2(x-2)-300 x \left (x^3-1\right ) \log (x-2)+500 x \left (x^3-1\right )-e^5 \left (2 x^4-4 x^3+x-2\right )\right ) \left (-\log ^4(x-2)+20 \log ^3(x-2)-150 \log ^2(x-2)+500 \log (x-2)-e^5 \log \left (\frac {x^3-1}{x}\right )-625 \left (1-\frac {e^8}{625}\right )\right )}{(1-x) (2-x) x \left (x^2+x+1\right )}dx}{e^{10}}\) |
| \(\Big \downarrow \) 7237 |
| \(\displaystyle \frac {\left (e^5 \log \left (-\frac {1-x^3}{x}\right )+\log ^4(x-2)-20 \log ^3(x-2)+150 \log ^2(x-2)-500 \log (x-2)-e^8+625\right )^2}{e^{10}}\) |
Int[(625000*x - 625000*x^4 + E^13*(4 - 2*x + 8*x^3 - 4*x^4) + E^5*(-2500 + 1250*x - 5000*x^3 + 2500*x^4 + E^3*(-1000*x + 1000*x^4)) + (-875000*x + 8 75000*x^4 + E^5*(2000 - 1000*x + 4000*x^3 - 2000*x^4 + E^3*(600*x - 600*x^ 4)))*Log[-2 + x] + (525000*x - 525000*x^4 + E^5*(-600 + 300*x - 1200*x^3 + 600*x^4 + E^3*(-120*x + 120*x^4)))*Log[-2 + x]^2 + (-175000*x + 175000*x^ 4 + E^5*(80 - 40*x + 160*x^3 - 80*x^4 + E^3*(8*x - 8*x^4)))*Log[-2 + x]^3 + (35000*x - 35000*x^4 + E^5*(-4 + 2*x - 8*x^3 + 4*x^4))*Log[-2 + x]^4 + ( -4200*x + 4200*x^4)*Log[-2 + x]^5 + (280*x - 280*x^4)*Log[-2 + x]^6 + (-8* x + 8*x^4)*Log[-2 + x]^7 + (E^5*(1000*x - 1000*x^4) + E^10*(-4 + 2*x - 8*x ^3 + 4*x^4) + E^5*(-600*x + 600*x^4)*Log[-2 + x] + E^5*(120*x - 120*x^4)*L og[-2 + x]^2 + E^5*(-8*x + 8*x^4)*Log[-2 + x]^3)*Log[(-1 + x^3)/x])/(E^10* (2*x - x^2 - 2*x^4 + x^5)),x]
(625 - E^8 - 500*Log[-2 + x] + 150*Log[-2 + x]^2 - 20*Log[-2 + x]^3 + Log[ -2 + x]^4 + E^5*Log[-((1 - x^3)/x)])^2/E^10
3.26.24.3.1 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[(Fx_.)*(Px_)^(p_.), x_Symbol] :> With[{r = Expon[Px, x, Min]}, Int[x^(p *r)*ExpandToSum[Px/x^r, x]^p*Fx, x] /; IGtQ[r, 0]] /; PolyQ[Px, x] && Integ erQ[p] && !MonomialQ[Px, x] && (ILtQ[p, 0] || !PolyQ[u, x])
Int[(u_.)*(Px_)^(p_), x_Symbol] :> With[{Qx = Factor[Px]}, Int[ExpandIntegr and[u, Qx^p, x], x] /; !SumQ[NonfreeFactors[Qx, x]]] /; PolyQ[Px, x] && Gt Q[Expon[Px, x], 2] && !BinomialQ[Px, x] && !TrinomialQ[Px, x] && ILtQ[p, 0]
Int[(u_)*(y_)^(m_.), x_Symbol] :> With[{q = DerivativeDivides[y, u, x]}, Si mp[q*(y^(m + 1)/(m + 1)), x] /; !FalseQ[q]] /; FreeQ[m, x] && NeQ[m, -1]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 36.63 (sec) , antiderivative size = 218135, normalized size of antiderivative = 6816.72
int((((8*x^4-8*x)*exp(5)*ln(-2+x)^3+(-120*x^4+120*x)*exp(5)*ln(-2+x)^2+(60 0*x^4-600*x)*exp(5)*ln(-2+x)+(4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000*x^4+1000* x)*exp(5))*ln((x^3-1)/x)+(8*x^4-8*x)*ln(-2+x)^7+(-280*x^4+280*x)*ln(-2+x)^ 6+(4200*x^4-4200*x)*ln(-2+x)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35000*x^4+35000 *x)*ln(-2+x)^4+(((-8*x^4+8*x)*exp(3)-80*x^4+160*x^3-40*x+80)*exp(5)+175000 *x^4-175000*x)*ln(-2+x)^3+(((120*x^4-120*x)*exp(3)+600*x^4-1200*x^3+300*x- 600)*exp(5)-525000*x^4+525000*x)*ln(-2+x)^2+(((-600*x^4+600*x)*exp(3)-2000 *x^4+4000*x^3-1000*x+2000)*exp(5)+875000*x^4-875000*x)*ln(-2+x)+(-4*x^4+8* x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500*x^4-5000*x^3+125 0*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x)/exp(5)^2,x,metho d=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 155 vs. \(2 (28) = 56\).
Time = 0.26 (sec) , antiderivative size = 155, normalized size of antiderivative = 4.84 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx={\left (\log \left (x - 2\right )^{8} - 40 \, \log \left (x - 2\right )^{7} + 700 \, \log \left (x - 2\right )^{6} - 2 \, {\left (e^{8} - 21875\right )} \log \left (x - 2\right )^{4} - 7000 \, \log \left (x - 2\right )^{5} + 40 \, {\left (e^{8} - 4375\right )} \log \left (x - 2\right )^{3} - 100 \, {\left (3 \, e^{8} - 4375\right )} \log \left (x - 2\right )^{2} + e^{10} \log \left (\frac {x^{3} - 1}{x}\right )^{2} + 1000 \, {\left (e^{8} - 625\right )} \log \left (x - 2\right ) + 2 \, {\left (e^{5} \log \left (x - 2\right )^{4} - 20 \, e^{5} \log \left (x - 2\right )^{3} + 150 \, e^{5} \log \left (x - 2\right )^{2} - 500 \, e^{5} \log \left (x - 2\right ) - e^{13} + 625 \, e^{5}\right )} \log \left (\frac {x^{3} - 1}{x}\right )\right )} e^{\left (-10\right )} \]
integrate((((8*x^4-8*x)*exp(5)*log(-2+x)^3+(-120*x^4+120*x)*exp(5)*log(-2+ x)^2+(600*x^4-600*x)*exp(5)*log(-2+x)+(4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000* x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(-2+x)^7+(-280*x^4+280*x )*log(-2+x)^6+(4200*x^4-4200*x)*log(-2+x)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35 000*x^4+35000*x)*log(-2+x)^4+(((-8*x^4+8*x)*exp(3)-80*x^4+160*x^3-40*x+80) *exp(5)+175000*x^4-175000*x)*log(-2+x)^3+(((120*x^4-120*x)*exp(3)+600*x^4- 1200*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(-2+x)^2+(((-600*x^4+60 0*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000)*exp(5)+875000*x^4-875000*x)*log (-2+x)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500 *x^4-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x) /exp(5)^2,x, algorithm=\
(log(x - 2)^8 - 40*log(x - 2)^7 + 700*log(x - 2)^6 - 2*(e^8 - 21875)*log(x - 2)^4 - 7000*log(x - 2)^5 + 40*(e^8 - 4375)*log(x - 2)^3 - 100*(3*e^8 - 4375)*log(x - 2)^2 + e^10*log((x^3 - 1)/x)^2 + 1000*(e^8 - 625)*log(x - 2) + 2*(e^5*log(x - 2)^4 - 20*e^5*log(x - 2)^3 + 150*e^5*log(x - 2)^2 - 500* e^5*log(x - 2) - e^13 + 625*e^5)*log((x^3 - 1)/x))*e^(-10)
Leaf count of result is larger than twice the leaf count of optimal. 272 vs. \(2 (24) = 48\).
Time = 13.84 (sec) , antiderivative size = 272, normalized size of antiderivative = 8.50 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=\frac {\left (2 \log {\left (x - 2 \right )}^{4} - 40 \log {\left (x - 2 \right )}^{3} + 300 \log {\left (x - 2 \right )}^{2} - 1000 \log {\left (x - 2 \right )}\right ) \log {\left (\frac {x^{3} - 1}{x} \right )}}{e^{5}} + \log {\left (\frac {x^{3} - 1}{x} \right )}^{2} + \frac {\log {\left (x - 2 \right )}^{8}}{e^{10}} - \frac {40 \log {\left (x - 2 \right )}^{7}}{e^{10}} + \frac {700 \log {\left (x - 2 \right )}^{6}}{e^{10}} - \frac {7000 \log {\left (x - 2 \right )}^{5}}{e^{10}} + \frac {\left (43750 - 2 e^{8}\right ) \log {\left (x - 2 \right )}^{4}}{e^{10}} + \frac {\left (-175000 + 40 e^{8}\right ) \log {\left (x - 2 \right )}^{3}}{e^{10}} + \frac {\left (437500 - 300 e^{8}\right ) \log {\left (x - 2 \right )}^{2}}{e^{10}} + \frac {\left (-1250 + 2 e^{8}\right ) \log {\left (x + \frac {- 2 e^{13} + 1250 e^{5} + \left (-1250 + 2 e^{8}\right ) e^{5}}{- 500 e^{8} - 625 e^{5} + 312500 + e^{13}} \right )}}{e^{5}} + \frac {\left (-625000 + 1000 e^{8}\right ) \log {\left (x + \frac {- 2 e^{13} - 625000 + 1250 e^{5} + 1000 e^{8}}{- 500 e^{8} - 625 e^{5} + 312500 + e^{13}} \right )}}{e^{10}} - \frac {2 \left (-5 + e^{2}\right ) \left (5 + e^{2}\right ) \left (25 + e^{4}\right ) \log {\left (x^{3} - 1 \right )}}{e^{5}} \]
integrate((((8*x**4-8*x)*exp(5)*ln(-2+x)**3+(-120*x**4+120*x)*exp(5)*ln(-2 +x)**2+(600*x**4-600*x)*exp(5)*ln(-2+x)+(4*x**4-8*x**3+2*x-4)*exp(5)**2+(- 1000*x**4+1000*x)*exp(5))*ln((x**3-1)/x)+(8*x**4-8*x)*ln(-2+x)**7+(-280*x* *4+280*x)*ln(-2+x)**6+(4200*x**4-4200*x)*ln(-2+x)**5+((4*x**4-8*x**3+2*x-4 )*exp(5)-35000*x**4+35000*x)*ln(-2+x)**4+(((-8*x**4+8*x)*exp(3)-80*x**4+16 0*x**3-40*x+80)*exp(5)+175000*x**4-175000*x)*ln(-2+x)**3+(((120*x**4-120*x )*exp(3)+600*x**4-1200*x**3+300*x-600)*exp(5)-525000*x**4+525000*x)*ln(-2+ x)**2+(((-600*x**4+600*x)*exp(3)-2000*x**4+4000*x**3-1000*x+2000)*exp(5)+8 75000*x**4-875000*x)*ln(-2+x)+(-4*x**4+8*x**3-2*x+4)*exp(3)*exp(5)**2+((10 00*x**4-1000*x)*exp(3)+2500*x**4-5000*x**3+1250*x-2500)*exp(5)-625000*x**4 +625000*x)/(x**5-2*x**4-x**2+2*x)/exp(5)**2,x)
(2*log(x - 2)**4 - 40*log(x - 2)**3 + 300*log(x - 2)**2 - 1000*log(x - 2)) *exp(-5)*log((x**3 - 1)/x) + log((x**3 - 1)/x)**2 + exp(-10)*log(x - 2)**8 - 40*exp(-10)*log(x - 2)**7 + 700*exp(-10)*log(x - 2)**6 - 7000*exp(-10)* log(x - 2)**5 + (43750 - 2*exp(8))*exp(-10)*log(x - 2)**4 + (-175000 + 40* exp(8))*exp(-10)*log(x - 2)**3 + (437500 - 300*exp(8))*exp(-10)*log(x - 2) **2 + (-1250 + 2*exp(8))*exp(-5)*log(x + (-2*exp(13) + 1250*exp(5) + (-125 0 + 2*exp(8))*exp(5))/(-500*exp(8) - 625*exp(5) + 312500 + exp(13))) + (-6 25000 + 1000*exp(8))*exp(-10)*log(x + (-2*exp(13) - 625000 + 1250*exp(5) + 1000*exp(8))/(-500*exp(8) - 625*exp(5) + 312500 + exp(13))) - 2*(-5 + exp (2))*(5 + exp(2))*(25 + exp(4))*exp(-5)*log(x**3 - 1)
Leaf count of result is larger than twice the leaf count of optimal. 392 vs. \(2 (28) = 56\).
Time = 0.61 (sec) , antiderivative size = 392, normalized size of antiderivative = 12.25 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=\frac {1}{21} \, {\left (21 \, \log \left (x - 2\right )^{8} - 840 \, \log \left (x - 2\right )^{7} + 14700 \, \log \left (x - 2\right )^{6} - 42 \, {\left (e^{5} \log \left (x\right ) + e^{8} - 21875\right )} \log \left (x - 2\right )^{4} - 147000 \, \log \left (x - 2\right )^{5} + 840 \, {\left (e^{5} \log \left (x\right ) + e^{8} - 4375\right )} \log \left (x - 2\right )^{3} + 21 \, e^{10} \log \left (x^{2} + x + 1\right )^{2} + 21 \, e^{10} \log \left (x - 1\right )^{2} - 2100 \, {\left (3 \, e^{5} \log \left (x\right ) + 3 \, e^{8} - 4375\right )} \log \left (x - 2\right )^{2} + 21 \, e^{10} \log \left (x\right )^{2} - 4 \, \sqrt {3} {\left (e^{13} - 625 \, e^{5}\right )} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) + 2 \, {\left (2 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) - 5 \, \log \left (x^{2} + x + 1\right ) - 14 \, \log \left (x - 1\right ) + 3 \, \log \left (x - 2\right ) + 21 \, \log \left (x\right )\right )} e^{13} - 1250 \, {\left (2 \, \sqrt {3} \arctan \left (\frac {1}{3} \, \sqrt {3} {\left (2 \, x + 1\right )}\right ) - 5 \, \log \left (x^{2} + x + 1\right ) - 14 \, \log \left (x - 1\right ) + 3 \, \log \left (x - 2\right ) + 21 \, \log \left (x\right )\right )} e^{5} + 2 \, {\left (21 \, e^{5} \log \left (x - 2\right )^{4} - 420 \, e^{5} \log \left (x - 2\right )^{3} + 3150 \, e^{5} \log \left (x - 2\right )^{2} + 21 \, e^{10} \log \left (x - 1\right ) - 10500 \, e^{5} \log \left (x - 2\right ) - 21 \, e^{10} \log \left (x\right ) - 16 \, e^{13} + 10000 \, e^{5}\right )} \log \left (x^{2} + x + 1\right ) + 14 \, {\left (3 \, e^{5} \log \left (x - 2\right )^{4} - 60 \, e^{5} \log \left (x - 2\right )^{3} + 450 \, e^{5} \log \left (x - 2\right )^{2} - 1500 \, e^{5} \log \left (x - 2\right ) - 3 \, e^{10} \log \left (x\right ) - e^{13} + 625 \, e^{5}\right )} \log \left (x - 1\right ) + 6 \, {\left (3500 \, e^{5} \log \left (x\right ) - e^{13} + 3500 \, e^{8} + 625 \, e^{5} - 2187500\right )} \log \left (x - 2\right )\right )} e^{\left (-10\right )} \]
integrate((((8*x^4-8*x)*exp(5)*log(-2+x)^3+(-120*x^4+120*x)*exp(5)*log(-2+ x)^2+(600*x^4-600*x)*exp(5)*log(-2+x)+(4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000* x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(-2+x)^7+(-280*x^4+280*x )*log(-2+x)^6+(4200*x^4-4200*x)*log(-2+x)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35 000*x^4+35000*x)*log(-2+x)^4+(((-8*x^4+8*x)*exp(3)-80*x^4+160*x^3-40*x+80) *exp(5)+175000*x^4-175000*x)*log(-2+x)^3+(((120*x^4-120*x)*exp(3)+600*x^4- 1200*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(-2+x)^2+(((-600*x^4+60 0*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000)*exp(5)+875000*x^4-875000*x)*log (-2+x)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500 *x^4-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x) /exp(5)^2,x, algorithm=\
1/21*(21*log(x - 2)^8 - 840*log(x - 2)^7 + 14700*log(x - 2)^6 - 42*(e^5*lo g(x) + e^8 - 21875)*log(x - 2)^4 - 147000*log(x - 2)^5 + 840*(e^5*log(x) + e^8 - 4375)*log(x - 2)^3 + 21*e^10*log(x^2 + x + 1)^2 + 21*e^10*log(x - 1 )^2 - 2100*(3*e^5*log(x) + 3*e^8 - 4375)*log(x - 2)^2 + 21*e^10*log(x)^2 - 4*sqrt(3)*(e^13 - 625*e^5)*arctan(1/3*sqrt(3)*(2*x + 1)) + 2*(2*sqrt(3)*a rctan(1/3*sqrt(3)*(2*x + 1)) - 5*log(x^2 + x + 1) - 14*log(x - 1) + 3*log( x - 2) + 21*log(x))*e^13 - 1250*(2*sqrt(3)*arctan(1/3*sqrt(3)*(2*x + 1)) - 5*log(x^2 + x + 1) - 14*log(x - 1) + 3*log(x - 2) + 21*log(x))*e^5 + 2*(2 1*e^5*log(x - 2)^4 - 420*e^5*log(x - 2)^3 + 3150*e^5*log(x - 2)^2 + 21*e^1 0*log(x - 1) - 10500*e^5*log(x - 2) - 21*e^10*log(x) - 16*e^13 + 10000*e^5 )*log(x^2 + x + 1) + 14*(3*e^5*log(x - 2)^4 - 60*e^5*log(x - 2)^3 + 450*e^ 5*log(x - 2)^2 - 1500*e^5*log(x - 2) - 3*e^10*log(x) - e^13 + 625*e^5)*log (x - 1) + 6*(3500*e^5*log(x) - e^13 + 3500*e^8 + 625*e^5 - 2187500)*log(x - 2))*e^(-10)
Timed out. \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=\text {Timed out} \]
integrate((((8*x^4-8*x)*exp(5)*log(-2+x)^3+(-120*x^4+120*x)*exp(5)*log(-2+ x)^2+(600*x^4-600*x)*exp(5)*log(-2+x)+(4*x^4-8*x^3+2*x-4)*exp(5)^2+(-1000* x^4+1000*x)*exp(5))*log((x^3-1)/x)+(8*x^4-8*x)*log(-2+x)^7+(-280*x^4+280*x )*log(-2+x)^6+(4200*x^4-4200*x)*log(-2+x)^5+((4*x^4-8*x^3+2*x-4)*exp(5)-35 000*x^4+35000*x)*log(-2+x)^4+(((-8*x^4+8*x)*exp(3)-80*x^4+160*x^3-40*x+80) *exp(5)+175000*x^4-175000*x)*log(-2+x)^3+(((120*x^4-120*x)*exp(3)+600*x^4- 1200*x^3+300*x-600)*exp(5)-525000*x^4+525000*x)*log(-2+x)^2+(((-600*x^4+60 0*x)*exp(3)-2000*x^4+4000*x^3-1000*x+2000)*exp(5)+875000*x^4-875000*x)*log (-2+x)+(-4*x^4+8*x^3-2*x+4)*exp(3)*exp(5)^2+((1000*x^4-1000*x)*exp(3)+2500 *x^4-5000*x^3+1250*x-2500)*exp(5)-625000*x^4+625000*x)/(x^5-2*x^4-x^2+2*x) /exp(5)^2,x, algorithm=\
Time = 11.61 (sec) , antiderivative size = 238, normalized size of antiderivative = 7.44 \[ \int \frac {625000 x-625000 x^4+e^{13} \left (4-2 x+8 x^3-4 x^4\right )+e^5 \left (-2500+1250 x-5000 x^3+2500 x^4+e^3 \left (-1000 x+1000 x^4\right )\right )+\left (-875000 x+875000 x^4+e^5 \left (2000-1000 x+4000 x^3-2000 x^4+e^3 \left (600 x-600 x^4\right )\right )\right ) \log (-2+x)+\left (525000 x-525000 x^4+e^5 \left (-600+300 x-1200 x^3+600 x^4+e^3 \left (-120 x+120 x^4\right )\right )\right ) \log ^2(-2+x)+\left (-175000 x+175000 x^4+e^5 \left (80-40 x+160 x^3-80 x^4+e^3 \left (8 x-8 x^4\right )\right )\right ) \log ^3(-2+x)+\left (35000 x-35000 x^4+e^5 \left (-4+2 x-8 x^3+4 x^4\right )\right ) \log ^4(-2+x)+\left (-4200 x+4200 x^4\right ) \log ^5(-2+x)+\left (280 x-280 x^4\right ) \log ^6(-2+x)+\left (-8 x+8 x^4\right ) \log ^7(-2+x)+\left (e^5 \left (1000 x-1000 x^4\right )+e^{10} \left (-4+2 x-8 x^3+4 x^4\right )+e^5 \left (-600 x+600 x^4\right ) \log (-2+x)+e^5 \left (120 x-120 x^4\right ) \log ^2(-2+x)+e^5 \left (-8 x+8 x^4\right ) \log ^3(-2+x)\right ) \log \left (\frac {-1+x^3}{x}\right )}{e^{10} \left (2 x-x^2-2 x^4+x^5\right )} \, dx=1000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-2}-625000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-10}+{\ln \left (\frac {x^3-1}{x}\right )}^2-300\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-2}-2\,{\mathrm {e}}^3\,\ln \left (x^3-1\right )+40\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-2}-2\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-2}+1250\,{\mathrm {e}}^{-5}\,\ln \left (x^3-1\right )+437500\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-10}-175000\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-10}+43750\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-10}-7000\,{\ln \left (x-2\right )}^5\,{\mathrm {e}}^{-10}+700\,{\ln \left (x-2\right )}^6\,{\mathrm {e}}^{-10}-40\,{\ln \left (x-2\right )}^7\,{\mathrm {e}}^{-10}+{\ln \left (x-2\right )}^8\,{\mathrm {e}}^{-10}+2\,{\mathrm {e}}^3\,\ln \left (x\right )-1250\,{\mathrm {e}}^{-5}\,\ln \left (x\right )+300\,{\ln \left (x-2\right )}^2\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )-40\,{\ln \left (x-2\right )}^3\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )+2\,{\ln \left (x-2\right )}^4\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right )-1000\,\ln \left (x-2\right )\,{\mathrm {e}}^{-5}\,\ln \left (\frac {x^3-1}{x}\right ) \]
int((exp(-10)*(625000*x + log(x - 2)^3*(exp(5)*(exp(3)*(8*x - 8*x^4) - 40* x + 160*x^3 - 80*x^4 + 80) - 175000*x + 175000*x^4) - log(x - 2)^2*(exp(5) *(exp(3)*(120*x - 120*x^4) - 300*x + 1200*x^3 - 600*x^4 + 600) - 525000*x + 525000*x^4) + log((x^3 - 1)/x)*(exp(5)*(1000*x - 1000*x^4) + exp(10)*(2* x - 8*x^3 + 4*x^4 - 4) - log(x - 2)*exp(5)*(600*x - 600*x^4) - log(x - 2)^ 3*exp(5)*(8*x - 8*x^4) + log(x - 2)^2*exp(5)*(120*x - 120*x^4)) - exp(13)* (2*x - 8*x^3 + 4*x^4 - 4) - log(x - 2)^7*(8*x - 8*x^4) + log(x - 2)^6*(280 *x - 280*x^4) - log(x - 2)^5*(4200*x - 4200*x^4) - exp(5)*(exp(3)*(1000*x - 1000*x^4) - 1250*x + 5000*x^3 - 2500*x^4 + 2500) + log(x - 2)*(exp(5)*(e xp(3)*(600*x - 600*x^4) - 1000*x + 4000*x^3 - 2000*x^4 + 2000) - 875000*x + 875000*x^4) - 625000*x^4 + log(x - 2)^4*(35000*x + exp(5)*(2*x - 8*x^3 + 4*x^4 - 4) - 35000*x^4)))/(2*x - x^2 - 2*x^4 + x^5),x)
1000*log(x - 2)*exp(-2) - 625000*log(x - 2)*exp(-10) + log((x^3 - 1)/x)^2 - 300*log(x - 2)^2*exp(-2) - 2*exp(3)*log(x^3 - 1) + 40*log(x - 2)^3*exp(- 2) - 2*log(x - 2)^4*exp(-2) + 1250*exp(-5)*log(x^3 - 1) + 437500*log(x - 2 )^2*exp(-10) - 175000*log(x - 2)^3*exp(-10) + 43750*log(x - 2)^4*exp(-10) - 7000*log(x - 2)^5*exp(-10) + 700*log(x - 2)^6*exp(-10) - 40*log(x - 2)^7 *exp(-10) + log(x - 2)^8*exp(-10) + 2*exp(3)*log(x) - 1250*exp(-5)*log(x) + 300*log(x - 2)^2*exp(-5)*log((x^3 - 1)/x) - 40*log(x - 2)^3*exp(-5)*log( (x^3 - 1)/x) + 2*log(x - 2)^4*exp(-5)*log((x^3 - 1)/x) - 1000*log(x - 2)*e xp(-5)*log((x^3 - 1)/x)