\(\int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+(6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5) \log (2)+(1600-375 x+25 x^2) \log ^2(2)}{100-20 x^3+x^6+(100-10 x^3) \log (2)+25 \log ^2(2)}} (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+(-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7) \log (2)+(-8050+700 x+1125 x^3-150 x^4) \log ^2(2)+(-1875+250 x) \log ^3(2))}{1000-300 x^3+30 x^6-x^9+(1500-300 x^3+15 x^6) \log (2)+(750-75 x^3) \log ^2(2)+125 \log ^3(2)} \, dx\) [1314]

Optimal result

Integrand size = 258, antiderivative size = 31 \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=e^{x+\left (x-2 \left (4+\frac {4}{-x^2+\frac {5 (2+\log (2))}{x}}\right )\right )^2} \] Output:

exp(x+(x-8-8/(5*(ln(2)+2)/x-x^2))^2)
 

Mathematica [F]

\[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=\int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx \] Input:

Integrate[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 
- 15*x^7 + x^8 + (6400 - 860*x + 20*x^2 - 640*x^3 + 150*x^4 - 10*x^5)*Log[ 
2] + (1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x^3 
)*Log[2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76 
*x^7 + 15*x^9 - 2*x^10 + (-9700 + 440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 3 
0*x^7)*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875 + 2 
50*x)*Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6 
)*Log[2] + (750 - 75*x^3)*Log[2]^2 + 125*Log[2]^3),x]
 

Output:

Integrate[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 
- 15*x^7 + x^8 + (6400 - 860*x + 20*x^2 - 640*x^3 + 150*x^4 - 10*x^5)*Log[ 
2] + (1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x^3 
)*Log[2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76 
*x^7 + 15*x^9 - 2*x^10 + (-9700 + 440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 3 
0*x^7)*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875 + 2 
50*x)*Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6 
)*Log[2] + (750 - 75*x^3)*Log[2]^2 + 125*Log[2]^3), x]
 

Rubi [F]

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.

\(\displaystyle \int \frac {\left (-2 x^{10}+15 x^9+76 x^7-706 x^6-184 x^4+5780 x^3+\left (-150 x^4+1125 x^3+700 x-8050\right ) \log ^2(2)+\left (30 x^7-225 x^6-520 x^4+5140 x^3+440 x-9700\right ) \log (2)+80 x+(250 x-1875) \log ^3(2)-2200\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+\left (25 x^2-375 x+1600\right ) \log ^2(2)+\left (-10 x^5+150 x^4-640 x^3+20 x^2-860 x+6400\right ) \log (2)-220 x+6400}{x^6-20 x^3+\left (100-10 x^3\right ) \log (2)+100+25 \log ^2(2)}\right )}{-x^9+30 x^6-300 x^3+\left (750-75 x^3\right ) \log ^2(2)+\left (15 x^6-300 x^3+1500\right ) \log (2)+1000+125 \log ^3(2)} \, dx\)

\(\Big \downarrow \) 2463

\(\displaystyle \int -\frac {\left (-2 x^{10}+15 x^9+76 x^7-706 x^6-184 x^4+5780 x^3+\left (-150 x^4+1125 x^3+700 x-8050\right ) \log ^2(2)+\left (30 x^7-225 x^6-520 x^4+5140 x^3+440 x-9700\right ) \log (2)+80 x+(250 x-1875) \log ^3(2)-2200\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+\left (25 x^2-375 x+1600\right ) \log ^2(2)+\left (-10 x^5+150 x^4-640 x^3+20 x^2-860 x+6400\right ) \log (2)-220 x+6400}{x^6-20 x^3+\left (100-10 x^3\right ) \log (2)+100+25 \log ^2(2)}\right )}{\left (x^3-10-5 \log (2)\right )^3}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -\int -\frac {2^{\frac {-10 x^5+150 x^4-640 x^3+20 x^2-860 x+6400}{x^6-20 x^3+25 \log ^2(2)+\left (100-10 x^3\right ) \log (2)+100}} \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2-220 x+25 \left (x^2-15 x+64\right ) \log ^2(2)+6400}{-x^6+20 x^3-25 \left (4+\log ^2(2)\right )-10 \left (10-x^3\right ) \log (2)}\right ) \left (2 x^{10}-15 x^9-76 x^7+706 x^6+184 x^4-5780 x^3-80 x+125 (15-2 x) \log ^3(2)+25 \left (6 x^4-45 x^3-28 x+322\right ) \log ^2(2)+5 \left (-6 x^7+45 x^6+104 x^4-1028 x^3-88 x+1940\right ) \log (2)+2200\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 25

\(\displaystyle \int \frac {2^{-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+20 x^3-10 \left (10-x^3\right ) \log (2)-25 \left (4+\log ^2(2)\right )}} \left (2 x^{10}-15 x^9-76 x^7+706 x^6+184 x^4-5780 x^3+25 \left (6 x^4-45 x^3-28 x+322\right ) \log ^2(2)+5 \left (-6 x^7+45 x^6+104 x^4-1028 x^3-88 x+1940\right ) \log (2)-80 x+125 (15-2 x) \log ^3(2)+2200\right ) \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+20 x^3-10 \left (10-x^3\right ) \log (2)-25 \left (4+\log ^2(2)\right )}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7292

\(\displaystyle \int \frac {2^{-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} \left (2 x^{10}-15 x^9-76 x^7+706 x^6+184 x^4-5780 x^3+25 \left (6 x^4-45 x^3-28 x+322\right ) \log ^2(2)+5 \left (-6 x^7+45 x^6+104 x^4-1028 x^3-88 x+1940\right ) \log (2)-80 x+125 (15-2 x) \log ^3(2)+2200\right ) \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )+x 2^{1-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )+\frac {2^{4-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}-\frac {15 x (2+\log (2)) 2^{7-\frac {10 \left (-x^5+15 x^4-64 x^3+2 x^2-86 x+640\right )}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}} \exp \left (-\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+4 x^2+25 \left (x^2-15 x+64\right ) \log ^2(2)-220 x+6400}{-x^6+10 x^3 (2+\log (2))-25 (2+\log (2))^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) (2+\log (32))^2+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (-\frac {(x-16) 2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{x^3-10-5 \log (2)}-15\ 2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+x 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )+\frac {2^{4-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} (120 (2+\log (2))-x (46+15 \log (2))) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (-x^3+10+5 \log (2)\right )^2}+\frac {5 x (2+\log (2)) \left (-192+25 \log ^2(2)-\log ^2(32)\right ) 2^{1-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-10-5 \log (2)\right )^3}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2^{-\frac {10 \left (x^5-15 x^4+64 x^3-2 x^2+86 x-640\right )}{\left (x^3-5 (2+\log (2))\right )^2}} \left (2 x^{10}-15 x^9-2 x^7 (38+15 \log (2))+x^6 (706+225 \log (2))+2 x^4 \left (92+75 \log ^2(2)+260 \log (2)\right )-5 x^3 \left (1156+225 \log ^2(2)+1028 \log (2)\right )-10 x (2+\log (2)) \left (4+\log ^2(32)+20 \log (2)\right )+25 (2+\log (2))^2 (22+75 \log (2))\right ) \exp \left (\frac {x^8-15 x^7+64 x^6-4 x^5+172 x^4-1280 x^3+x^2 \left (4+25 \log ^2(2)\right )-5 x \left (44+75 \log ^2(2)\right )+1600 \left (4+\log ^2(2)\right )}{\left (x^3-5 (2+\log (2))\right )^2}\right )}{\left (x^3-5 (2+\log (2))\right )^3}dx\)

Input:

Int[(E^((6400 - 220*x + 4*x^2 - 1280*x^3 + 172*x^4 - 4*x^5 + 64*x^6 - 15*x 
^7 + x^8 + (6400 - 860*x + 20*x^2 - 640*x^3 + 150*x^4 - 10*x^5)*Log[2] + ( 
1600 - 375*x + 25*x^2)*Log[2]^2)/(100 - 20*x^3 + x^6 + (100 - 10*x^3)*Log[ 
2] + 25*Log[2]^2))*(-2200 + 80*x + 5780*x^3 - 184*x^4 - 706*x^6 + 76*x^7 + 
 15*x^9 - 2*x^10 + (-9700 + 440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7) 
*Log[2] + (-8050 + 700*x + 1125*x^3 - 150*x^4)*Log[2]^2 + (-1875 + 250*x)* 
Log[2]^3))/(1000 - 300*x^3 + 30*x^6 - x^9 + (1500 - 300*x^3 + 15*x^6)*Log[ 
2] + (750 - 75*x^3)*Log[2]^2 + 125*Log[2]^3),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(128\) vs. \(2(27)=54\).

Time = 0.02 (sec) , antiderivative size = 129, normalized size of antiderivative = 4.16

\[{\mathrm e}^{\frac {x^{8}-15 x^{7}-10 x^{5} \ln \left (2\right )+64 x^{6}+150 x^{4} \ln \left (2\right )-4 x^{5}+25 x^{2} \ln \left (2\right )^{2}-640 x^{3} \ln \left (2\right )+172 x^{4}-375 x \ln \left (2\right )^{2}+20 x^{2} \ln \left (2\right )-1280 x^{3}+1600 \ln \left (2\right )^{2}-860 x \ln \left (2\right )+4 x^{2}+6400 \ln \left (2\right )-220 x +6400}{x^{6}-10 x^{3} \ln \left (2\right )-20 x^{3}+25 \ln \left (2\right )^{2}+100 \ln \left (2\right )+100}}\]

Input:

int(((250*x-1875)*ln(2)^3+(-150*x^4+1125*x^3+700*x-8050)*ln(2)^2+(30*x^7-2 
25*x^6-520*x^4+5140*x^3+440*x-9700)*ln(2)-2*x^10+15*x^9+76*x^7-706*x^6-184 
*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*ln(2)^2+(-10*x^5+150*x^4 
-640*x^3+20*x^2-860*x+6400)*ln(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-1280*x^3 
+4*x^2-220*x+6400)/(25*ln(2)^2+(-10*x^3+100)*ln(2)+x^6-20*x^3+100))/(125*l 
n(2)^3+(-75*x^3+750)*ln(2)^2+(15*x^6-300*x^3+1500)*ln(2)-x^9+30*x^6-300*x^ 
3+1000),x)
 

Output:

exp((x^8-15*x^7-10*x^5*ln(2)+64*x^6+150*x^4*ln(2)-4*x^5+25*x^2*ln(2)^2-640 
*x^3*ln(2)+172*x^4-375*x*ln(2)^2+20*x^2*ln(2)-1280*x^3+1600*ln(2)^2-860*x* 
ln(2)+4*x^2+6400*ln(2)-220*x+6400)/(x^6-10*x^3*ln(2)-20*x^3+25*ln(2)^2+100 
*ln(2)+100))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 108 vs. \(2 (25) = 50\).

Time = 0.08 (sec) , antiderivative size = 108, normalized size of antiderivative = 3.48 \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=e^{\left (\frac {x^{8} - 15 \, x^{7} + 64 \, x^{6} - 4 \, x^{5} + 172 \, x^{4} - 1280 \, x^{3} + 25 \, {\left (x^{2} - 15 \, x + 64\right )} \log \left (2\right )^{2} + 4 \, x^{2} - 10 \, {\left (x^{5} - 15 \, x^{4} + 64 \, x^{3} - 2 \, x^{2} + 86 \, x - 640\right )} \log \left (2\right ) - 220 \, x + 6400}{x^{6} - 20 \, x^{3} - 10 \, {\left (x^{3} - 10\right )} \log \left (2\right ) + 25 \, \log \left (2\right )^{2} + 100}\right )} \] Input:

integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+( 
30*x^7-225*x^6-520*x^4+5140*x^3+440*x-9700)*log(2)-2*x^10+15*x^9+76*x^7-70 
6*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10*x 
^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x 
^4-1280*x^3+4*x^2-220*x+6400)/(25*log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3 
+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(2)-x 
^9+30*x^6-300*x^3+1000),x, algorithm="fricas")
 

Output:

e^((x^8 - 15*x^7 + 64*x^6 - 4*x^5 + 172*x^4 - 1280*x^3 + 25*(x^2 - 15*x + 
64)*log(2)^2 + 4*x^2 - 10*(x^5 - 15*x^4 + 64*x^3 - 2*x^2 + 86*x - 640)*log 
(2) - 220*x + 6400)/(x^6 - 20*x^3 - 10*(x^3 - 10)*log(2) + 25*log(2)^2 + 1 
00))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 110 vs. \(2 (20) = 40\).

Time = 3.21 (sec) , antiderivative size = 110, normalized size of antiderivative = 3.55 \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=e^{\frac {x^{8} - 15 x^{7} + 64 x^{6} - 4 x^{5} + 172 x^{4} - 1280 x^{3} + 4 x^{2} - 220 x + \left (25 x^{2} - 375 x + 1600\right ) \log {\left (2 \right )}^{2} + \left (- 10 x^{5} + 150 x^{4} - 640 x^{3} + 20 x^{2} - 860 x + 6400\right ) \log {\left (2 \right )} + 6400}{x^{6} - 20 x^{3} + \left (100 - 10 x^{3}\right ) \log {\left (2 \right )} + 25 \log {\left (2 \right )}^{2} + 100}} \] Input:

integrate(((250*x-1875)*ln(2)**3+(-150*x**4+1125*x**3+700*x-8050)*ln(2)**2 
+(30*x**7-225*x**6-520*x**4+5140*x**3+440*x-9700)*ln(2)-2*x**10+15*x**9+76 
*x**7-706*x**6-184*x**4+5780*x**3+80*x-2200)*exp(((25*x**2-375*x+1600)*ln( 
2)**2+(-10*x**5+150*x**4-640*x**3+20*x**2-860*x+6400)*ln(2)+x**8-15*x**7+6 
4*x**6-4*x**5+172*x**4-1280*x**3+4*x**2-220*x+6400)/(25*ln(2)**2+(-10*x**3 
+100)*ln(2)+x**6-20*x**3+100))/(125*ln(2)**3+(-75*x**3+750)*ln(2)**2+(15*x 
**6-300*x**3+1500)*ln(2)-x**9+30*x**6-300*x**3+1000),x)
 

Output:

exp((x**8 - 15*x**7 + 64*x**6 - 4*x**5 + 172*x**4 - 1280*x**3 + 4*x**2 - 2 
20*x + (25*x**2 - 375*x + 1600)*log(2)**2 + (-10*x**5 + 150*x**4 - 640*x** 
3 + 20*x**2 - 860*x + 6400)*log(2) + 6400)/(x**6 - 20*x**3 + (100 - 10*x** 
3)*log(2) + 25*log(2)**2 + 100))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (25) = 50\).

Time = 0.96 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.26 \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=e^{\left (x^{2} - 15 \, x + \frac {64 \, x^{2}}{x^{6} - 10 \, x^{3} {\left (\log \left (2\right ) + 2\right )} + 25 \, \log \left (2\right )^{2} + 100 \, \log \left (2\right ) + 100} + \frac {16 \, x^{2}}{x^{3} - 5 \, \log \left (2\right ) - 10} - \frac {128 \, x}{x^{3} - 5 \, \log \left (2\right ) - 10} + 64\right )} \] Input:

integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+( 
30*x^7-225*x^6-520*x^4+5140*x^3+440*x-9700)*log(2)-2*x^10+15*x^9+76*x^7-70 
6*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10*x 
^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x 
^4-1280*x^3+4*x^2-220*x+6400)/(25*log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3 
+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(2)-x 
^9+30*x^6-300*x^3+1000),x, algorithm="maxima")
 

Output:

e^(x^2 - 15*x + 64*x^2/(x^6 - 10*x^3*(log(2) + 2) + 25*log(2)^2 + 100*log( 
2) + 100) + 16*x^2/(x^3 - 5*log(2) - 10) - 128*x/(x^3 - 5*log(2) - 10) + 6 
4)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 622 vs. \(2 (25) = 50\).

Time = 0.20 (sec) , antiderivative size = 622, normalized size of antiderivative = 20.06 \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx =\text {Too large to display} \] Input:

integrate(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+( 
30*x^7-225*x^6-520*x^4+5140*x^3+440*x-9700)*log(2)-2*x^10+15*x^9+76*x^7-70 
6*x^6-184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10*x 
^5+150*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x 
^4-1280*x^3+4*x^2-220*x+6400)/(25*log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3 
+100))/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(2)-x 
^9+30*x^6-300*x^3+1000),x, algorithm="giac")
 

Output:

e^(x^8/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 1 
5*x^7/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 64 
*x^6/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 10* 
x^5*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) 
 - 4*x^5/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 
 150*x^4*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 
 100) + 172*x^4/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 
 100) - 640*x^3*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 + 100*l 
og(2) + 100) + 25*x^2*log(2)^2/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^2 
 + 100*log(2) + 100) - 1280*x^3/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*log(2)^ 
2 + 100*log(2) + 100) + 20*x^2*log(2)/(x^6 - 10*x^3*log(2) - 20*x^3 + 25*l 
og(2)^2 + 100*log(2) + 100) - 375*x*log(2)^2/(x^6 - 10*x^3*log(2) - 20*x^3 
 + 25*log(2)^2 + 100*log(2) + 100) + 4*x^2/(x^6 - 10*x^3*log(2) - 20*x^3 + 
 25*log(2)^2 + 100*log(2) + 100) - 860*x*log(2)/(x^6 - 10*x^3*log(2) - 20* 
x^3 + 25*log(2)^2 + 100*log(2) + 100) + 1600*log(2)^2/(x^6 - 10*x^3*log(2) 
 - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) - 220*x/(x^6 - 10*x^3*log(2) - 
 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 6400*log(2)/(x^6 - 10*x^3*log( 
2) - 20*x^3 + 25*log(2)^2 + 100*log(2) + 100) + 6400/(x^6 - 10*x^3*log(2) 
- 20*x^3 + 25*log(2)^2 + 100*log(2) + 100))
 

Mupad [F(-1)]

Timed out. \[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=\text {Hanged} \] Input:

int((exp((log(2)^2*(25*x^2 - 375*x + 1600) - 220*x + 4*x^2 - 1280*x^3 + 17 
2*x^4 - 4*x^5 + 64*x^6 - 15*x^7 + x^8 - log(2)*(860*x - 20*x^2 + 640*x^3 - 
 150*x^4 + 10*x^5 - 6400) + 6400)/(25*log(2)^2 - log(2)*(10*x^3 - 100) - 2 
0*x^3 + x^6 + 100))*(80*x + log(2)^3*(250*x - 1875) + log(2)^2*(700*x + 11 
25*x^3 - 150*x^4 - 8050) + 5780*x^3 - 184*x^4 - 706*x^6 + 76*x^7 + 15*x^9 
- 2*x^10 + log(2)*(440*x + 5140*x^3 - 520*x^4 - 225*x^6 + 30*x^7 - 9700) - 
 2200))/(log(2)*(15*x^6 - 300*x^3 + 1500) - log(2)^2*(75*x^3 - 750) + 125* 
log(2)^3 - 300*x^3 + 30*x^6 - x^9 + 1000),x)
 

Output:

\text{Hanged}
 

Reduce [F]

\[ \int \frac {e^{\frac {6400-220 x+4 x^2-1280 x^3+172 x^4-4 x^5+64 x^6-15 x^7+x^8+\left (6400-860 x+20 x^2-640 x^3+150 x^4-10 x^5\right ) \log (2)+\left (1600-375 x+25 x^2\right ) \log ^2(2)}{100-20 x^3+x^6+\left (100-10 x^3\right ) \log (2)+25 \log ^2(2)}} \left (-2200+80 x+5780 x^3-184 x^4-706 x^6+76 x^7+15 x^9-2 x^{10}+\left (-9700+440 x+5140 x^3-520 x^4-225 x^6+30 x^7\right ) \log (2)+\left (-8050+700 x+1125 x^3-150 x^4\right ) \log ^2(2)+(-1875+250 x) \log ^3(2)\right )}{1000-300 x^3+30 x^6-x^9+\left (1500-300 x^3+15 x^6\right ) \log (2)+\left (750-75 x^3\right ) \log ^2(2)+125 \log ^3(2)} \, dx=\int \frac {\left (\left (250 x -1875\right ) \mathrm {log}\left (2\right )^{3}+\left (-150 x^{4}+1125 x^{3}+700 x -8050\right ) \mathrm {log}\left (2\right )^{2}+\left (30 x^{7}-225 x^{6}-520 x^{4}+5140 x^{3}+440 x -9700\right ) \mathrm {log}\left (2\right )-2 x^{10}+15 x^{9}+76 x^{7}-706 x^{6}-184 x^{4}+5780 x^{3}+80 x -2200\right ) {\mathrm e}^{\frac {\left (25 x^{2}-375 x +1600\right ) \mathrm {log}\left (2\right )^{2}+\left (-10 x^{5}+150 x^{4}-640 x^{3}+20 x^{2}-860 x +6400\right ) \mathrm {log}\left (2\right )+x^{8}-15 x^{7}+64 x^{6}-4 x^{5}+172 x^{4}-1280 x^{3}+4 x^{2}-220 x +6400}{25 \mathrm {log}\left (2\right )^{2}+\left (-10 x^{3}+100\right ) \mathrm {log}\left (2\right )+x^{6}-20 x^{3}+100}}}{125 \mathrm {log}\left (2\right )^{3}+\left (-75 x^{3}+750\right ) \mathrm {log}\left (2\right )^{2}+\left (15 x^{6}-300 x^{3}+1500\right ) \mathrm {log}\left (2\right )-x^{9}+30 x^{6}-300 x^{3}+1000}d x \] Input:

int(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+(30*x^7 
-225*x^6-520*x^4+5140*x^3+440*x-9700)*log(2)-2*x^10+15*x^9+76*x^7-706*x^6- 
184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10*x^5+150 
*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-128 
0*x^3+4*x^2-220*x+6400)/(25*log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3+100)) 
/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(2)-x^9+30* 
x^6-300*x^3+1000),x)
 

Output:

int(((250*x-1875)*log(2)^3+(-150*x^4+1125*x^3+700*x-8050)*log(2)^2+(30*x^7 
-225*x^6-520*x^4+5140*x^3+440*x-9700)*log(2)-2*x^10+15*x^9+76*x^7-706*x^6- 
184*x^4+5780*x^3+80*x-2200)*exp(((25*x^2-375*x+1600)*log(2)^2+(-10*x^5+150 
*x^4-640*x^3+20*x^2-860*x+6400)*log(2)+x^8-15*x^7+64*x^6-4*x^5+172*x^4-128 
0*x^3+4*x^2-220*x+6400)/(25*log(2)^2+(-10*x^3+100)*log(2)+x^6-20*x^3+100)) 
/(125*log(2)^3+(-75*x^3+750)*log(2)^2+(15*x^6-300*x^3+1500)*log(2)-x^9+30* 
x^6-300*x^3+1000),x)