\(\int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5)+(15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x (-20+120 x+40 x^2-120 x^3-20 x^4)) \log (x)+(3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x (10 x-10 x^3)) \log ^2(x)+(200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5) \log ^3(x)+(-200 x+600 x^2-600 x^3+200 x^4) \log ^4(x)}{50 x} \, dx\) [133]

Optimal result

Integrand size = 247, antiderivative size = 28 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=\left (\frac {1}{10} \left (e^x+x\right )-(1-x)^2 (5+x+\log (x))^2\right )^2 \] Output:

(1/10*exp(x)+1/10*x-(5+ln(x)+x)^2*(1-x)^2)^2
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(177\) vs. \(2(28)=56\).

Time = 0.11 (sec) , antiderivative size = 177, normalized size of antiderivative = 6.32 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=\frac {1}{50} \left (\frac {e^{2 x}}{2}-100250 x+\frac {190801 x^2}{2}-4060 x^3-27780 x^4+790 x^5+3800 x^6+800 x^7+50 x^8-e^x \left (250-401 x+60 x^2+80 x^3+10 x^4\right )+20 (-1+x)^2 (5+x) \left (250-e^x-401 x+60 x^2+80 x^3+10 x^4\right ) \log (x)+10 (-1+x)^2 \left (750-e^x-1201 x+180 x^2+240 x^3+30 x^4\right ) \log ^2(x)+200 (-1+x)^4 (5+x) \log ^3(x)+50 (-1+x)^4 \log ^4(x)\right ) \] Input:

Integrate[(25000 - 185350*x + E^(2*x)*x + 283981*x^2 - 34040*x^3 - 128940* 
x^4 + 8150*x^5 + 25000*x^6 + 5800*x^7 + 400*x^8 + E^x*(-100 + 331*x + 221* 
x^2 - 320*x^3 - 120*x^4 - 10*x^5) + (15000 - 139120*x + 253000*x^2 - 92000 
*x^3 - 76680*x^4 + 24600*x^5 + 13800*x^6 + 1400*x^7 + E^x*(-20 + 120*x + 4 
0*x^2 - 120*x^3 - 20*x^4))*Log[x] + (3000 - 38410*x + 82240*x^2 - 48030*x^ 
3 - 10200*x^4 + 9600*x^5 + 1800*x^6 + E^x*(10*x - 10*x^3))*Log[x]^2 + (200 
 - 4600*x + 11600*x^2 - 9200*x^3 + 1000*x^4 + 1000*x^5)*Log[x]^3 + (-200*x 
 + 600*x^2 - 600*x^3 + 200*x^4)*Log[x]^4)/(50*x),x]
 

Output:

(E^(2*x)/2 - 100250*x + (190801*x^2)/2 - 4060*x^3 - 27780*x^4 + 790*x^5 + 
3800*x^6 + 800*x^7 + 50*x^8 - E^x*(250 - 401*x + 60*x^2 + 80*x^3 + 10*x^4) 
 + 20*(-1 + x)^2*(5 + x)*(250 - E^x - 401*x + 60*x^2 + 80*x^3 + 10*x^4)*Lo 
g[x] + 10*(-1 + x)^2*(750 - E^x - 1201*x + 180*x^2 + 240*x^3 + 30*x^4)*Log 
[x]^2 + 200*(-1 + x)^4*(5 + x)*Log[x]^3 + 50*(-1 + x)^4*Log[x]^4)/50
 

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.

\(\displaystyle \int \frac {400 x^8+5800 x^7+25000 x^6+8150 x^5-128940 x^4-34040 x^3+283981 x^2+\left (200 x^4-600 x^3+600 x^2-200 x\right ) \log ^4(x)+e^x \left (-10 x^5-120 x^4-320 x^3+221 x^2+331 x-100\right )+\left (1000 x^5+1000 x^4-9200 x^3+11600 x^2-4600 x+200\right ) \log ^3(x)+\left (1800 x^6+9600 x^5-10200 x^4-48030 x^3+e^x \left (10 x-10 x^3\right )+82240 x^2-38410 x+3000\right ) \log ^2(x)+\left (1400 x^7+13800 x^6+24600 x^5-76680 x^4-92000 x^3+253000 x^2+e^x \left (-20 x^4-120 x^3+40 x^2+120 x-20\right )-139120 x+15000\right ) \log (x)+e^{2 x} x-185350 x+25000}{50 x} \, dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{50} \int \frac {400 x^8+5800 x^7+25000 x^6+8150 x^5-128940 x^4-34040 x^3+283981 x^2+e^{2 x} x-185350 x-200 \left (-x^4+3 x^3-3 x^2+x\right ) \log ^4(x)+200 \left (5 x^5+5 x^4-46 x^3+58 x^2-23 x+1\right ) \log ^3(x)+10 \left (180 x^6+960 x^5-1020 x^4-4803 x^3+8224 x^2-3841 x+e^x \left (x-x^3\right )+300\right ) \log ^2(x)-e^x \left (10 x^5+120 x^4+320 x^3-221 x^2-331 x+100\right )+20 \left (70 x^7+690 x^6+1230 x^5-3834 x^4-4600 x^3+12650 x^2-6956 x-e^x \left (x^4+6 x^3-2 x^2-6 x+1\right )+750\right ) \log (x)+25000}{x}dx\)

\(\Big \downarrow \) 2010

\(\displaystyle \frac {1}{50} \int \left (-\frac {e^x (x+1) \left (10 x^4+20 \log (x) x^3+110 x^3+10 \log ^2(x) x^2+100 \log (x) x^2+210 x^2-10 \log ^2(x) x-140 \log (x) x-431 x+20 \log (x)+100\right )}{x}+e^{2 x}+\frac {400 x^8+1400 \log (x) x^7+5800 x^7+1800 \log ^2(x) x^6+13800 \log (x) x^6+25000 x^6+1000 \log ^3(x) x^5+9600 \log ^2(x) x^5+24600 \log (x) x^5+8150 x^5+200 \log ^4(x) x^4+1000 \log ^3(x) x^4-10200 \log ^2(x) x^4-76680 \log (x) x^4-128940 x^4-600 \log ^4(x) x^3-9200 \log ^3(x) x^3-48030 \log ^2(x) x^3-92000 \log (x) x^3-34040 x^3+600 \log ^4(x) x^2+11600 \log ^3(x) x^2+82240 \log ^2(x) x^2+253000 \log (x) x^2+283981 x^2-200 \log ^4(x) x-4600 \log ^3(x) x-38410 \log ^2(x) x-139120 \log (x) x-185350 x+200 \log ^3(x)+3000 \log ^2(x)+15000 \log (x)+25000}{x}\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle \frac {1}{50} \left (-10 \int e^x x^2 \log ^2(x)dx+10 \int e^x \log ^2(x)dx+20 x \, _3F_3(1,1,1;2,2,2;x)+20 \log (x) (\operatorname {ExpIntegralE}(1,-x)+\operatorname {ExpIntegralEi}(x))-60 \operatorname {ExpIntegralEi}(x)-20 \operatorname {ExpIntegralEi}(x) \log (x)+50 x^8+800 x^7+200 x^7 \log (x)+3800 x^6+300 x^6 \log ^2(x)+2200 x^6 \log (x)+790 x^5+200 x^5 \log ^3(x)+1800 x^5 \log ^2(x)+4200 x^5 \log (x)-10 e^x x^4-27780 x^4+50 x^4 \log ^4(x)+200 x^4 \log ^3(x)-2700 x^4 \log ^2(x)-17820 x^4 \log (x)-80 e^x x^3-4060 x^3-200 x^3 \log ^4(x)-2800 x^3 \log ^3(x)-13210 x^3 \log ^2(x)-20 e^x x^3 \log (x)-21860 x^3 \log (x)-60 e^x x^2+\frac {190801 x^2}{2}+300 x^2 \log ^4(x)+5200 x^2 \log ^3(x)+33320 x^2 \log ^2(x)-60 e^x x^2 \log (x)+93180 x^2 \log (x)+401 e^x x-100250 x-230 e^x+\frac {e^{2 x}}{2}-200 x \log ^4(x)+50 \log ^4(x)-3800 x \log ^3(x)+1000 \log ^3(x)-27010 x \log ^2(x)+10 \log ^2(-x)+7500 \log ^2(x)+160 e^x x \log (x)-85100 x \log (x)-40 e^x \log (x)+20 \gamma \log (x)+25000 \log (x)\right )\)

Input:

Int[(25000 - 185350*x + E^(2*x)*x + 283981*x^2 - 34040*x^3 - 128940*x^4 + 
8150*x^5 + 25000*x^6 + 5800*x^7 + 400*x^8 + E^x*(-100 + 331*x + 221*x^2 - 
320*x^3 - 120*x^4 - 10*x^5) + (15000 - 139120*x + 253000*x^2 - 92000*x^3 - 
 76680*x^4 + 24600*x^5 + 13800*x^6 + 1400*x^7 + E^x*(-20 + 120*x + 40*x^2 
- 120*x^3 - 20*x^4))*Log[x] + (3000 - 38410*x + 82240*x^2 - 48030*x^3 - 10 
200*x^4 + 9600*x^5 + 1800*x^6 + E^x*(10*x - 10*x^3))*Log[x]^2 + (200 - 460 
0*x + 11600*x^2 - 9200*x^3 + 1000*x^4 + 1000*x^5)*Log[x]^3 + (-200*x + 600 
*x^2 - 600*x^3 + 200*x^4)*Log[x]^4)/(50*x),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(232\) vs. \(2(26)=52\).

Time = 0.03 (sec) , antiderivative size = 233, normalized size of antiderivative = 8.32

\[\left (-1+x \right )^{4} \ln \left (x \right )^{4}+\frac {\left (200 x^{5}+200 x^{4}-2800 x^{3}+5200 x^{2}-3800 x +1000\right ) \ln \left (x \right )^{3}}{50}+\frac {\left (300 x^{6}+1800 x^{5}-2700 x^{4}-13210 x^{3}-10 \,{\mathrm e}^{x} x^{2}+33320 x^{2}+20 \,{\mathrm e}^{x} x -27010 x -10 \,{\mathrm e}^{x}+7500\right ) \ln \left (x \right )^{2}}{50}+\frac {\left (200 x^{7}+2200 x^{6}+4200 x^{5}-17820 x^{4}-20 \,{\mathrm e}^{x} x^{3}-21860 x^{3}-60 \,{\mathrm e}^{x} x^{2}+93180 x^{2}+180 \,{\mathrm e}^{x} x -85100 x -100 \,{\mathrm e}^{x}\right ) \ln \left (x \right )}{50}+x^{8}+16 x^{7}+76 x^{6}+\frac {79 x^{5}}{5}-\frac {2778 x^{4}}{5}-\frac {406 x^{3}}{5}+\frac {190801 x^{2}}{100}-2005 x +625+500 \ln \left (x \right )+\frac {{\mathrm e}^{2 x}}{100}-\frac {{\mathrm e}^{x} x^{4}}{5}-\frac {8 \,{\mathrm e}^{x} x^{3}}{5}-\frac {6 \,{\mathrm e}^{x} x^{2}}{5}+\frac {401 \,{\mathrm e}^{x} x}{50}-5 \,{\mathrm e}^{x}\]

Input:

int(1/50*((200*x^4-600*x^3+600*x^2-200*x)*ln(x)^4+(1000*x^5+1000*x^4-9200* 
x^3+11600*x^2-4600*x+200)*ln(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+9600*x^5 
-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*ln(x)^2+((-20*x^4-120*x^3+40* 
x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+2530 
00*x^2-139120*x+15000)*ln(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3+221*x^2+3 
31*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4-34040*x^3+ 
283981*x^2-185350*x+25000)/x,x)
 

Output:

(-1+x)^4*ln(x)^4+1/50*(200*x^5+200*x^4-2800*x^3+5200*x^2-3800*x+1000)*ln(x 
)^3+1/50*(300*x^6+1800*x^5-2700*x^4-13210*x^3-10*exp(x)*x^2+33320*x^2+20*e 
xp(x)*x-27010*x-10*exp(x)+7500)*ln(x)^2+1/50*(200*x^7+2200*x^6+4200*x^5-17 
820*x^4-20*exp(x)*x^3-21860*x^3-60*exp(x)*x^2+93180*x^2+180*exp(x)*x-85100 
*x-100*exp(x))*ln(x)+x^8+16*x^7+76*x^6+79/5*x^5-2778/5*x^4-406/5*x^3+19080 
1/100*x^2-2005*x+625+500*ln(x)+1/100*exp(2*x)-1/5*exp(x)*x^4-8/5*exp(x)*x^ 
3-6/5*exp(x)*x^2+401/50*exp(x)*x-5*exp(x)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 221 vs. \(2 (26) = 52\).

Time = 0.10 (sec) , antiderivative size = 221, normalized size of antiderivative = 7.89 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=x^{8} + 16 \, x^{7} + 76 \, x^{6} + \frac {79}{5} \, x^{5} + {\left (x^{4} - 4 \, x^{3} + 6 \, x^{2} - 4 \, x + 1\right )} \log \left (x\right )^{4} - \frac {2778}{5} \, x^{4} + 4 \, {\left (x^{5} + x^{4} - 14 \, x^{3} + 26 \, x^{2} - 19 \, x + 5\right )} \log \left (x\right )^{3} - \frac {406}{5} \, x^{3} + \frac {1}{5} \, {\left (30 \, x^{6} + 180 \, x^{5} - 270 \, x^{4} - 1321 \, x^{3} + 3332 \, x^{2} - {\left (x^{2} - 2 \, x + 1\right )} e^{x} - 2701 \, x + 750\right )} \log \left (x\right )^{2} + \frac {190801}{100} \, x^{2} - \frac {1}{50} \, {\left (10 \, x^{4} + 80 \, x^{3} + 60 \, x^{2} - 401 \, x + 250\right )} e^{x} + \frac {2}{5} \, {\left (10 \, x^{7} + 110 \, x^{6} + 210 \, x^{5} - 891 \, x^{4} - 1093 \, x^{3} + 4659 \, x^{2} - {\left (x^{3} + 3 \, x^{2} - 9 \, x + 5\right )} e^{x} - 4255 \, x + 1250\right )} \log \left (x\right ) - 2005 \, x + \frac {1}{100} \, e^{\left (2 \, x\right )} \] Input:

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^ 
4-9200*x^3+11600*x^2-4600*x+200)*log(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+ 
9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-12 
0*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000 
*x^3+253000*x^2-139120*x+15000)*log(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3 
+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4- 
34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="fricas")
 

Output:

x^8 + 16*x^7 + 76*x^6 + 79/5*x^5 + (x^4 - 4*x^3 + 6*x^2 - 4*x + 1)*log(x)^ 
4 - 2778/5*x^4 + 4*(x^5 + x^4 - 14*x^3 + 26*x^2 - 19*x + 5)*log(x)^3 - 406 
/5*x^3 + 1/5*(30*x^6 + 180*x^5 - 270*x^4 - 1321*x^3 + 3332*x^2 - (x^2 - 2* 
x + 1)*e^x - 2701*x + 750)*log(x)^2 + 190801/100*x^2 - 1/50*(10*x^4 + 80*x 
^3 + 60*x^2 - 401*x + 250)*e^x + 2/5*(10*x^7 + 110*x^6 + 210*x^5 - 891*x^4 
 - 1093*x^3 + 4659*x^2 - (x^3 + 3*x^2 - 9*x + 5)*e^x - 4255*x + 1250)*log( 
x) - 2005*x + 1/100*e^(2*x)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 272 vs. \(2 (22) = 44\).

Time = 0.52 (sec) , antiderivative size = 272, normalized size of antiderivative = 9.71 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=x^{8} + 16 x^{7} + 76 x^{6} + \frac {79 x^{5}}{5} - \frac {2778 x^{4}}{5} - \frac {406 x^{3}}{5} + \frac {190801 x^{2}}{100} - 2005 x + \left (x^{4} - 4 x^{3} + 6 x^{2} - 4 x + 1\right ) \log {\left (x \right )}^{4} + \left (4 x^{5} + 4 x^{4} - 56 x^{3} + 104 x^{2} - 76 x + 20\right ) \log {\left (x \right )}^{3} + \left (6 x^{6} + 36 x^{5} - 54 x^{4} - \frac {1321 x^{3}}{5} + \frac {3332 x^{2}}{5} - \frac {2701 x}{5} + 150\right ) \log {\left (x \right )}^{2} + \left (4 x^{7} + 44 x^{6} + 84 x^{5} - \frac {1782 x^{4}}{5} - \frac {2186 x^{3}}{5} + \frac {9318 x^{2}}{5} - 1702 x\right ) \log {\left (x \right )} + \frac {\left (- 1000 x^{4} - 2000 x^{3} \log {\left (x \right )} - 8000 x^{3} - 1000 x^{2} \log {\left (x \right )}^{2} - 6000 x^{2} \log {\left (x \right )} - 6000 x^{2} + 2000 x \log {\left (x \right )}^{2} + 18000 x \log {\left (x \right )} + 40100 x - 1000 \log {\left (x \right )}^{2} - 10000 \log {\left (x \right )} - 25000\right ) e^{x}}{5000} + \frac {e^{2 x}}{100} + 500 \log {\left (x \right )} \] Input:

integrate(1/50*((200*x**4-600*x**3+600*x**2-200*x)*ln(x)**4+(1000*x**5+100 
0*x**4-9200*x**3+11600*x**2-4600*x+200)*ln(x)**3+((-10*x**3+10*x)*exp(x)+1 
800*x**6+9600*x**5-10200*x**4-48030*x**3+82240*x**2-38410*x+3000)*ln(x)**2 
+((-20*x**4-120*x**3+40*x**2+120*x-20)*exp(x)+1400*x**7+13800*x**6+24600*x 
**5-76680*x**4-92000*x**3+253000*x**2-139120*x+15000)*ln(x)+x*exp(x)**2+(- 
10*x**5-120*x**4-320*x**3+221*x**2+331*x-100)*exp(x)+400*x**8+5800*x**7+25 
000*x**6+8150*x**5-128940*x**4-34040*x**3+283981*x**2-185350*x+25000)/x,x)
 

Output:

x**8 + 16*x**7 + 76*x**6 + 79*x**5/5 - 2778*x**4/5 - 406*x**3/5 + 190801*x 
**2/100 - 2005*x + (x**4 - 4*x**3 + 6*x**2 - 4*x + 1)*log(x)**4 + (4*x**5 
+ 4*x**4 - 56*x**3 + 104*x**2 - 76*x + 20)*log(x)**3 + (6*x**6 + 36*x**5 - 
 54*x**4 - 1321*x**3/5 + 3332*x**2/5 - 2701*x/5 + 150)*log(x)**2 + (4*x**7 
 + 44*x**6 + 84*x**5 - 1782*x**4/5 - 2186*x**3/5 + 9318*x**2/5 - 1702*x)*l 
og(x) + (-1000*x**4 - 2000*x**3*log(x) - 8000*x**3 - 1000*x**2*log(x)**2 - 
 6000*x**2*log(x) - 6000*x**2 + 2000*x*log(x)**2 + 18000*x*log(x) + 40100* 
x - 1000*log(x)**2 - 10000*log(x) - 25000)*exp(x)/5000 + exp(2*x)/100 + 50 
0*log(x)
 

Maxima [F]

\[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=\int { \frac {400 \, x^{8} + 5800 \, x^{7} + 25000 \, x^{6} + 8150 \, x^{5} + 200 \, {\left (x^{4} - 3 \, x^{3} + 3 \, x^{2} - x\right )} \log \left (x\right )^{4} - 128940 \, x^{4} + 200 \, {\left (5 \, x^{5} + 5 \, x^{4} - 46 \, x^{3} + 58 \, x^{2} - 23 \, x + 1\right )} \log \left (x\right )^{3} - 34040 \, x^{3} + 10 \, {\left (180 \, x^{6} + 960 \, x^{5} - 1020 \, x^{4} - 4803 \, x^{3} + 8224 \, x^{2} - {\left (x^{3} - x\right )} e^{x} - 3841 \, x + 300\right )} \log \left (x\right )^{2} + 283981 \, x^{2} + x e^{\left (2 \, x\right )} - {\left (10 \, x^{5} + 120 \, x^{4} + 320 \, x^{3} - 221 \, x^{2} - 331 \, x + 100\right )} e^{x} + 20 \, {\left (70 \, x^{7} + 690 \, x^{6} + 1230 \, x^{5} - 3834 \, x^{4} - 4600 \, x^{3} + 12650 \, x^{2} - {\left (x^{4} + 6 \, x^{3} - 2 \, x^{2} - 6 \, x + 1\right )} e^{x} - 6956 \, x + 750\right )} \log \left (x\right ) - 185350 \, x + 25000}{50 \, x} \,d x } \] Input:

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^ 
4-9200*x^3+11600*x^2-4600*x+200)*log(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+ 
9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-12 
0*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000 
*x^3+253000*x^2-139120*x+15000)*log(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3 
+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4- 
34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="maxima")
 

Output:

x^8 + 4*x^7*log(x) + 16*x^7 + 46*x^6*log(x) + 76*x^6 + 492/5*x^5*log(x) + 
79/5*x^5 - 1917/5*x^4*log(x) + (x^4 - 4*x^3 + 6*x^2 - 4*x + 1)*log(x)^4 - 
2778/5*x^4 - 1840/3*x^3*log(x) + 4*(x^5 + x^4 - 14*x^3 + 26*x^2 - 19*x + 5 
)*log(x)^3 - 406/5*x^3 + 2530*x^2*log(x) + 1/5*(30*x^6 + 180*x^5 - 270*x^4 
 - 1321*x^3 + 3332*x^2 - 2701*x)*log(x)^2 + 190801/100*x^2 - 1/5*(x^4 - 4* 
x^3 + 12*x^2 - 24*x + 24)*e^x - 12/5*(x^3 - 3*x^2 + 6*x - 6)*e^x - 1/5*((x 
^2 - 2*x + 1)*log(x)^2 + 2*(x^3 + 3*x^2 - 9*x + 11)*log(x))*e^x - 32/5*(x^ 
2 - 2*x + 2)*e^x + 221/50*(x - 1)*e^x - 1/15*(30*x^6 + 216*x^5 - 405*x^4 - 
 2642*x^3 + 9996*x^2 - 16206*x)*log(x) - 13912/5*x*log(x) + 12/5*e^x*log(x 
) + 150*log(x)^2 - 2005*x - 22/5*Ei(x) + 1/100*e^(2*x) + 331/50*e^x + 1/50 
*integrate(20*(x^3 + 3*x^2 - 9*x + 11)*e^x/x, x) + 500*log(x)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 327 vs. \(2 (26) = 52\).

Time = 0.14 (sec) , antiderivative size = 327, normalized size of antiderivative = 11.68 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=x^{8} + 4 \, x^{7} \log \left (x\right ) + 6 \, x^{6} \log \left (x\right )^{2} + 4 \, x^{5} \log \left (x\right )^{3} + x^{4} \log \left (x\right )^{4} + 16 \, x^{7} + 44 \, x^{6} \log \left (x\right ) + 36 \, x^{5} \log \left (x\right )^{2} + 4 \, x^{4} \log \left (x\right )^{3} - 4 \, x^{3} \log \left (x\right )^{4} + 76 \, x^{6} + 84 \, x^{5} \log \left (x\right ) - 54 \, x^{4} \log \left (x\right )^{2} - 56 \, x^{3} \log \left (x\right )^{3} + 6 \, x^{2} \log \left (x\right )^{4} + \frac {79}{5} \, x^{5} - \frac {1}{5} \, x^{4} e^{x} - \frac {1782}{5} \, x^{4} \log \left (x\right ) - \frac {2}{5} \, x^{3} e^{x} \log \left (x\right ) - \frac {1321}{5} \, x^{3} \log \left (x\right )^{2} - \frac {1}{5} \, x^{2} e^{x} \log \left (x\right )^{2} + 104 \, x^{2} \log \left (x\right )^{3} - 4 \, x \log \left (x\right )^{4} - \frac {2778}{5} \, x^{4} - \frac {8}{5} \, x^{3} e^{x} - \frac {2186}{5} \, x^{3} \log \left (x\right ) - \frac {6}{5} \, x^{2} e^{x} \log \left (x\right ) + \frac {3332}{5} \, x^{2} \log \left (x\right )^{2} + \frac {2}{5} \, x e^{x} \log \left (x\right )^{2} - 76 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - \frac {406}{5} \, x^{3} - \frac {6}{5} \, x^{2} e^{x} + \frac {9318}{5} \, x^{2} \log \left (x\right ) + \frac {18}{5} \, x e^{x} \log \left (x\right ) - \frac {2701}{5} \, x \log \left (x\right )^{2} - \frac {1}{5} \, e^{x} \log \left (x\right )^{2} + 20 \, \log \left (x\right )^{3} + \frac {190801}{100} \, x^{2} + \frac {401}{50} \, x e^{x} - 1702 \, x \log \left (x\right ) - 2 \, e^{x} \log \left (x\right ) + 150 \, \log \left (x\right )^{2} - 2005 \, x + \frac {1}{100} \, e^{\left (2 \, x\right )} - 5 \, e^{x} + 500 \, \log \left (x\right ) \] Input:

integrate(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^ 
4-9200*x^3+11600*x^2-4600*x+200)*log(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+ 
9600*x^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-12 
0*x^3+40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000 
*x^3+253000*x^2-139120*x+15000)*log(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3 
+221*x^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4- 
34040*x^3+283981*x^2-185350*x+25000)/x,x, algorithm="giac")
 

Output:

x^8 + 4*x^7*log(x) + 6*x^6*log(x)^2 + 4*x^5*log(x)^3 + x^4*log(x)^4 + 16*x 
^7 + 44*x^6*log(x) + 36*x^5*log(x)^2 + 4*x^4*log(x)^3 - 4*x^3*log(x)^4 + 7 
6*x^6 + 84*x^5*log(x) - 54*x^4*log(x)^2 - 56*x^3*log(x)^3 + 6*x^2*log(x)^4 
 + 79/5*x^5 - 1/5*x^4*e^x - 1782/5*x^4*log(x) - 2/5*x^3*e^x*log(x) - 1321/ 
5*x^3*log(x)^2 - 1/5*x^2*e^x*log(x)^2 + 104*x^2*log(x)^3 - 4*x*log(x)^4 - 
2778/5*x^4 - 8/5*x^3*e^x - 2186/5*x^3*log(x) - 6/5*x^2*e^x*log(x) + 3332/5 
*x^2*log(x)^2 + 2/5*x*e^x*log(x)^2 - 76*x*log(x)^3 + log(x)^4 - 406/5*x^3 
- 6/5*x^2*e^x + 9318/5*x^2*log(x) + 18/5*x*e^x*log(x) - 2701/5*x*log(x)^2 
- 1/5*e^x*log(x)^2 + 20*log(x)^3 + 190801/100*x^2 + 401/50*x*e^x - 1702*x* 
log(x) - 2*e^x*log(x) + 150*log(x)^2 - 2005*x + 1/100*e^(2*x) - 5*e^x + 50 
0*log(x)
 

Mupad [B] (verification not implemented)

Time = 2.74 (sec) , antiderivative size = 229, normalized size of antiderivative = 8.18 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=\frac {{\mathrm {e}}^{2\,x}}{100}-2005\,x+500\,\ln \left (x\right )-{\mathrm {e}}^x\,\left (\frac {x^4}{5}+\frac {8\,x^3}{5}+\frac {6\,x^2}{5}-\frac {401\,x}{50}+5\right )+{\ln \left (x\right )}^4\,\left (x^4-4\,x^3+6\,x^2-4\,x+1\right )-{\ln \left (x\right )}^2\,\left (\frac {2701\,x}{5}+{\mathrm {e}}^x\,\left (\frac {x^2}{5}-\frac {2\,x}{5}+\frac {1}{5}\right )-\frac {3332\,x^2}{5}+\frac {1321\,x^3}{5}+54\,x^4-36\,x^5-6\,x^6-150\right )-\ln \left (x\right )\,\left (1702\,x-\frac {9318\,x^2}{5}+\frac {2186\,x^3}{5}+\frac {1782\,x^4}{5}-84\,x^5-44\,x^6-4\,x^7+{\mathrm {e}}^x\,\left (\frac {2\,x^3}{5}+\frac {6\,x^2}{5}-\frac {18\,x}{5}+2\right )\right )+{\ln \left (x\right )}^3\,\left (4\,x^5+4\,x^4-56\,x^3+104\,x^2-76\,x+20\right )+\frac {190801\,x^2}{100}-\frac {406\,x^3}{5}-\frac {2778\,x^4}{5}+\frac {79\,x^5}{5}+76\,x^6+16\,x^7+x^8 \] Input:

int(((x*exp(2*x))/50 - 3707*x - (exp(x)*(320*x^3 - 221*x^2 - 331*x + 120*x 
^4 + 10*x^5 + 100))/50 - (log(x)^4*(200*x - 600*x^2 + 600*x^3 - 200*x^4))/ 
50 + (log(x)^2*(exp(x)*(10*x - 10*x^3) - 38410*x + 82240*x^2 - 48030*x^3 - 
 10200*x^4 + 9600*x^5 + 1800*x^6 + 3000))/50 + (log(x)^3*(11600*x^2 - 4600 
*x - 9200*x^3 + 1000*x^4 + 1000*x^5 + 200))/50 + (283981*x^2)/50 - (3404*x 
^3)/5 - (12894*x^4)/5 + 163*x^5 + 500*x^6 + 116*x^7 + 8*x^8 + (log(x)*(253 
000*x^2 - exp(x)*(120*x^3 - 40*x^2 - 120*x + 20*x^4 + 20) - 139120*x - 920 
00*x^3 - 76680*x^4 + 24600*x^5 + 13800*x^6 + 1400*x^7 + 15000))/50 + 500)/ 
x,x)
 

Output:

exp(2*x)/100 - 2005*x + 500*log(x) - exp(x)*((6*x^2)/5 - (401*x)/50 + (8*x 
^3)/5 + x^4/5 + 5) + log(x)^4*(6*x^2 - 4*x - 4*x^3 + x^4 + 1) - log(x)^2*( 
(2701*x)/5 + exp(x)*(x^2/5 - (2*x)/5 + 1/5) - (3332*x^2)/5 + (1321*x^3)/5 
+ 54*x^4 - 36*x^5 - 6*x^6 - 150) - log(x)*(1702*x - (9318*x^2)/5 + (2186*x 
^3)/5 + (1782*x^4)/5 - 84*x^5 - 44*x^6 - 4*x^7 + exp(x)*((6*x^2)/5 - (18*x 
)/5 + (2*x^3)/5 + 2)) + log(x)^3*(104*x^2 - 76*x - 56*x^3 + 4*x^4 + 4*x^5 
+ 20) + (190801*x^2)/100 - (406*x^3)/5 - (2778*x^4)/5 + (79*x^5)/5 + 76*x^ 
6 + 16*x^7 + x^8
 

Reduce [B] (verification not implemented)

Time = 0.24 (sec) , antiderivative size = 340, normalized size of antiderivative = 12.14 \[ \int \frac {25000-185350 x+e^{2 x} x+283981 x^2-34040 x^3-128940 x^4+8150 x^5+25000 x^6+5800 x^7+400 x^8+e^x \left (-100+331 x+221 x^2-320 x^3-120 x^4-10 x^5\right )+\left (15000-139120 x+253000 x^2-92000 x^3-76680 x^4+24600 x^5+13800 x^6+1400 x^7+e^x \left (-20+120 x+40 x^2-120 x^3-20 x^4\right )\right ) \log (x)+\left (3000-38410 x+82240 x^2-48030 x^3-10200 x^4+9600 x^5+1800 x^6+e^x \left (10 x-10 x^3\right )\right ) \log ^2(x)+\left (200-4600 x+11600 x^2-9200 x^3+1000 x^4+1000 x^5\right ) \log ^3(x)+\left (-200 x+600 x^2-600 x^3+200 x^4\right ) \log ^4(x)}{50 x} \, dx=-2005 x -54 \mathrm {log}\left (x \right )^{2} x^{4}-\frac {1321 \mathrm {log}\left (x \right )^{2} x^{3}}{5}+4 \mathrm {log}\left (x \right )^{3} x^{4}+4 \mathrm {log}\left (x \right )^{3} x^{5}+36 \mathrm {log}\left (x \right )^{2} x^{5}-\frac {e^{x} x^{4}}{5}-\frac {8 e^{x} x^{3}}{5}-\frac {e^{x} \mathrm {log}\left (x \right )^{2}}{5}-\frac {2 e^{x} \mathrm {log}\left (x \right ) x^{3}}{5}-56 \mathrm {log}\left (x \right )^{3} x^{3}+\frac {3332 \mathrm {log}\left (x \right )^{2} x^{2}}{5}-\frac {1782 \,\mathrm {log}\left (x \right ) x^{4}}{5}+\frac {190801 x^{2}}{100}+\frac {79 x^{5}}{5}+16 x^{7}-\frac {6 e^{x} \mathrm {log}\left (x \right ) x^{2}}{5}+4 \,\mathrm {log}\left (x \right ) x^{7}-\frac {406 x^{3}}{5}+\frac {2 e^{x} \mathrm {log}\left (x \right )^{2} x}{5}-\frac {6 e^{x} x^{2}}{5}+x^{8}+76 x^{6}+500 \,\mathrm {log}\left (x \right )+\frac {9318 \,\mathrm {log}\left (x \right ) x^{2}}{5}-4 \mathrm {log}\left (x \right )^{4} x^{3}+6 \mathrm {log}\left (x \right )^{4} x^{2}+6 \mathrm {log}\left (x \right )^{2} x^{6}+\mathrm {log}\left (x \right )^{4} x^{4}-4 \mathrm {log}\left (x \right )^{4} x -\frac {e^{x} \mathrm {log}\left (x \right )^{2} x^{2}}{5}-5 e^{x}+\frac {e^{2 x}}{100}+84 \,\mathrm {log}\left (x \right ) x^{5}-\frac {2186 \,\mathrm {log}\left (x \right ) x^{3}}{5}-76 \mathrm {log}\left (x \right )^{3} x +\mathrm {log}\left (x \right )^{4}-\frac {2778 x^{4}}{5}+150 \mathrm {log}\left (x \right )^{2}+\frac {18 e^{x} \mathrm {log}\left (x \right ) x}{5}+\frac {401 e^{x} x}{50}-1702 \,\mathrm {log}\left (x \right ) x -\frac {2701 \mathrm {log}\left (x \right )^{2} x}{5}+20 \mathrm {log}\left (x \right )^{3}+104 \mathrm {log}\left (x \right )^{3} x^{2}+44 \,\mathrm {log}\left (x \right ) x^{6}-2 e^{x} \mathrm {log}\left (x \right ) \] Input:

int(1/50*((200*x^4-600*x^3+600*x^2-200*x)*log(x)^4+(1000*x^5+1000*x^4-9200 
*x^3+11600*x^2-4600*x+200)*log(x)^3+((-10*x^3+10*x)*exp(x)+1800*x^6+9600*x 
^5-10200*x^4-48030*x^3+82240*x^2-38410*x+3000)*log(x)^2+((-20*x^4-120*x^3+ 
40*x^2+120*x-20)*exp(x)+1400*x^7+13800*x^6+24600*x^5-76680*x^4-92000*x^3+2 
53000*x^2-139120*x+15000)*log(x)+x*exp(x)^2+(-10*x^5-120*x^4-320*x^3+221*x 
^2+331*x-100)*exp(x)+400*x^8+5800*x^7+25000*x^6+8150*x^5-128940*x^4-34040* 
x^3+283981*x^2-185350*x+25000)/x,x)
 

Output:

(e**(2*x) - 20*e**x*log(x)**2*x**2 + 40*e**x*log(x)**2*x - 20*e**x*log(x)* 
*2 - 40*e**x*log(x)*x**3 - 120*e**x*log(x)*x**2 + 360*e**x*log(x)*x - 200* 
e**x*log(x) - 20*e**x*x**4 - 160*e**x*x**3 - 120*e**x*x**2 + 802*e**x*x - 
500*e**x + 100*log(x)**4*x**4 - 400*log(x)**4*x**3 + 600*log(x)**4*x**2 - 
400*log(x)**4*x + 100*log(x)**4 + 400*log(x)**3*x**5 + 400*log(x)**3*x**4 
- 5600*log(x)**3*x**3 + 10400*log(x)**3*x**2 - 7600*log(x)**3*x + 2000*log 
(x)**3 + 600*log(x)**2*x**6 + 3600*log(x)**2*x**5 - 5400*log(x)**2*x**4 - 
26420*log(x)**2*x**3 + 66640*log(x)**2*x**2 - 54020*log(x)**2*x + 15000*lo 
g(x)**2 + 400*log(x)*x**7 + 4400*log(x)*x**6 + 8400*log(x)*x**5 - 35640*lo 
g(x)*x**4 - 43720*log(x)*x**3 + 186360*log(x)*x**2 - 170200*log(x)*x + 500 
00*log(x) + 100*x**8 + 1600*x**7 + 7600*x**6 + 1580*x**5 - 55560*x**4 - 81 
20*x**3 + 190801*x**2 - 200500*x)/100