\(\int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} (-2 x^2-2 x^3+54 x^4+18 x^5)+e^5 (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6)+(144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} (2 x+6 x^2-162 x^3-54 x^4)+e^5 (34 x+120 x^2-1434 x^3-972 x^4-162 x^5)) \log (x)+(-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} (-4 x+162 x^2+54 x^3)+e^5 (-72 x+1440 x^2+972 x^3+162 x^4)) \log ^2(x)+(-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} (-54 x-18 x^2)+e^5 (-486 x-324 x^2-54 x^3)) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} (-27 x^3-9 x^4)+e^5 (-243 x^3-162 x^4-27 x^5)+(2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} (81 x^2+27 x^3)+e^5 (729 x^2+486 x^3+81 x^4)) \log (x)+(-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} (-81 x-27 x^2)+e^5 (-729 x-486 x^2-81 x^3)) \log ^2(x)+(729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 (243+162 x+27 x^2)) \log ^3(x)} \, dx\) [451]

Optimal result

Integrand size = 571, antiderivative size = 28 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=2-\left (x+\frac {x}{\left (9+e^5+3 x\right ) (-x+\log (x))}\right )^2 \] Output:

2-(x+x/(ln(x)-x)/(9+exp(5)+3*x))^2
                                                                                    
                                                                                    
 

Mathematica [A] (verified)

Time = 0.17 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.64 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=-x^2 \left (1+\frac {1}{\left (9+e^5+3 x\right )^2 (x-\log (x))^2}+\frac {2}{\left (9+e^5+3 x\right ) (-x+\log (x))}\right ) \] Input:

Integrate[(18*x - 156*x^2 - 276*x^3 + 1386*x^4 + 2*E^15*x^4 + 1458*x^5 + 4 
86*x^6 + 54*x^7 + E^10*(-2*x^2 - 2*x^3 + 54*x^4 + 18*x^5) + E^5*(2*x - 36* 
x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) + (144*x + 594*x^2 - 4140*x^3 - 
 6*E^15*x^3 - 4356*x^4 - 1458*x^5 - 162*x^6 + E^10*(2*x + 6*x^2 - 162*x^3 
- 54*x^4) + E^5*(34*x + 120*x^2 - 1434*x^3 - 972*x^4 - 162*x^5))*Log[x] + 
(-324*x + 4212*x^2 + 6*E^15*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5 + E^10*(-4 
*x + 162*x^2 + 54*x^3) + E^5*(-72*x + 1440*x^2 + 972*x^3 + 162*x^4))*Log[x 
]^2 + (-1458*x - 2*E^15*x - 1458*x^2 - 486*x^3 - 54*x^4 + E^10*(-54*x - 18 
*x^2) + E^5*(-486*x - 324*x^2 - 54*x^3))*Log[x]^3)/(-729*x^3 - E^15*x^3 - 
729*x^4 - 243*x^5 - 27*x^6 + E^10*(-27*x^3 - 9*x^4) + E^5*(-243*x^3 - 162* 
x^4 - 27*x^5) + (2187*x^2 + 3*E^15*x^2 + 2187*x^3 + 729*x^4 + 81*x^5 + E^1 
0*(81*x^2 + 27*x^3) + E^5*(729*x^2 + 486*x^3 + 81*x^4))*Log[x] + (-2187*x 
- 3*E^15*x - 2187*x^2 - 729*x^3 - 81*x^4 + E^10*(-81*x - 27*x^2) + E^5*(-7 
29*x - 486*x^2 - 81*x^3))*Log[x]^2 + (729 + E^15 + 729*x + 243*x^2 + 27*x^ 
3 + E^10*(27 + 9*x) + E^5*(243 + 162*x + 27*x^2))*Log[x]^3),x]
 

Output:

-(x^2*(1 + 1/((9 + E^5 + 3*x)^2*(x - Log[x])^2) + 2/((9 + E^5 + 3*x)*(-x + 
 Log[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.

\(\displaystyle \int \frac {54 x^7+486 x^6+1458 x^5+2 e^{15} x^4+1386 x^4-276 x^3-156 x^2+\left (-54 x^4-486 x^3-1458 x^2+e^{10} \left (-18 x^2-54 x\right )+e^5 \left (-54 x^3-324 x^2-486 x\right )-2 e^{15} x-1458 x\right ) \log ^3(x)+e^{10} \left (18 x^5+54 x^4-2 x^3-2 x^2\right )+\left (162 x^5+1458 x^4+4356 x^3+6 e^{15} x^2+4212 x^2+e^{10} \left (54 x^3+162 x^2-4 x\right )+e^5 \left (162 x^4+972 x^3+1440 x^2-72 x\right )-324 x\right ) \log ^2(x)+e^5 \left (54 x^6+324 x^5+480 x^4-48 x^3-36 x^2+2 x\right )+\left (-162 x^6-1458 x^5-4356 x^4-6 e^{15} x^3-4140 x^3+594 x^2+e^{10} \left (-54 x^4-162 x^3+6 x^2+2 x\right )+e^5 \left (-162 x^5-972 x^4-1434 x^3+120 x^2+34 x\right )+144 x\right ) \log (x)+18 x}{-27 x^6-243 x^5-729 x^4-e^{15} x^3-729 x^3+e^{10} \left (-9 x^4-27 x^3\right )+\left (27 x^3+243 x^2+e^5 \left (27 x^2+162 x+243\right )+729 x+e^{10} (9 x+27)+e^{15}+729\right ) \log ^3(x)+e^5 \left (-27 x^5-162 x^4-243 x^3\right )+\left (-81 x^4-729 x^3-2187 x^2+e^{10} \left (-27 x^2-81 x\right )+e^5 \left (-81 x^3-486 x^2-729 x\right )-3 e^{15} x-2187 x\right ) \log ^2(x)+\left (81 x^5+729 x^4+2187 x^3+3 e^{15} x^2+2187 x^2+e^{10} \left (27 x^3+81 x^2\right )+e^5 \left (81 x^4+486 x^3+729 x^2\right )\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {54 x^7+486 x^6+1458 x^5+2 e^{15} x^4+1386 x^4-276 x^3-156 x^2+\left (-54 x^4-486 x^3-1458 x^2+e^{10} \left (-18 x^2-54 x\right )+e^5 \left (-54 x^3-324 x^2-486 x\right )-2 e^{15} x-1458 x\right ) \log ^3(x)+e^{10} \left (18 x^5+54 x^4-2 x^3-2 x^2\right )+\left (162 x^5+1458 x^4+4356 x^3+6 e^{15} x^2+4212 x^2+e^{10} \left (54 x^3+162 x^2-4 x\right )+e^5 \left (162 x^4+972 x^3+1440 x^2-72 x\right )-324 x\right ) \log ^2(x)+e^5 \left (54 x^6+324 x^5+480 x^4-48 x^3-36 x^2+2 x\right )+\left (-162 x^6-1458 x^5-4356 x^4-6 e^{15} x^3-4140 x^3+594 x^2+e^{10} \left (-54 x^4-162 x^3+6 x^2+2 x\right )+e^5 \left (-162 x^5-972 x^4-1434 x^3+120 x^2+34 x\right )+144 x\right ) \log (x)+18 x}{-27 x^6-243 x^5-729 x^4+\left (-729-e^{15}\right ) x^3+e^{10} \left (-9 x^4-27 x^3\right )+\left (27 x^3+243 x^2+e^5 \left (27 x^2+162 x+243\right )+729 x+e^{10} (9 x+27)+e^{15}+729\right ) \log ^3(x)+e^5 \left (-27 x^5-162 x^4-243 x^3\right )+\left (-81 x^4-729 x^3-2187 x^2+e^{10} \left (-27 x^2-81 x\right )+e^5 \left (-81 x^3-486 x^2-729 x\right )-3 e^{15} x-2187 x\right ) \log ^2(x)+\left (81 x^5+729 x^4+2187 x^3+3 e^{15} x^2+2187 x^2+e^{10} \left (27 x^3+81 x^2\right )+e^5 \left (81 x^4+486 x^3+729 x^2\right )\right ) \log (x)}dx\)

\(\Big \downarrow \) 6

\(\displaystyle \int \frac {54 x^7+486 x^6+1458 x^5+\left (1386+2 e^{15}\right ) x^4-276 x^3-156 x^2+\left (-54 x^4-486 x^3-1458 x^2+e^{10} \left (-18 x^2-54 x\right )+e^5 \left (-54 x^3-324 x^2-486 x\right )-2 e^{15} x-1458 x\right ) \log ^3(x)+e^{10} \left (18 x^5+54 x^4-2 x^3-2 x^2\right )+\left (162 x^5+1458 x^4+4356 x^3+6 e^{15} x^2+4212 x^2+e^{10} \left (54 x^3+162 x^2-4 x\right )+e^5 \left (162 x^4+972 x^3+1440 x^2-72 x\right )-324 x\right ) \log ^2(x)+e^5 \left (54 x^6+324 x^5+480 x^4-48 x^3-36 x^2+2 x\right )+\left (-162 x^6-1458 x^5-4356 x^4-6 e^{15} x^3-4140 x^3+594 x^2+e^{10} \left (-54 x^4-162 x^3+6 x^2+2 x\right )+e^5 \left (-162 x^5-972 x^4-1434 x^3+120 x^2+34 x\right )+144 x\right ) \log (x)+18 x}{-27 x^6-243 x^5-729 x^4+\left (-729-e^{15}\right ) x^3+e^{10} \left (-9 x^4-27 x^3\right )+\left (27 x^3+243 x^2+e^5 \left (27 x^2+162 x+243\right )+729 x+e^{10} (9 x+27)+e^{15}+729\right ) \log ^3(x)+e^5 \left (-27 x^5-162 x^4-243 x^3\right )+\left (-81 x^4-729 x^3-2187 x^2+e^{10} \left (-27 x^2-81 x\right )+e^5 \left (-81 x^3-486 x^2-729 x\right )-3 e^{15} x-2187 x\right ) \log ^2(x)+\left (81 x^5+729 x^4+2187 x^3+3 e^{15} x^2+2187 x^2+e^{10} \left (27 x^3+81 x^2\right )+e^5 \left (81 x^4+486 x^3+729 x^2\right )\right ) \log (x)}dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {2 x \left (-e^{15} x^3-e^{10} \left (9 x^3+27 x^2-x-1\right ) x-\left (e^{10} \left (27 x^2+81 x-2\right )+9 e^5 \left (9 x^3+54 x^2+80 x-4\right )+9 \left (9 x^4+81 x^3+242 x^2+234 x-18\right )+3 e^{15} x\right ) \log ^2(x)-e^5 \left (27 x^5+162 x^4+240 x^3-24 x^2-18 x+1\right )+\left (3 e^{15} x^2+e^{10} \left (27 x^3+81 x^2-3 x-1\right )+e^5 \left (81 x^4+486 x^3+717 x^2-60 x-17\right )+9 \left (9 x^5+81 x^4+242 x^3+230 x^2-33 x-8\right )\right ) \log (x)-3 \left (9 x^6+81 x^5+243 x^4+231 x^3-46 x^2-26 x+3\right )+\left (3 x+e^5+9\right )^3 \log ^3(x)\right )}{\left (3 x+e^5+9\right )^3 (x-\log (x))^3}dx\)

\(\Big \downarrow \) 27

\(\displaystyle 2 \int -\frac {x \left (e^{15} x^3-e^{10} \left (-9 x^3-27 x^2+x+1\right ) x-\left (3 x+e^5+9\right )^3 \log ^3(x)+\left (3 e^{15} x-e^{10} \left (-27 x^2-81 x+2\right )-9 e^5 \left (-9 x^3-54 x^2-80 x+4\right )-9 \left (-9 x^4-81 x^3-242 x^2-234 x+18\right )\right ) \log ^2(x)+e^5 \left (27 x^5+162 x^4+240 x^3-24 x^2-18 x+1\right )+3 \left (9 x^6+81 x^5+243 x^4+231 x^3-46 x^2-26 x+3\right )-\left (3 e^{15} x^2-e^{10} \left (-27 x^3-81 x^2+3 x+1\right )-e^5 \left (-81 x^4-486 x^3-717 x^2+60 x+17\right )-9 \left (-9 x^5-81 x^4-242 x^3-230 x^2+33 x+8\right )\right ) \log (x)\right )}{\left (3 x+e^5+9\right )^3 (x-\log (x))^3}dx\)

\(\Big \downarrow \) 25

\(\displaystyle -2 \int \frac {x \left (e^{15} x^3-e^{10} \left (-9 x^3-27 x^2+x+1\right ) x-\left (3 x+e^5+9\right )^3 \log ^3(x)+\left (3 e^{15} x-e^{10} \left (-27 x^2-81 x+2\right )-9 e^5 \left (-9 x^3-54 x^2-80 x+4\right )-9 \left (-9 x^4-81 x^3-242 x^2-234 x+18\right )\right ) \log ^2(x)+e^5 \left (27 x^5+162 x^4+240 x^3-24 x^2-18 x+1\right )+3 \left (9 x^6+81 x^5+243 x^4+231 x^3-46 x^2-26 x+3\right )-\left (3 e^{15} x^2-e^{10} \left (-27 x^3-81 x^2+3 x+1\right )-e^5 \left (-81 x^4-486 x^3-717 x^2+60 x+17\right )-9 \left (-9 x^5-81 x^4-242 x^3-230 x^2+33 x+8\right )\right ) \log (x)\right )}{\left (3 x+e^5+9\right )^3 (x-\log (x))^3}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -2 \int \left (-\frac {\left (3 x+2 e^5+18\right ) x}{\left (3 x+e^5+9\right )^2 (x-\log (x))}+\frac {\left (9 x^3+3 \left (15+2 e^5\right ) x^2+\left (27+12 e^5+e^{10}\right ) x-e^{10}-17 e^5-72\right ) x}{\left (3 x+e^5+9\right )^3 (x-\log (x))^2}-\frac {(x-1) x}{\left (3 x+e^5+9\right )^2 (x-\log (x))^3}+x\right )dx\)

\(\Big \downarrow \) 2009

\(\displaystyle -2 \left (-\frac {1}{9} \int \frac {1}{(x-\log (x))^3}dx-\frac {1}{9} \left (108+21 e^5+e^{10}\right ) \int \frac {1}{\left (3 x+e^5+9\right )^2 (x-\log (x))^3}dx+\frac {1}{9} \left (21+2 e^5\right ) \int \frac {1}{\left (3 x+e^5+9\right ) (x-\log (x))^3}dx-\frac {1}{9} \left (12+e^5\right ) \int \frac {1}{(x-\log (x))^2}dx+\frac {1}{3} \int \frac {x}{(x-\log (x))^2}dx-\frac {1}{3} \left (9+e^5\right )^2 \int \frac {1}{\left (3 x+e^5+9\right )^3 (x-\log (x))^2}dx+\frac {1}{3} \left (9+e^5\right ) \int \frac {1}{\left (3 x+e^5+9\right )^2 (x-\log (x))^2}dx+\frac {1}{9} \left (108+21 e^5+e^{10}\right ) \int \frac {1}{\left (3 x+e^5+9\right ) (x-\log (x))^2}dx-\frac {1}{3} \int \frac {1}{x-\log (x)}dx+\frac {1}{3} \left (9+e^5\right )^2 \int \frac {1}{\left (3 x+e^5+9\right )^2 (x-\log (x))}dx+\frac {x^2}{2}\right )\)

Input:

Int[(18*x - 156*x^2 - 276*x^3 + 1386*x^4 + 2*E^15*x^4 + 1458*x^5 + 486*x^6 
 + 54*x^7 + E^10*(-2*x^2 - 2*x^3 + 54*x^4 + 18*x^5) + E^5*(2*x - 36*x^2 - 
48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) + (144*x + 594*x^2 - 4140*x^3 - 6*E^1 
5*x^3 - 4356*x^4 - 1458*x^5 - 162*x^6 + E^10*(2*x + 6*x^2 - 162*x^3 - 54*x 
^4) + E^5*(34*x + 120*x^2 - 1434*x^3 - 972*x^4 - 162*x^5))*Log[x] + (-324* 
x + 4212*x^2 + 6*E^15*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5 + E^10*(-4*x + 1 
62*x^2 + 54*x^3) + E^5*(-72*x + 1440*x^2 + 972*x^3 + 162*x^4))*Log[x]^2 + 
(-1458*x - 2*E^15*x - 1458*x^2 - 486*x^3 - 54*x^4 + E^10*(-54*x - 18*x^2) 
+ E^5*(-486*x - 324*x^2 - 54*x^3))*Log[x]^3)/(-729*x^3 - E^15*x^3 - 729*x^ 
4 - 243*x^5 - 27*x^6 + E^10*(-27*x^3 - 9*x^4) + E^5*(-243*x^3 - 162*x^4 - 
27*x^5) + (2187*x^2 + 3*E^15*x^2 + 2187*x^3 + 729*x^4 + 81*x^5 + E^10*(81* 
x^2 + 27*x^3) + E^5*(729*x^2 + 486*x^3 + 81*x^4))*Log[x] + (-2187*x - 3*E^ 
15*x - 2187*x^2 - 729*x^3 - 81*x^4 + E^10*(-81*x - 27*x^2) + E^5*(-729*x - 
 486*x^2 - 81*x^3))*Log[x]^2 + (729 + E^15 + 729*x + 243*x^2 + 27*x^3 + E^ 
10*(27 + 9*x) + E^5*(243 + 162*x + 27*x^2))*Log[x]^3),x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(175\) vs. \(2(27)=54\).

Time = 2.43 (sec) , antiderivative size = 176, normalized size of antiderivative = 6.29

\[-x^{2}-\frac {2 \,{\mathrm e}^{10} \ln \left (x \right )^{2}-4 \ln \left (x \right ) {\mathrm e}^{10+\ln \left (x \right )}+2 \,{\mathrm e}^{10+2 \ln \left (x \right )}+12 \ln \left (x \right )^{2} {\mathrm e}^{5+\ln \left (x \right )}-18 \ln \left (x \right ) {\mathrm e}^{5+2 \ln \left (x \right )}+6 \,{\mathrm e}^{3 \ln \left (x \right )+5}+18 x^{2} \ln \left (x \right )^{2}-18 x^{3} \ln \left (x \right )+36 \,{\mathrm e}^{5} \ln \left (x \right )^{2}-72 \ln \left (x \right ) {\mathrm e}^{5+\ln \left (x \right )}+36 \,{\mathrm e}^{5+2 \ln \left (x \right )}+108 x \ln \left (x \right )^{2}-162 x^{2} \ln \left (x \right )+54 x^{3}+162 \ln \left (x \right )^{2}-324 x \ln \left (x \right )+165 x^{2}}{3 \left ({\mathrm e}^{5} \ln \left (x \right )-{\mathrm e}^{5+\ln \left (x \right )}+3 x \ln \left (x \right )-3 x^{2}+9 \ln \left (x \right )-9 x \right )^{2}}\]

Input:

int(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5) 
-54*x^4-486*x^3-1458*x^2-1458*x)*ln(x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2-4 
*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^4+4356* 
x^3+4212*x^2-324*x)*ln(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x)*e 
xp(5)^2+(-162*x^5-972*x^4-1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5-4 
356*x^4-4140*x^3+594*x^2+144*x)*ln(x)+2*x^4*exp(5)^3+(18*x^5+54*x^4-2*x^3- 
2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^7+4 
86*x^6+1458*x^5+1386*x^4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp(5)^ 
2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*ln(x)^3+(-3*x*exp(5) 
^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x^3-2 
187*x^2-2187*x)*ln(x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81*x^4+4 
86*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*ln(x)-x^3*exp(5)^ 
3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-243*x^5 
-729*x^4-729*x^3),x)
 

Output:

-x^2-1/3*(2*exp(10)*ln(x)^2-4*ln(x)*exp(10+ln(x))+2*exp(10+2*ln(x))+12*ln( 
x)^2*exp(5+ln(x))-18*ln(x)*exp(5+2*ln(x))+6*exp(3*ln(x)+5)+18*x^2*ln(x)^2- 
18*x^3*ln(x)+36*exp(5)*ln(x)^2-72*ln(x)*exp(5+ln(x))+36*exp(5+2*ln(x))+108 
*x*ln(x)^2-162*x^2*ln(x)+54*x^3+162*ln(x)^2-324*x*ln(x)+165*x^2)/(exp(5)*l 
n(x)-exp(5+ln(x))+3*x*ln(x)-3*x^2+9*ln(x)-9*x)^2
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 236 vs. \(2 (28) = 56\).

Time = 0.12 (sec) , antiderivative size = 236, normalized size of antiderivative = 8.43 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=-\frac {9 \, x^{6} + 54 \, x^{5} + x^{4} e^{10} + 75 \, x^{4} - 18 \, x^{3} + {\left (9 \, x^{4} + 54 \, x^{3} + x^{2} e^{10} + 81 \, x^{2} + 6 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5}\right )} \log \left (x\right )^{2} + x^{2} + 2 \, {\left (3 \, x^{5} + 9 \, x^{4} - x^{3}\right )} e^{5} - 2 \, {\left (9 \, x^{5} + 54 \, x^{4} + x^{3} e^{10} + 78 \, x^{3} - 9 \, x^{2} + {\left (6 \, x^{4} + 18 \, x^{3} - x^{2}\right )} e^{5}\right )} \log \left (x\right )}{9 \, x^{4} + 54 \, x^{3} + x^{2} e^{10} + {\left (9 \, x^{2} + 6 \, {\left (x + 3\right )} e^{5} + 54 \, x + e^{10} + 81\right )} \log \left (x\right )^{2} + 81 \, x^{2} + 6 \, {\left (x^{3} + 3 \, x^{2}\right )} e^{5} - 2 \, {\left (9 \, x^{3} + 54 \, x^{2} + x e^{10} + 6 \, {\left (x^{2} + 3 \, x\right )} e^{5} + 81 \, x\right )} \log \left (x\right )} \] Input:

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)* 
exp(5)-54*x^4-486*x^3-1458*x^2-1458*x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+16 
2*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^ 
4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^ 
2+2*x)*exp(5)^2+(-162*x^5-972*x^4-1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-14 
58*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+54*x 
^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5) 
+54*x^7+486*x^6+1458*x^5+1386*x^4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27 
)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x)^3+(- 
3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4 
-729*x^3-2187*x^2-2187*x)*log(x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^ 
2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*log(x) 
-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27 
*x^6-243*x^5-729*x^4-729*x^3),x, algorithm="fricas")
 

Output:

-(9*x^6 + 54*x^5 + x^4*e^10 + 75*x^4 - 18*x^3 + (9*x^4 + 54*x^3 + x^2*e^10 
 + 81*x^2 + 6*(x^3 + 3*x^2)*e^5)*log(x)^2 + x^2 + 2*(3*x^5 + 9*x^4 - x^3)* 
e^5 - 2*(9*x^5 + 54*x^4 + x^3*e^10 + 78*x^3 - 9*x^2 + (6*x^4 + 18*x^3 - x^ 
2)*e^5)*log(x))/(9*x^4 + 54*x^3 + x^2*e^10 + (9*x^2 + 6*(x + 3)*e^5 + 54*x 
 + e^10 + 81)*log(x)^2 + 81*x^2 + 6*(x^3 + 3*x^2)*e^5 - 2*(9*x^3 + 54*x^2 
+ x*e^10 + 6*(x^2 + 3*x)*e^5 + 81*x)*log(x))
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 158 vs. \(2 (19) = 38\).

Time = 0.26 (sec) , antiderivative size = 158, normalized size of antiderivative = 5.64 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=- x^{2} + \frac {6 x^{4} + 18 x^{3} + 2 x^{3} e^{5} - x^{2} + \left (- 6 x^{3} - 2 x^{2} e^{5} - 18 x^{2}\right ) \log {\left (x \right )}}{9 x^{4} + 54 x^{3} + 6 x^{3} e^{5} + 81 x^{2} + 18 x^{2} e^{5} + x^{2} e^{10} + \left (9 x^{2} + 54 x + 6 x e^{5} + 81 + 18 e^{5} + e^{10}\right ) \log {\left (x \right )}^{2} + \left (- 18 x^{3} - 12 x^{2} e^{5} - 108 x^{2} - 2 x e^{10} - 36 x e^{5} - 162 x\right ) \log {\left (x \right )}} \] Input:

integrate(((-2*x*exp(5)**3+(-18*x**2-54*x)*exp(5)**2+(-54*x**3-324*x**2-48 
6*x)*exp(5)-54*x**4-486*x**3-1458*x**2-1458*x)*ln(x)**3+(6*x**2*exp(5)**3+ 
(54*x**3+162*x**2-4*x)*exp(5)**2+(162*x**4+972*x**3+1440*x**2-72*x)*exp(5) 
+162*x**5+1458*x**4+4356*x**3+4212*x**2-324*x)*ln(x)**2+(-6*x**3*exp(5)**3 
+(-54*x**4-162*x**3+6*x**2+2*x)*exp(5)**2+(-162*x**5-972*x**4-1434*x**3+12 
0*x**2+34*x)*exp(5)-162*x**6-1458*x**5-4356*x**4-4140*x**3+594*x**2+144*x) 
*ln(x)+2*x**4*exp(5)**3+(18*x**5+54*x**4-2*x**3-2*x**2)*exp(5)**2+(54*x**6 
+324*x**5+480*x**4-48*x**3-36*x**2+2*x)*exp(5)+54*x**7+486*x**6+1458*x**5+ 
1386*x**4-276*x**3-156*x**2+18*x)/((exp(5)**3+(9*x+27)*exp(5)**2+(27*x**2+ 
162*x+243)*exp(5)+27*x**3+243*x**2+729*x+729)*ln(x)**3+(-3*x*exp(5)**3+(-2 
7*x**2-81*x)*exp(5)**2+(-81*x**3-486*x**2-729*x)*exp(5)-81*x**4-729*x**3-2 
187*x**2-2187*x)*ln(x)**2+(3*x**2*exp(5)**3+(27*x**3+81*x**2)*exp(5)**2+(8 
1*x**4+486*x**3+729*x**2)*exp(5)+81*x**5+729*x**4+2187*x**3+2187*x**2)*ln( 
x)-x**3*exp(5)**3+(-9*x**4-27*x**3)*exp(5)**2+(-27*x**5-162*x**4-243*x**3) 
*exp(5)-27*x**6-243*x**5-729*x**4-729*x**3),x)
 

Output:

-x**2 + (6*x**4 + 18*x**3 + 2*x**3*exp(5) - x**2 + (-6*x**3 - 2*x**2*exp(5 
) - 18*x**2)*log(x))/(9*x**4 + 54*x**3 + 6*x**3*exp(5) + 81*x**2 + 18*x**2 
*exp(5) + x**2*exp(10) + (9*x**2 + 54*x + 6*x*exp(5) + 81 + 18*exp(5) + ex 
p(10))*log(x)**2 + (-18*x**3 - 12*x**2*exp(5) - 108*x**2 - 2*x*exp(10) - 3 
6*x*exp(5) - 162*x)*log(x))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 196 vs. \(2 (28) = 56\).

Time = 0.17 (sec) , antiderivative size = 196, normalized size of antiderivative = 7.00 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=-\frac {9 \, x^{6} + 6 \, x^{5} {\left (e^{5} + 9\right )} + x^{4} {\left (e^{10} + 18 \, e^{5} + 75\right )} - 2 \, x^{3} {\left (e^{5} + 9\right )} + {\left (9 \, x^{4} + 6 \, x^{3} {\left (e^{5} + 9\right )} + x^{2} {\left (e^{10} + 18 \, e^{5} + 81\right )}\right )} \log \left (x\right )^{2} + x^{2} - 2 \, {\left (9 \, x^{5} + 6 \, x^{4} {\left (e^{5} + 9\right )} + x^{3} {\left (e^{10} + 18 \, e^{5} + 78\right )} - x^{2} {\left (e^{5} + 9\right )}\right )} \log \left (x\right )}{9 \, x^{4} + 6 \, x^{3} {\left (e^{5} + 9\right )} + x^{2} {\left (e^{10} + 18 \, e^{5} + 81\right )} + {\left (9 \, x^{2} + 6 \, x {\left (e^{5} + 9\right )} + e^{10} + 18 \, e^{5} + 81\right )} \log \left (x\right )^{2} - 2 \, {\left (9 \, x^{3} + 6 \, x^{2} {\left (e^{5} + 9\right )} + x {\left (e^{10} + 18 \, e^{5} + 81\right )}\right )} \log \left (x\right )} \] Input:

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)* 
exp(5)-54*x^4-486*x^3-1458*x^2-1458*x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+16 
2*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^ 
4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^ 
2+2*x)*exp(5)^2+(-162*x^5-972*x^4-1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-14 
58*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+54*x 
^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5) 
+54*x^7+486*x^6+1458*x^5+1386*x^4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27 
)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x)^3+(- 
3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4 
-729*x^3-2187*x^2-2187*x)*log(x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^ 
2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*log(x) 
-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27 
*x^6-243*x^5-729*x^4-729*x^3),x, algorithm="maxima")
 

Output:

-(9*x^6 + 6*x^5*(e^5 + 9) + x^4*(e^10 + 18*e^5 + 75) - 2*x^3*(e^5 + 9) + ( 
9*x^4 + 6*x^3*(e^5 + 9) + x^2*(e^10 + 18*e^5 + 81))*log(x)^2 + x^2 - 2*(9* 
x^5 + 6*x^4*(e^5 + 9) + x^3*(e^10 + 18*e^5 + 78) - x^2*(e^5 + 9))*log(x))/ 
(9*x^4 + 6*x^3*(e^5 + 9) + x^2*(e^10 + 18*e^5 + 81) + (9*x^2 + 6*x*(e^5 + 
9) + e^10 + 18*e^5 + 81)*log(x)^2 - 2*(9*x^3 + 6*x^2*(e^5 + 9) + x*(e^10 + 
 18*e^5 + 81))*log(x))
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 302 vs. \(2 (28) = 56\).

Time = 0.26 (sec) , antiderivative size = 302, normalized size of antiderivative = 10.79 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=-\frac {9 \, x^{6} + 6 \, x^{5} e^{5} - 18 \, x^{5} \log \left (x\right ) - 12 \, x^{4} e^{5} \log \left (x\right ) + 9 \, x^{4} \log \left (x\right )^{2} + 6 \, x^{3} e^{5} \log \left (x\right )^{2} + 54 \, x^{5} + x^{4} e^{10} + 18 \, x^{4} e^{5} - 108 \, x^{4} \log \left (x\right ) - 2 \, x^{3} e^{10} \log \left (x\right ) - 36 \, x^{3} e^{5} \log \left (x\right ) + 54 \, x^{3} \log \left (x\right )^{2} + x^{2} e^{10} \log \left (x\right )^{2} + 18 \, x^{2} e^{5} \log \left (x\right )^{2} + 75 \, x^{4} - 2 \, x^{3} e^{5} - 156 \, x^{3} \log \left (x\right ) + 2 \, x^{2} e^{5} \log \left (x\right ) + 81 \, x^{2} \log \left (x\right )^{2} - 18 \, x^{3} + 18 \, x^{2} \log \left (x\right ) + x^{2}}{9 \, x^{4} + 6 \, x^{3} e^{5} - 18 \, x^{3} \log \left (x\right ) - 12 \, x^{2} e^{5} \log \left (x\right ) + 9 \, x^{2} \log \left (x\right )^{2} + 6 \, x e^{5} \log \left (x\right )^{2} + 54 \, x^{3} + x^{2} e^{10} + 18 \, x^{2} e^{5} - 108 \, x^{2} \log \left (x\right ) - 2 \, x e^{10} \log \left (x\right ) - 36 \, x e^{5} \log \left (x\right ) + 54 \, x \log \left (x\right )^{2} + e^{10} \log \left (x\right )^{2} + 18 \, e^{5} \log \left (x\right )^{2} + 81 \, x^{2} - 162 \, x \log \left (x\right ) + 81 \, \log \left (x\right )^{2}} \] Input:

integrate(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)* 
exp(5)-54*x^4-486*x^3-1458*x^2-1458*x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+16 
2*x^2-4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^ 
4+4356*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^ 
2+2*x)*exp(5)^2+(-162*x^5-972*x^4-1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-14 
58*x^5-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+54*x 
^4-2*x^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5) 
+54*x^7+486*x^6+1458*x^5+1386*x^4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27 
)*exp(5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x)^3+(- 
3*x*exp(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4 
-729*x^3-2187*x^2-2187*x)*log(x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^ 
2+(81*x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*log(x) 
-x^3*exp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27 
*x^6-243*x^5-729*x^4-729*x^3),x, algorithm="giac")
 

Output:

-(9*x^6 + 6*x^5*e^5 - 18*x^5*log(x) - 12*x^4*e^5*log(x) + 9*x^4*log(x)^2 + 
 6*x^3*e^5*log(x)^2 + 54*x^5 + x^4*e^10 + 18*x^4*e^5 - 108*x^4*log(x) - 2* 
x^3*e^10*log(x) - 36*x^3*e^5*log(x) + 54*x^3*log(x)^2 + x^2*e^10*log(x)^2 
+ 18*x^2*e^5*log(x)^2 + 75*x^4 - 2*x^3*e^5 - 156*x^3*log(x) + 2*x^2*e^5*lo 
g(x) + 81*x^2*log(x)^2 - 18*x^3 + 18*x^2*log(x) + x^2)/(9*x^4 + 6*x^3*e^5 
- 18*x^3*log(x) - 12*x^2*e^5*log(x) + 9*x^2*log(x)^2 + 6*x*e^5*log(x)^2 + 
54*x^3 + x^2*e^10 + 18*x^2*e^5 - 108*x^2*log(x) - 2*x*e^10*log(x) - 36*x*e 
^5*log(x) + 54*x*log(x)^2 + e^10*log(x)^2 + 18*e^5*log(x)^2 + 81*x^2 - 162 
*x*log(x) + 81*log(x)^2)
 

Mupad [F(-1)]

Timed out. \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=\int -\frac {18\,x+{\mathrm {e}}^5\,\left (54\,x^6+324\,x^5+480\,x^4-48\,x^3-36\,x^2+2\,x\right )-{\ln \left (x\right )}^3\,\left (1458\,x+{\mathrm {e}}^{10}\,\left (18\,x^2+54\,x\right )+2\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (54\,x^3+324\,x^2+486\,x\right )+1458\,x^2+486\,x^3+54\,x^4\right )+{\ln \left (x\right )}^2\,\left ({\mathrm {e}}^{10}\,\left (54\,x^3+162\,x^2-4\,x\right )-324\,x+6\,x^2\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (162\,x^4+972\,x^3+1440\,x^2-72\,x\right )+4212\,x^2+4356\,x^3+1458\,x^4+162\,x^5\right )+2\,x^4\,{\mathrm {e}}^{15}-\ln \left (x\right )\,\left (6\,x^3\,{\mathrm {e}}^{15}-144\,x-{\mathrm {e}}^{10}\,\left (-54\,x^4-162\,x^3+6\,x^2+2\,x\right )+{\mathrm {e}}^5\,\left (162\,x^5+972\,x^4+1434\,x^3-120\,x^2-34\,x\right )-594\,x^2+4140\,x^3+4356\,x^4+1458\,x^5+162\,x^6\right )-156\,x^2-276\,x^3+1386\,x^4+1458\,x^5+486\,x^6+54\,x^7-{\mathrm {e}}^{10}\,\left (-18\,x^5-54\,x^4+2\,x^3+2\,x^2\right )}{{\ln \left (x\right )}^2\,\left (2187\,x+{\mathrm {e}}^{10}\,\left (27\,x^2+81\,x\right )+3\,x\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (81\,x^3+486\,x^2+729\,x\right )+2187\,x^2+729\,x^3+81\,x^4\right )-\ln \left (x\right )\,\left ({\mathrm {e}}^{10}\,\left (27\,x^3+81\,x^2\right )+3\,x^2\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (81\,x^4+486\,x^3+729\,x^2\right )+2187\,x^2+2187\,x^3+729\,x^4+81\,x^5\right )+{\mathrm {e}}^{10}\,\left (9\,x^4+27\,x^3\right )+x^3\,{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (27\,x^5+162\,x^4+243\,x^3\right )+729\,x^3+729\,x^4+243\,x^5+27\,x^6-{\ln \left (x\right )}^3\,\left (729\,x+{\mathrm {e}}^{15}+{\mathrm {e}}^5\,\left (27\,x^2+162\,x+243\right )+243\,x^2+27\,x^3+{\mathrm {e}}^{10}\,\left (9\,x+27\right )+729\right )} \,d x \] Input:

int(-(18*x + exp(5)*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) - 
 log(x)^3*(1458*x + exp(10)*(54*x + 18*x^2) + 2*x*exp(15) + exp(5)*(486*x 
+ 324*x^2 + 54*x^3) + 1458*x^2 + 486*x^3 + 54*x^4) + log(x)^2*(exp(10)*(16 
2*x^2 - 4*x + 54*x^3) - 324*x + 6*x^2*exp(15) + exp(5)*(1440*x^2 - 72*x + 
972*x^3 + 162*x^4) + 4212*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5) + 2*x^4*exp 
(15) - log(x)*(6*x^3*exp(15) - 144*x - exp(10)*(2*x + 6*x^2 - 162*x^3 - 54 
*x^4) + exp(5)*(1434*x^3 - 120*x^2 - 34*x + 972*x^4 + 162*x^5) - 594*x^2 + 
 4140*x^3 + 4356*x^4 + 1458*x^5 + 162*x^6) - 156*x^2 - 276*x^3 + 1386*x^4 
+ 1458*x^5 + 486*x^6 + 54*x^7 - exp(10)*(2*x^2 + 2*x^3 - 54*x^4 - 18*x^5)) 
/(log(x)^2*(2187*x + exp(10)*(81*x + 27*x^2) + 3*x*exp(15) + exp(5)*(729*x 
 + 486*x^2 + 81*x^3) + 2187*x^2 + 729*x^3 + 81*x^4) - log(x)*(exp(10)*(81* 
x^2 + 27*x^3) + 3*x^2*exp(15) + exp(5)*(729*x^2 + 486*x^3 + 81*x^4) + 2187 
*x^2 + 2187*x^3 + 729*x^4 + 81*x^5) + exp(10)*(27*x^3 + 9*x^4) + x^3*exp(1 
5) + exp(5)*(243*x^3 + 162*x^4 + 27*x^5) + 729*x^3 + 729*x^4 + 243*x^5 + 2 
7*x^6 - log(x)^3*(729*x + exp(15) + exp(5)*(162*x + 27*x^2 + 243) + 243*x^ 
2 + 27*x^3 + exp(10)*(9*x + 27) + 729)),x)
 

Output:

int(-(18*x + exp(5)*(2*x - 36*x^2 - 48*x^3 + 480*x^4 + 324*x^5 + 54*x^6) - 
 log(x)^3*(1458*x + exp(10)*(54*x + 18*x^2) + 2*x*exp(15) + exp(5)*(486*x 
+ 324*x^2 + 54*x^3) + 1458*x^2 + 486*x^3 + 54*x^4) + log(x)^2*(exp(10)*(16 
2*x^2 - 4*x + 54*x^3) - 324*x + 6*x^2*exp(15) + exp(5)*(1440*x^2 - 72*x + 
972*x^3 + 162*x^4) + 4212*x^2 + 4356*x^3 + 1458*x^4 + 162*x^5) + 2*x^4*exp 
(15) - log(x)*(6*x^3*exp(15) - 144*x - exp(10)*(2*x + 6*x^2 - 162*x^3 - 54 
*x^4) + exp(5)*(1434*x^3 - 120*x^2 - 34*x + 972*x^4 + 162*x^5) - 594*x^2 + 
 4140*x^3 + 4356*x^4 + 1458*x^5 + 162*x^6) - 156*x^2 - 276*x^3 + 1386*x^4 
+ 1458*x^5 + 486*x^6 + 54*x^7 - exp(10)*(2*x^2 + 2*x^3 - 54*x^4 - 18*x^5)) 
/(log(x)^2*(2187*x + exp(10)*(81*x + 27*x^2) + 3*x*exp(15) + exp(5)*(729*x 
 + 486*x^2 + 81*x^3) + 2187*x^2 + 729*x^3 + 81*x^4) - log(x)*(exp(10)*(81* 
x^2 + 27*x^3) + 3*x^2*exp(15) + exp(5)*(729*x^2 + 486*x^3 + 81*x^4) + 2187 
*x^2 + 2187*x^3 + 729*x^4 + 81*x^5) + exp(10)*(27*x^3 + 9*x^4) + x^3*exp(1 
5) + exp(5)*(243*x^3 + 162*x^4 + 27*x^5) + 729*x^3 + 729*x^4 + 243*x^5 + 2 
7*x^6 - log(x)^3*(729*x + exp(15) + exp(5)*(162*x + 27*x^2 + 243) + 243*x^ 
2 + 27*x^3 + exp(10)*(9*x + 27) + 729)), x)
 

Reduce [B] (verification not implemented)

Time = 0.26 (sec) , antiderivative size = 295, normalized size of antiderivative = 10.54 \[ \int \frac {18 x-156 x^2-276 x^3+1386 x^4+2 e^{15} x^4+1458 x^5+486 x^6+54 x^7+e^{10} \left (-2 x^2-2 x^3+54 x^4+18 x^5\right )+e^5 \left (2 x-36 x^2-48 x^3+480 x^4+324 x^5+54 x^6\right )+\left (144 x+594 x^2-4140 x^3-6 e^{15} x^3-4356 x^4-1458 x^5-162 x^6+e^{10} \left (2 x+6 x^2-162 x^3-54 x^4\right )+e^5 \left (34 x+120 x^2-1434 x^3-972 x^4-162 x^5\right )\right ) \log (x)+\left (-324 x+4212 x^2+6 e^{15} x^2+4356 x^3+1458 x^4+162 x^5+e^{10} \left (-4 x+162 x^2+54 x^3\right )+e^5 \left (-72 x+1440 x^2+972 x^3+162 x^4\right )\right ) \log ^2(x)+\left (-1458 x-2 e^{15} x-1458 x^2-486 x^3-54 x^4+e^{10} \left (-54 x-18 x^2\right )+e^5 \left (-486 x-324 x^2-54 x^3\right )\right ) \log ^3(x)}{-729 x^3-e^{15} x^3-729 x^4-243 x^5-27 x^6+e^{10} \left (-27 x^3-9 x^4\right )+e^5 \left (-243 x^3-162 x^4-27 x^5\right )+\left (2187 x^2+3 e^{15} x^2+2187 x^3+729 x^4+81 x^5+e^{10} \left (81 x^2+27 x^3\right )+e^5 \left (729 x^2+486 x^3+81 x^4\right )\right ) \log (x)+\left (-2187 x-3 e^{15} x-2187 x^2-729 x^3-81 x^4+e^{10} \left (-81 x-27 x^2\right )+e^5 \left (-729 x-486 x^2-81 x^3\right )\right ) \log ^2(x)+\left (729+e^{15}+729 x+243 x^2+27 x^3+e^{10} (27+9 x)+e^5 \left (243+162 x+27 x^2\right )\right ) \log ^3(x)} \, dx=\frac {x^{2} \left (-\mathrm {log}\left (x \right )^{2} e^{10}-6 \mathrm {log}\left (x \right )^{2} e^{5} x -18 \mathrm {log}\left (x \right )^{2} e^{5}-9 \mathrm {log}\left (x \right )^{2} x^{2}-54 \mathrm {log}\left (x \right )^{2} x -81 \mathrm {log}\left (x \right )^{2}+2 \,\mathrm {log}\left (x \right ) e^{10} x +12 \,\mathrm {log}\left (x \right ) e^{5} x^{2}+36 \,\mathrm {log}\left (x \right ) e^{5} x -2 \,\mathrm {log}\left (x \right ) e^{5}+18 \,\mathrm {log}\left (x \right ) x^{3}+108 \,\mathrm {log}\left (x \right ) x^{2}+156 \,\mathrm {log}\left (x \right ) x -18 \,\mathrm {log}\left (x \right )-e^{10} x^{2}-6 e^{5} x^{3}-18 e^{5} x^{2}+2 e^{5} x -9 x^{4}-54 x^{3}-75 x^{2}+18 x -1\right )}{\mathrm {log}\left (x \right )^{2} e^{10}+6 \mathrm {log}\left (x \right )^{2} e^{5} x +18 \mathrm {log}\left (x \right )^{2} e^{5}+9 \mathrm {log}\left (x \right )^{2} x^{2}+54 \mathrm {log}\left (x \right )^{2} x +81 \mathrm {log}\left (x \right )^{2}-2 \,\mathrm {log}\left (x \right ) e^{10} x -12 \,\mathrm {log}\left (x \right ) e^{5} x^{2}-36 \,\mathrm {log}\left (x \right ) e^{5} x -18 \,\mathrm {log}\left (x \right ) x^{3}-108 \,\mathrm {log}\left (x \right ) x^{2}-162 \,\mathrm {log}\left (x \right ) x +e^{10} x^{2}+6 e^{5} x^{3}+18 e^{5} x^{2}+9 x^{4}+54 x^{3}+81 x^{2}} \] Input:

int(((-2*x*exp(5)^3+(-18*x^2-54*x)*exp(5)^2+(-54*x^3-324*x^2-486*x)*exp(5) 
-54*x^4-486*x^3-1458*x^2-1458*x)*log(x)^3+(6*x^2*exp(5)^3+(54*x^3+162*x^2- 
4*x)*exp(5)^2+(162*x^4+972*x^3+1440*x^2-72*x)*exp(5)+162*x^5+1458*x^4+4356 
*x^3+4212*x^2-324*x)*log(x)^2+(-6*x^3*exp(5)^3+(-54*x^4-162*x^3+6*x^2+2*x) 
*exp(5)^2+(-162*x^5-972*x^4-1434*x^3+120*x^2+34*x)*exp(5)-162*x^6-1458*x^5 
-4356*x^4-4140*x^3+594*x^2+144*x)*log(x)+2*x^4*exp(5)^3+(18*x^5+54*x^4-2*x 
^3-2*x^2)*exp(5)^2+(54*x^6+324*x^5+480*x^4-48*x^3-36*x^2+2*x)*exp(5)+54*x^ 
7+486*x^6+1458*x^5+1386*x^4-276*x^3-156*x^2+18*x)/((exp(5)^3+(9*x+27)*exp( 
5)^2+(27*x^2+162*x+243)*exp(5)+27*x^3+243*x^2+729*x+729)*log(x)^3+(-3*x*ex 
p(5)^3+(-27*x^2-81*x)*exp(5)^2+(-81*x^3-486*x^2-729*x)*exp(5)-81*x^4-729*x 
^3-2187*x^2-2187*x)*log(x)^2+(3*x^2*exp(5)^3+(27*x^3+81*x^2)*exp(5)^2+(81* 
x^4+486*x^3+729*x^2)*exp(5)+81*x^5+729*x^4+2187*x^3+2187*x^2)*log(x)-x^3*e 
xp(5)^3+(-9*x^4-27*x^3)*exp(5)^2+(-27*x^5-162*x^4-243*x^3)*exp(5)-27*x^6-2 
43*x^5-729*x^4-729*x^3),x)
 

Output:

(x**2*( - log(x)**2*e**10 - 6*log(x)**2*e**5*x - 18*log(x)**2*e**5 - 9*log 
(x)**2*x**2 - 54*log(x)**2*x - 81*log(x)**2 + 2*log(x)*e**10*x + 12*log(x) 
*e**5*x**2 + 36*log(x)*e**5*x - 2*log(x)*e**5 + 18*log(x)*x**3 + 108*log(x 
)*x**2 + 156*log(x)*x - 18*log(x) - e**10*x**2 - 6*e**5*x**3 - 18*e**5*x** 
2 + 2*e**5*x - 9*x**4 - 54*x**3 - 75*x**2 + 18*x - 1))/(log(x)**2*e**10 + 
6*log(x)**2*e**5*x + 18*log(x)**2*e**5 + 9*log(x)**2*x**2 + 54*log(x)**2*x 
 + 81*log(x)**2 - 2*log(x)*e**10*x - 12*log(x)*e**5*x**2 - 36*log(x)*e**5* 
x - 18*log(x)*x**3 - 108*log(x)*x**2 - 162*log(x)*x + e**10*x**2 + 6*e**5* 
x**3 + 18*e**5*x**2 + 9*x**4 + 54*x**3 + 81*x**2)