\(\int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} (8 e^{29 x} x+e^{33 x} (2 x+33 x^2)+(56 e^{25 x} x+e^{29 x} (16 x+232 x^2)) \log (x)+(168 e^{21 x} x+e^{25 x} (56 x+700 x^2)) \log ^2(x)+(280 e^{17 x} x+e^{21 x} (112 x+1176 x^2)) \log ^3(x)+(280 e^{13 x} x+e^{17 x} (140 x+1190 x^2)) \log ^4(x)+(168 e^{9 x} x+e^{13 x} (112 x+728 x^2)) \log ^5(x)+(56 e^{5 x} x+e^{9 x} (56 x+252 x^2)) \log ^6(x)+(8 e^x x+e^{5 x} (16 x+40 x^2)) \log ^7(x)+e^x (2 x+x^2) \log ^8(x)) \, dx\) [2324]

Optimal result

Integrand size = 370, antiderivative size = 24 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\frac {1}{3} e^{-4+x} x^2 \left (e^{4 x}+\log (x)\right )^8} \] Output:

exp(1/3*exp(x)/exp(4)*(ln(x)+exp(2*x)^2)^8*x^2)
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(107\) vs. \(2(24)=48\).

Time = 0.23 (sec) , antiderivative size = 107, normalized size of antiderivative = 4.46 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\frac {1}{3} e^{-4+x} x^2 \left (e^{32 x}+28 e^{24 x} \log ^2(x)+56 e^{20 x} \log ^3(x)+70 e^{16 x} \log ^4(x)+56 e^{12 x} \log ^5(x)+28 e^{8 x} \log ^6(x)+8 e^{4 x} \log ^7(x)+\log ^8(x)\right )} x^{\frac {8}{3} e^{-4+29 x} x^2} \] Input:

Integrate[(E^(-4 + (E^(33*x)*x^2 + 8*E^(29*x)*x^2*Log[x] + 28*E^(25*x)*x^2 
*Log[x]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13 
*x)*x^2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x* 
x^2*Log[x]^8)/(3*E^4))*(8*E^(29*x)*x + E^(33*x)*(2*x + 33*x^2) + (56*E^(25 
*x)*x + E^(29*x)*(16*x + 232*x^2))*Log[x] + (168*E^(21*x)*x + E^(25*x)*(56 
*x + 700*x^2))*Log[x]^2 + (280*E^(17*x)*x + E^(21*x)*(112*x + 1176*x^2))*L 
og[x]^3 + (280*E^(13*x)*x + E^(17*x)*(140*x + 1190*x^2))*Log[x]^4 + (168*E 
^(9*x)*x + E^(13*x)*(112*x + 728*x^2))*Log[x]^5 + (56*E^(5*x)*x + E^(9*x)* 
(56*x + 252*x^2))*Log[x]^6 + (8*E^x*x + E^(5*x)*(16*x + 40*x^2))*Log[x]^7 
+ E^x*(2*x + x^2)*Log[x]^8))/3,x]
 

Output:

E^((E^(-4 + x)*x^2*(E^(32*x) + 28*E^(24*x)*Log[x]^2 + 56*E^(20*x)*Log[x]^3 
 + 70*E^(16*x)*Log[x]^4 + 56*E^(12*x)*Log[x]^5 + 28*E^(8*x)*Log[x]^6 + 8*E 
^(4*x)*Log[x]^7 + Log[x]^8))/3)*x^((8*E^(-4 + 29*x)*x^2)/3)
 

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.

\(\displaystyle \int \frac {1}{3} \left (e^{33 x} \left (33 x^2+2 x\right )+e^x \left (x^2+2 x\right ) \log ^8(x)+\left (e^{5 x} \left (40 x^2+16 x\right )+8 e^x x\right ) \log ^7(x)+\left (e^{9 x} \left (252 x^2+56 x\right )+56 e^{5 x} x\right ) \log ^6(x)+\left (e^{13 x} \left (728 x^2+112 x\right )+168 e^{9 x} x\right ) \log ^5(x)+\left (e^{17 x} \left (1190 x^2+140 x\right )+280 e^{13 x} x\right ) \log ^4(x)+\left (e^{21 x} \left (1176 x^2+112 x\right )+280 e^{17 x} x\right ) \log ^3(x)+\left (e^{25 x} \left (700 x^2+56 x\right )+168 e^{21 x} x\right ) \log ^2(x)+\left (e^{29 x} \left (232 x^2+16 x\right )+56 e^{25 x} x\right ) \log (x)+8 e^{29 x} x\right ) \exp \left (\frac {e^{33 x} x^2+e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+8 e^{29 x} x^2 \log (x)}{3 e^4}-4\right ) \, dx\)

\(\Big \downarrow \) 27

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+8 e^{29 x} x^2 \log (x)+e^{33 x} x^2}{3 e^4}-4\right ) \left (e^x \left (x^2+2 x\right ) \log ^8(x)+8 \left (e^x x+e^{5 x} \left (5 x^2+2 x\right )\right ) \log ^7(x)+28 \left (2 e^{5 x} x+e^{9 x} \left (9 x^2+2 x\right )\right ) \log ^6(x)+56 \left (3 e^{9 x} x+e^{13 x} \left (13 x^2+2 x\right )\right ) \log ^5(x)+70 \left (4 e^{13 x} x+e^{17 x} \left (17 x^2+2 x\right )\right ) \log ^4(x)+56 \left (5 e^{17 x} x+e^{21 x} \left (21 x^2+2 x\right )\right ) \log ^3(x)+28 \left (6 e^{21 x} x+e^{25 x} \left (25 x^2+2 x\right )\right ) \log ^2(x)+8 \left (7 e^{25 x} x+e^{29 x} \left (29 x^2+2 x\right )\right ) \log (x)+8 e^{29 x} x+e^{33 x} \left (33 x^2+2 x\right )\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{33 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{5 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{9 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{13 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{17 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{21 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{25 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{29 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2-12 e^4}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \frac {1}{3} \int \left (e^{32 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (33 x+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+e^{\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^7(x) (x \log (x)+2 \log (x)+8) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{4 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^6(x) (5 x \log (x)+2 \log (x)+7) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{8 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^5(x) (9 x \log (x)+2 \log (x)+6) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{12 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^4(x) (13 x \log (x)+2 \log (x)+5) x^{\frac {8}{3} e^{29 x-4} x^2+1}+70 e^{16 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^3(x) (17 x \log (x)+2 \log (x)+4) x^{\frac {8}{3} e^{29 x-4} x^2+1}+56 e^{20 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log ^2(x) (21 x \log (x)+2 \log (x)+3) x^{\frac {8}{3} e^{29 x-4} x^2+1}+28 e^{24 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} \log (x) (25 x \log (x)+2 \log (x)+2) x^{\frac {8}{3} e^{29 x-4} x^2+1}+8 e^{28 x+\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}} (29 x \log (x)+2 \log (x)+1) x^{\frac {8}{3} e^{29 x-4} x^2+1}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \frac {1}{3} \int \exp \left (\frac {e^x x^2 \log ^8(x)+8 e^{5 x} x^2 \log ^7(x)+28 e^{9 x} x^2 \log ^6(x)+56 e^{13 x} x^2 \log ^5(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{21 x} x^2 \log ^3(x)+28 e^{25 x} x^2 \log ^2(x)+e^{33 x} x^2+3 e^4 (x-4)}{3 e^4}\right ) x^{\frac {8}{3} e^{29 x-4} x^2+1} \left (\log (x)+e^{4 x}\right )^7 \left (e^{4 x} (33 x+2)+(x+2) \log (x)+8\right )dx\)

Input:

Int[(E^(-4 + (E^(33*x)*x^2 + 8*E^(29*x)*x^2*Log[x] + 28*E^(25*x)*x^2*Log[x 
]^2 + 56*E^(21*x)*x^2*Log[x]^3 + 70*E^(17*x)*x^2*Log[x]^4 + 56*E^(13*x)*x^ 
2*Log[x]^5 + 28*E^(9*x)*x^2*Log[x]^6 + 8*E^(5*x)*x^2*Log[x]^7 + E^x*x^2*Lo 
g[x]^8)/(3*E^4))*(8*E^(29*x)*x + E^(33*x)*(2*x + 33*x^2) + (56*E^(25*x)*x 
+ E^(29*x)*(16*x + 232*x^2))*Log[x] + (168*E^(21*x)*x + E^(25*x)*(56*x + 7 
00*x^2))*Log[x]^2 + (280*E^(17*x)*x + E^(21*x)*(112*x + 1176*x^2))*Log[x]^ 
3 + (280*E^(13*x)*x + E^(17*x)*(140*x + 1190*x^2))*Log[x]^4 + (168*E^(9*x) 
*x + E^(13*x)*(112*x + 728*x^2))*Log[x]^5 + (56*E^(5*x)*x + E^(9*x)*(56*x 
+ 252*x^2))*Log[x]^6 + (8*E^x*x + E^(5*x)*(16*x + 40*x^2))*Log[x]^7 + E^x* 
(2*x + x^2)*Log[x]^8))/3,x]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(88\) vs. \(2(23)=46\).

Time = 0.35 (sec) , antiderivative size = 89, normalized size of antiderivative = 3.71

\[{\mathrm e}^{\frac {x^{2} \left ({\mathrm e}^{x} \ln \left (x \right )^{8}+8 \,{\mathrm e}^{5 x} \ln \left (x \right )^{7}+28 \,{\mathrm e}^{9 x} \ln \left (x \right )^{6}+56 \,{\mathrm e}^{13 x} \ln \left (x \right )^{5}+70 \,{\mathrm e}^{17 x} \ln \left (x \right )^{4}+56 \,{\mathrm e}^{21 x} \ln \left (x \right )^{3}+28 \,{\mathrm e}^{25 x} \ln \left (x \right )^{2}+8 \,{\mathrm e}^{29 x} \ln \left (x \right )+{\mathrm e}^{33 x}\right ) {\mathrm e}^{-4}}{3}}\]

Input:

int(1/3*((x^2+2*x)*exp(x)*ln(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp(x 
)*x)*ln(x)^7+((252*x^2+56*x)*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*ln( 
x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)*ln(x)^5+( 
(1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*ln(x)^4+((1176 
*x^2+112*x)*exp(x)*exp(2*x)^10+280*x*exp(x)*exp(2*x)^8)*ln(x)^3+((700*x^2+ 
56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*ln(x)^2+((232*x^2+16*x) 
*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*ln(x)+(33*x^2+2*x)*exp(x)*exp 
(2*x)^16+8*x*exp(x)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*ln(x)^8+8*x^2*exp(x)* 
exp(2*x)^2*ln(x)^7+28*x^2*exp(x)*exp(2*x)^4*ln(x)^6+56*x^2*exp(x)*exp(2*x) 
^6*ln(x)^5+70*x^2*exp(x)*exp(2*x)^8*ln(x)^4+56*x^2*exp(x)*exp(2*x)^10*ln(x 
)^3+28*x^2*exp(x)*exp(2*x)^12*ln(x)^2+8*x^2*exp(x)*exp(2*x)^14*ln(x)+x^2*e 
xp(x)*exp(2*x)^16)/exp(4))/exp(4),x)
 

Output:

exp(1/3*x^2*(exp(x)*ln(x)^8+8*exp(5*x)*ln(x)^7+28*exp(9*x)*ln(x)^6+56*exp( 
13*x)*ln(x)^5+70*exp(17*x)*ln(x)^4+56*exp(21*x)*ln(x)^3+28*exp(25*x)*ln(x) 
^2+8*exp(29*x)*ln(x)+exp(33*x))*exp(-4))
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 119 vs. \(2 (19) = 38\).

Time = 0.13 (sec) , antiderivative size = 119, normalized size of antiderivative = 4.96 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\left (\frac {1}{3} \, {\left (x^{2} e^{x} \log \left (x\right )^{8} + 8 \, x^{2} e^{\left (5 \, x\right )} \log \left (x\right )^{7} + 28 \, x^{2} e^{\left (9 \, x\right )} \log \left (x\right )^{6} + 56 \, x^{2} e^{\left (13 \, x\right )} \log \left (x\right )^{5} + 70 \, x^{2} e^{\left (17 \, x\right )} \log \left (x\right )^{4} + 56 \, x^{2} e^{\left (21 \, x\right )} \log \left (x\right )^{3} + 28 \, x^{2} e^{\left (25 \, x\right )} \log \left (x\right )^{2} + 8 \, x^{2} e^{\left (29 \, x\right )} \log \left (x\right ) + x^{2} e^{\left (33 \, x\right )} - 12 \, e^{4}\right )} e^{\left (-4\right )} + 4\right )} \] Input:

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+ 
8*exp(x)*x)*log(x)^7+((252*x^2+56*x)*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x 
)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)* 
log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log( 
x)^4+((1176*x^2+112*x)*exp(x)*exp(2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^ 
3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^2+(( 
232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2 
*x)*exp(x)*exp(2*x)^16+8*x*exp(x)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^ 
8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6+56*x^ 
2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp( 
x)*exp(2*x)^10*log(x)^3+28*x^2*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*ex 
p(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorithm="fric 
as")
 

Output:

e^(1/3*(x^2*e^x*log(x)^8 + 8*x^2*e^(5*x)*log(x)^7 + 28*x^2*e^(9*x)*log(x)^ 
6 + 56*x^2*e^(13*x)*log(x)^5 + 70*x^2*e^(17*x)*log(x)^4 + 56*x^2*e^(21*x)* 
log(x)^3 + 28*x^2*e^(25*x)*log(x)^2 + 8*x^2*e^(29*x)*log(x) + x^2*e^(33*x) 
 - 12*e^4)*e^(-4) + 4)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 144 vs. \(2 (22) = 44\).

Time = 1.57 (sec) , antiderivative size = 144, normalized size of antiderivative = 6.00 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\frac {\frac {x^{2} e^{33 x}}{3} + \frac {8 x^{2} e^{29 x} \log {\left (x \right )}}{3} + \frac {28 x^{2} e^{25 x} \log {\left (x \right )}^{2}}{3} + \frac {56 x^{2} e^{21 x} \log {\left (x \right )}^{3}}{3} + \frac {70 x^{2} e^{17 x} \log {\left (x \right )}^{4}}{3} + \frac {56 x^{2} e^{13 x} \log {\left (x \right )}^{5}}{3} + \frac {28 x^{2} e^{9 x} \log {\left (x \right )}^{6}}{3} + \frac {8 x^{2} e^{5 x} \log {\left (x \right )}^{7}}{3} + \frac {x^{2} e^{x} \log {\left (x \right )}^{8}}{3}}{e^{4}}} \] Input:

integrate(1/3*((x**2+2*x)*exp(x)*ln(x)**8+((40*x**2+16*x)*exp(x)*exp(2*x)* 
*2+8*exp(x)*x)*ln(x)**7+((252*x**2+56*x)*exp(x)*exp(2*x)**4+56*x*exp(x)*ex 
p(2*x)**2)*ln(x)**6+((728*x**2+112*x)*exp(x)*exp(2*x)**6+168*x*exp(x)*exp( 
2*x)**4)*ln(x)**5+((1190*x**2+140*x)*exp(x)*exp(2*x)**8+280*x*exp(x)*exp(2 
*x)**6)*ln(x)**4+((1176*x**2+112*x)*exp(x)*exp(2*x)**10+280*x*exp(x)*exp(2 
*x)**8)*ln(x)**3+((700*x**2+56*x)*exp(x)*exp(2*x)**12+168*x*exp(x)*exp(2*x 
)**10)*ln(x)**2+((232*x**2+16*x)*exp(x)*exp(2*x)**14+56*x*exp(x)*exp(2*x)* 
*12)*ln(x)+(33*x**2+2*x)*exp(x)*exp(2*x)**16+8*x*exp(x)*exp(2*x)**14)*exp( 
1/3*(x**2*exp(x)*ln(x)**8+8*x**2*exp(x)*exp(2*x)**2*ln(x)**7+28*x**2*exp(x 
)*exp(2*x)**4*ln(x)**6+56*x**2*exp(x)*exp(2*x)**6*ln(x)**5+70*x**2*exp(x)* 
exp(2*x)**8*ln(x)**4+56*x**2*exp(x)*exp(2*x)**10*ln(x)**3+28*x**2*exp(x)*e 
xp(2*x)**12*ln(x)**2+8*x**2*exp(x)*exp(2*x)**14*ln(x)+x**2*exp(x)*exp(2*x) 
**16)/exp(4))/exp(4),x)
 

Output:

exp((x**2*exp(33*x)/3 + 8*x**2*exp(29*x)*log(x)/3 + 28*x**2*exp(25*x)*log( 
x)**2/3 + 56*x**2*exp(21*x)*log(x)**3/3 + 70*x**2*exp(17*x)*log(x)**4/3 + 
56*x**2*exp(13*x)*log(x)**5/3 + 28*x**2*exp(9*x)*log(x)**6/3 + 8*x**2*exp( 
5*x)*log(x)**7/3 + x**2*exp(x)*log(x)**8/3)*exp(-4))
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 129 vs. \(2 (19) = 38\).

Time = 0.47 (sec) , antiderivative size = 129, normalized size of antiderivative = 5.38 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\left (\frac {1}{3} \, x^{2} e^{\left (x - 4\right )} \log \left (x\right )^{8} + \frac {8}{3} \, x^{2} e^{\left (5 \, x - 4\right )} \log \left (x\right )^{7} + \frac {28}{3} \, x^{2} e^{\left (9 \, x - 4\right )} \log \left (x\right )^{6} + \frac {56}{3} \, x^{2} e^{\left (13 \, x - 4\right )} \log \left (x\right )^{5} + \frac {70}{3} \, x^{2} e^{\left (17 \, x - 4\right )} \log \left (x\right )^{4} + \frac {56}{3} \, x^{2} e^{\left (21 \, x - 4\right )} \log \left (x\right )^{3} + \frac {28}{3} \, x^{2} e^{\left (25 \, x - 4\right )} \log \left (x\right )^{2} + \frac {8}{3} \, x^{2} e^{\left (29 \, x - 4\right )} \log \left (x\right ) + \frac {1}{3} \, x^{2} e^{\left (33 \, x - 4\right )}\right )} \] Input:

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+ 
8*exp(x)*x)*log(x)^7+((252*x^2+56*x)*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x 
)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)* 
log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log( 
x)^4+((1176*x^2+112*x)*exp(x)*exp(2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^ 
3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^2+(( 
232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2 
*x)*exp(x)*exp(2*x)^16+8*x*exp(x)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^ 
8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6+56*x^ 
2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp( 
x)*exp(2*x)^10*log(x)^3+28*x^2*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*ex 
p(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorithm="maxi 
ma")
 

Output:

e^(1/3*x^2*e^(x - 4)*log(x)^8 + 8/3*x^2*e^(5*x - 4)*log(x)^7 + 28/3*x^2*e^ 
(9*x - 4)*log(x)^6 + 56/3*x^2*e^(13*x - 4)*log(x)^5 + 70/3*x^2*e^(17*x - 4 
)*log(x)^4 + 56/3*x^2*e^(21*x - 4)*log(x)^3 + 28/3*x^2*e^(25*x - 4)*log(x) 
^2 + 8/3*x^2*e^(29*x - 4)*log(x) + 1/3*x^2*e^(33*x - 4))
 

Giac [F]

\[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=\int { \frac {1}{3} \, {\left ({\left (x^{2} + 2 \, x\right )} e^{x} \log \left (x\right )^{8} + 8 \, {\left ({\left (5 \, x^{2} + 2 \, x\right )} e^{\left (5 \, x\right )} + x e^{x}\right )} \log \left (x\right )^{7} + 28 \, {\left ({\left (9 \, x^{2} + 2 \, x\right )} e^{\left (9 \, x\right )} + 2 \, x e^{\left (5 \, x\right )}\right )} \log \left (x\right )^{6} + 56 \, {\left ({\left (13 \, x^{2} + 2 \, x\right )} e^{\left (13 \, x\right )} + 3 \, x e^{\left (9 \, x\right )}\right )} \log \left (x\right )^{5} + 70 \, {\left ({\left (17 \, x^{2} + 2 \, x\right )} e^{\left (17 \, x\right )} + 4 \, x e^{\left (13 \, x\right )}\right )} \log \left (x\right )^{4} + 56 \, {\left ({\left (21 \, x^{2} + 2 \, x\right )} e^{\left (21 \, x\right )} + 5 \, x e^{\left (17 \, x\right )}\right )} \log \left (x\right )^{3} + 28 \, {\left ({\left (25 \, x^{2} + 2 \, x\right )} e^{\left (25 \, x\right )} + 6 \, x e^{\left (21 \, x\right )}\right )} \log \left (x\right )^{2} + {\left (33 \, x^{2} + 2 \, x\right )} e^{\left (33 \, x\right )} + 8 \, x e^{\left (29 \, x\right )} + 8 \, {\left ({\left (29 \, x^{2} + 2 \, x\right )} e^{\left (29 \, x\right )} + 7 \, x e^{\left (25 \, x\right )}\right )} \log \left (x\right )\right )} e^{\left (\frac {1}{3} \, {\left (x^{2} e^{x} \log \left (x\right )^{8} + 8 \, x^{2} e^{\left (5 \, x\right )} \log \left (x\right )^{7} + 28 \, x^{2} e^{\left (9 \, x\right )} \log \left (x\right )^{6} + 56 \, x^{2} e^{\left (13 \, x\right )} \log \left (x\right )^{5} + 70 \, x^{2} e^{\left (17 \, x\right )} \log \left (x\right )^{4} + 56 \, x^{2} e^{\left (21 \, x\right )} \log \left (x\right )^{3} + 28 \, x^{2} e^{\left (25 \, x\right )} \log \left (x\right )^{2} + 8 \, x^{2} e^{\left (29 \, x\right )} \log \left (x\right ) + x^{2} e^{\left (33 \, x\right )}\right )} e^{\left (-4\right )} - 4\right )} \,d x } \] Input:

integrate(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+ 
8*exp(x)*x)*log(x)^7+((252*x^2+56*x)*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x 
)^2)*log(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)* 
log(x)^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log( 
x)^4+((1176*x^2+112*x)*exp(x)*exp(2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^ 
3+((700*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^2+(( 
232*x^2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2 
*x)*exp(x)*exp(2*x)^16+8*x*exp(x)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^ 
8+8*x^2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6+56*x^ 
2*exp(x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp( 
x)*exp(2*x)^10*log(x)^3+28*x^2*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*ex 
p(2*x)^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x, algorithm="giac 
")
 

Output:

integrate(1/3*((x^2 + 2*x)*e^x*log(x)^8 + 8*((5*x^2 + 2*x)*e^(5*x) + x*e^x 
)*log(x)^7 + 28*((9*x^2 + 2*x)*e^(9*x) + 2*x*e^(5*x))*log(x)^6 + 56*((13*x 
^2 + 2*x)*e^(13*x) + 3*x*e^(9*x))*log(x)^5 + 70*((17*x^2 + 2*x)*e^(17*x) + 
 4*x*e^(13*x))*log(x)^4 + 56*((21*x^2 + 2*x)*e^(21*x) + 5*x*e^(17*x))*log( 
x)^3 + 28*((25*x^2 + 2*x)*e^(25*x) + 6*x*e^(21*x))*log(x)^2 + (33*x^2 + 2* 
x)*e^(33*x) + 8*x*e^(29*x) + 8*((29*x^2 + 2*x)*e^(29*x) + 7*x*e^(25*x))*lo 
g(x))*e^(1/3*(x^2*e^x*log(x)^8 + 8*x^2*e^(5*x)*log(x)^7 + 28*x^2*e^(9*x)*l 
og(x)^6 + 56*x^2*e^(13*x)*log(x)^5 + 70*x^2*e^(17*x)*log(x)^4 + 56*x^2*e^( 
21*x)*log(x)^3 + 28*x^2*e^(25*x)*log(x)^2 + 8*x^2*e^(29*x)*log(x) + x^2*e^ 
(33*x))*e^(-4) - 4), x)
 

Mupad [B] (verification not implemented)

Time = 3.91 (sec) , antiderivative size = 137, normalized size of antiderivative = 5.71 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx={\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{29\,x}\,{\mathrm {e}}^{-4}\,\ln \left (x\right )}{3}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^x\,{\ln \left (x\right )}^8}{3}}\,{\mathrm {e}}^{\frac {x^2\,{\mathrm {e}}^{33\,x}\,{\mathrm {e}}^{-4}}{3}}\,{\mathrm {e}}^{\frac {8\,x^2\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^7}{3}}\,{\mathrm {e}}^{\frac {28\,x^2\,{\mathrm {e}}^{9\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^6}{3}}\,{\mathrm {e}}^{\frac {28\,x^2\,{\mathrm {e}}^{25\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^2}{3}}\,{\mathrm {e}}^{\frac {56\,x^2\,{\mathrm {e}}^{13\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^5}{3}}\,{\mathrm {e}}^{\frac {56\,x^2\,{\mathrm {e}}^{21\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^3}{3}}\,{\mathrm {e}}^{\frac {70\,x^2\,{\mathrm {e}}^{17\,x}\,{\mathrm {e}}^{-4}\,{\ln \left (x\right )}^4}{3}} \] Input:

int((exp(-4)*exp(exp(-4)*((x^2*exp(33*x))/3 + (8*x^2*exp(29*x)*log(x))/3 + 
 (x^2*exp(x)*log(x)^8)/3 + (8*x^2*exp(5*x)*log(x)^7)/3 + (28*x^2*exp(9*x)* 
log(x)^6)/3 + (56*x^2*exp(13*x)*log(x)^5)/3 + (70*x^2*exp(17*x)*log(x)^4)/ 
3 + (56*x^2*exp(21*x)*log(x)^3)/3 + (28*x^2*exp(25*x)*log(x)^2)/3))*(exp(3 
3*x)*(2*x + 33*x^2) + 8*x*exp(29*x) + log(x)^6*(exp(9*x)*(56*x + 252*x^2) 
+ 56*x*exp(5*x)) + log(x)^2*(exp(25*x)*(56*x + 700*x^2) + 168*x*exp(21*x)) 
 + log(x)^5*(exp(13*x)*(112*x + 728*x^2) + 168*x*exp(9*x)) + log(x)^3*(exp 
(21*x)*(112*x + 1176*x^2) + 280*x*exp(17*x)) + log(x)^4*(exp(17*x)*(140*x 
+ 1190*x^2) + 280*x*exp(13*x)) + log(x)*(exp(29*x)*(16*x + 232*x^2) + 56*x 
*exp(25*x)) + log(x)^7*(exp(5*x)*(16*x + 40*x^2) + 8*x*exp(x)) + exp(x)*lo 
g(x)^8*(2*x + x^2)))/3,x)
 

Output:

exp((8*x^2*exp(29*x)*exp(-4)*log(x))/3)*exp((x^2*exp(-4)*exp(x)*log(x)^8)/ 
3)*exp((x^2*exp(33*x)*exp(-4))/3)*exp((8*x^2*exp(5*x)*exp(-4)*log(x)^7)/3) 
*exp((28*x^2*exp(9*x)*exp(-4)*log(x)^6)/3)*exp((28*x^2*exp(25*x)*exp(-4)*l 
og(x)^2)/3)*exp((56*x^2*exp(13*x)*exp(-4)*log(x)^5)/3)*exp((56*x^2*exp(21* 
x)*exp(-4)*log(x)^3)/3)*exp((70*x^2*exp(17*x)*exp(-4)*log(x)^4)/3)
 

Reduce [B] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 124, normalized size of antiderivative = 5.17 \[ \int \frac {1}{3} e^{-4+\frac {e^{33 x} x^2+8 e^{29 x} x^2 \log (x)+28 e^{25 x} x^2 \log ^2(x)+56 e^{21 x} x^2 \log ^3(x)+70 e^{17 x} x^2 \log ^4(x)+56 e^{13 x} x^2 \log ^5(x)+28 e^{9 x} x^2 \log ^6(x)+8 e^{5 x} x^2 \log ^7(x)+e^x x^2 \log ^8(x)}{3 e^4}} \left (8 e^{29 x} x+e^{33 x} \left (2 x+33 x^2\right )+\left (56 e^{25 x} x+e^{29 x} \left (16 x+232 x^2\right )\right ) \log (x)+\left (168 e^{21 x} x+e^{25 x} \left (56 x+700 x^2\right )\right ) \log ^2(x)+\left (280 e^{17 x} x+e^{21 x} \left (112 x+1176 x^2\right )\right ) \log ^3(x)+\left (280 e^{13 x} x+e^{17 x} \left (140 x+1190 x^2\right )\right ) \log ^4(x)+\left (168 e^{9 x} x+e^{13 x} \left (112 x+728 x^2\right )\right ) \log ^5(x)+\left (56 e^{5 x} x+e^{9 x} \left (56 x+252 x^2\right )\right ) \log ^6(x)+\left (8 e^x x+e^{5 x} \left (16 x+40 x^2\right )\right ) \log ^7(x)+e^x \left (2 x+x^2\right ) \log ^8(x)\right ) \, dx=e^{\frac {e^{33 x} x^{2}+8 e^{29 x} \mathrm {log}\left (x \right ) x^{2}+28 e^{25 x} \mathrm {log}\left (x \right )^{2} x^{2}+56 e^{21 x} \mathrm {log}\left (x \right )^{3} x^{2}+70 e^{17 x} \mathrm {log}\left (x \right )^{4} x^{2}+56 e^{13 x} \mathrm {log}\left (x \right )^{5} x^{2}+28 e^{9 x} \mathrm {log}\left (x \right )^{6} x^{2}+8 e^{5 x} \mathrm {log}\left (x \right )^{7} x^{2}+e^{x} \mathrm {log}\left (x \right )^{8} x^{2}}{3 e^{4}}} \] Input:

int(1/3*((x^2+2*x)*exp(x)*log(x)^8+((40*x^2+16*x)*exp(x)*exp(2*x)^2+8*exp( 
x)*x)*log(x)^7+((252*x^2+56*x)*exp(x)*exp(2*x)^4+56*x*exp(x)*exp(2*x)^2)*l 
og(x)^6+((728*x^2+112*x)*exp(x)*exp(2*x)^6+168*x*exp(x)*exp(2*x)^4)*log(x) 
^5+((1190*x^2+140*x)*exp(x)*exp(2*x)^8+280*x*exp(x)*exp(2*x)^6)*log(x)^4+( 
(1176*x^2+112*x)*exp(x)*exp(2*x)^10+280*x*exp(x)*exp(2*x)^8)*log(x)^3+((70 
0*x^2+56*x)*exp(x)*exp(2*x)^12+168*x*exp(x)*exp(2*x)^10)*log(x)^2+((232*x^ 
2+16*x)*exp(x)*exp(2*x)^14+56*x*exp(x)*exp(2*x)^12)*log(x)+(33*x^2+2*x)*ex 
p(x)*exp(2*x)^16+8*x*exp(x)*exp(2*x)^14)*exp(1/3*(x^2*exp(x)*log(x)^8+8*x^ 
2*exp(x)*exp(2*x)^2*log(x)^7+28*x^2*exp(x)*exp(2*x)^4*log(x)^6+56*x^2*exp( 
x)*exp(2*x)^6*log(x)^5+70*x^2*exp(x)*exp(2*x)^8*log(x)^4+56*x^2*exp(x)*exp 
(2*x)^10*log(x)^3+28*x^2*exp(x)*exp(2*x)^12*log(x)^2+8*x^2*exp(x)*exp(2*x) 
^14*log(x)+x^2*exp(x)*exp(2*x)^16)/exp(4))/exp(4),x)
 

Output:

e**((e**(33*x)*x**2 + 8*e**(29*x)*log(x)*x**2 + 28*e**(25*x)*log(x)**2*x** 
2 + 56*e**(21*x)*log(x)**3*x**2 + 70*e**(17*x)*log(x)**4*x**2 + 56*e**(13* 
x)*log(x)**5*x**2 + 28*e**(9*x)*log(x)**6*x**2 + 8*e**(5*x)*log(x)**7*x**2 
 + e**x*log(x)**8*x**2)/(3*e**4))