3.30.55 \(\int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10})+(-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 (-36 x^6-8 x^8+4 x^9)) \log (x)+(486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}) \log ^2(x)+(-36 x^6-8 x^8+4 x^9) \log ^3(x)+x^8 \log ^4(x)}{x^8}} (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10})+(17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 (72 x^6+4 x^8+4 x^9)) \log (x)+(-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}) \log ^2(x)+(72 x^6+4 x^8+4 x^9) \log ^3(x))}{x^9} \, dx\) [2955]

3.30.55.1 Optimal result

Integrand size = 469, antiderivative size = 30 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=-1+e^{e^5+\left (e^2+\left (2+\frac {9}{x^2}-x-\log (x)\right )^2\right )^2} \]

output

exp((exp(2)+(9/x^2-ln(x)+2-x)^2)^2+exp(5))-1
 

3.30.55.2 Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(137\) vs. \(2(30)=60\).

Time = 2.40 (sec) , antiderivative size = 137, normalized size of antiderivative = 4.57 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=e^{e^4+e^5+\frac {2 e^2 \left (-9-2 x^2+x^3\right )^2}{x^4}+\frac {\left (-9-2 x^2+x^3\right )^4}{x^8}+2 \left (e^2+\frac {3 \left (-9-2 x^2+x^3\right )^2}{x^4}\right ) \log ^2(x)+4 \left (-2-\frac {9}{x^2}+x\right ) \log ^3(x)+\log ^4(x)} x^{\frac {4 \left (-9-2 x^2+x^3\right ) \left (81+36 x^2-18 x^3+\left (4+e^2\right ) x^4-4 x^5+x^6\right )}{x^6}} \]

input

Integrate[(E^((6561 + 5832*x^2 - 2916*x^3 + 1944*x^4 - 1944*x^5 + 774*x^6 
- 432*x^7 + 232*x^8 + E^4*x^8 + E^5*x^8 - 68*x^9 + 24*x^10 - 8*x^11 + x^12 
 + E^2*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) + (-2916*x^2 - 
 1944*x^4 + 972*x^5 - 432*x^6 + 432*x^7 - 140*x^8 + 48*x^9 - 24*x^10 + 4*x 
^11 + E^2*(-36*x^6 - 8*x^8 + 4*x^9))*Log[x] + (486*x^4 + 216*x^6 - 108*x^7 
 + 24*x^8 + 2*E^2*x^8 - 24*x^9 + 6*x^10)*Log[x]^2 + (-36*x^6 - 8*x^8 + 4*x 
^9)*Log[x]^3 + x^8*Log[x]^4)/x^8)*(-52488 - 37908*x^2 + 14580*x^3 - 9720*x 
^4 + 6804*x^5 - 1980*x^6 + 864*x^7 - 140*x^8 - 20*x^9 + 24*x^10 - 20*x^11 
+ 4*x^12 + E^2*(-648*x^4 - 180*x^6 + 36*x^7 - 8*x^8 - 4*x^9 + 4*x^10) + (1 
7496*x^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8 - 36*x^10 + 1 
2*x^11 + E^2*(72*x^6 + 4*x^8 + 4*x^9))*Log[x] + (-1944*x^4 - 540*x^6 + 108 
*x^7 - 24*x^8 - 12*x^9 + 12*x^10)*Log[x]^2 + (72*x^6 + 4*x^8 + 4*x^9)*Log[ 
x]^3))/x^9,x]
 

output

E^(E^4 + E^5 + (2*E^2*(-9 - 2*x^2 + x^3)^2)/x^4 + (-9 - 2*x^2 + x^3)^4/x^8 
 + 2*(E^2 + (3*(-9 - 2*x^2 + x^3)^2)/x^4)*Log[x]^2 + 4*(-2 - 9/x^2 + x)*Lo 
g[x]^3 + Log[x]^4)*x^((4*(-9 - 2*x^2 + x^3)*(81 + 36*x^2 - 18*x^3 + (4 + E 
^2)*x^4 - 4*x^5 + x^6))/x^6)
 

3.30.55.3 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.

\(\displaystyle \int \frac {\left (4 x^{12}-20 x^{11}+24 x^{10}-20 x^9-140 x^8+864 x^7-1980 x^6+6804 x^5-9720 x^4+14580 x^3-37908 x^2+\left (4 x^9+4 x^8+72 x^6\right ) \log ^3(x)+e^2 \left (4 x^{10}-4 x^9-8 x^8+36 x^7-180 x^6-648 x^4\right )+\left (12 x^{10}-12 x^9-24 x^8+108 x^7-540 x^6-1944 x^4\right ) \log ^2(x)+\left (12 x^{11}-36 x^{10}+48 x^8-648 x^7+1296 x^6-2916 x^5+8748 x^4+17496 x^2+e^2 \left (4 x^9+4 x^8+72 x^6\right )\right ) \log (x)-52488\right ) \exp \left (\frac {x^{12}-8 x^{11}+24 x^{10}-68 x^9+e^5 x^8+e^4 x^8+232 x^8+x^8 \log ^4(x)-432 x^7+774 x^6-1944 x^5+1944 x^4-2916 x^3+5832 x^2+\left (4 x^9-8 x^8-36 x^6\right ) \log ^3(x)+e^2 \left (2 x^{10}-8 x^9+8 x^8-36 x^7+72 x^6+162 x^4\right )+\left (6 x^{10}-24 x^9+2 e^2 x^8+24 x^8-108 x^7+216 x^6+486 x^4\right ) \log ^2(x)+\left (4 x^{11}-24 x^{10}+48 x^9-140 x^8+432 x^7-432 x^6+972 x^5-1944 x^4-2916 x^2+e^2 \left (4 x^9-8 x^8-36 x^6\right )\right ) \log (x)+6561}{x^8}\right )}{x^9} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int 4 x^{-\frac {2916}{x^6}-\frac {1944}{x^4}+4 x^3+\frac {972}{x^3}-24 x^2+4 e^2 \left (-\frac {9}{x^2}+x-2\right )-\frac {432}{x^2}+48 x+\frac {432}{x}-149} \left (x^3+x^2+18\right ) \left (-x^3+2 x^2-x^2 \log (x)+9\right ) \left (-x^6+4 x^5-\left (4+e^2\right ) x^4-x^4 \log ^2(x)+18 x^3-36 x^2-2 \left (x^3-2 x^2-9\right ) x^2 \log (x)-81\right ) \exp \left (4 \left (-\frac {9}{x^2}+x-2\right ) \log ^3(x)+\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+\log ^4(x)+e^4 (1+e)\right )dx\)

\(\Big \downarrow \) 27

\(\displaystyle 4 \int -\exp \left (\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3-2 \left (-x^3+2 x^2+9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 25

\(\displaystyle -4 \int \exp \left (\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3-2 \left (-x^3+2 x^2+9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (-x^3+2 x^2+9\right )^4}{x^8}+\frac {2 e^2 \left (-x^3+2 x^2+9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (-x^3+2 x^2+9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x-4 e^2 \left (-x+2+\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle -4 \int \exp \left (\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}} \left (x^3+x^2+18\right ) \left (-x^3-\log (x) x^2+2 x^2+9\right ) \left (x^6-4 x^5+\log ^2(x) x^4+\left (4+e^2\right ) x^4-18 x^3+2 \left (x^3-2 x^2-9\right ) \log (x) x^2+36 x^2+81\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle -4 \int \left (729 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-149+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+486 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^3+x^2+18\right ) \left (-3 x^6+12 x^5-12 \left (1+\frac {e^2}{12}\right ) x^4+54 x^3-108 x^2-243\right ) \log (x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-147+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-243 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-146+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-3 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (x^6-x^5-2 x^4+9 x^3-45 x^2-162\right ) \log ^2(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+72 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-145+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-108 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-144+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) \log ^3(x) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+27 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {2}{27} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-143+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-8 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} \left (1+\frac {1}{8} \left (4+e^2\right )\right ) (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-142+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}+6 e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-141+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}-e^{\frac {\left (x^3-2 x^2-9\right )^4}{x^8}+\frac {2 e^2 \left (x^3-2 x^2-9\right )^2}{x^4}+\log ^4(x)-4 \left (-x+2+\frac {9}{x^2}\right ) \log ^3(x)+2 \left (\frac {3 \left (x^3-2 x^2-9\right )^2}{x^4}+e^2\right ) \log ^2(x)+e^4 (1+e)} (x+3) \left (x^2-2 x+6\right ) x^{4 x^3-24 x^2+48 x+4 e^2 \left (x-2-\frac {9}{x^2}\right )-140+\frac {432}{x}-\frac {432}{x^2}+\frac {972}{x^3}-\frac {1944}{x^4}-\frac {2916}{x^6}}\right )dx\)

input

Int[(E^((6561 + 5832*x^2 - 2916*x^3 + 1944*x^4 - 1944*x^5 + 774*x^6 - 432* 
x^7 + 232*x^8 + E^4*x^8 + E^5*x^8 - 68*x^9 + 24*x^10 - 8*x^11 + x^12 + E^2 
*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) + (-2916*x^2 - 1944* 
x^4 + 972*x^5 - 432*x^6 + 432*x^7 - 140*x^8 + 48*x^9 - 24*x^10 + 4*x^11 + 
E^2*(-36*x^6 - 8*x^8 + 4*x^9))*Log[x] + (486*x^4 + 216*x^6 - 108*x^7 + 24* 
x^8 + 2*E^2*x^8 - 24*x^9 + 6*x^10)*Log[x]^2 + (-36*x^6 - 8*x^8 + 4*x^9)*Lo 
g[x]^3 + x^8*Log[x]^4)/x^8)*(-52488 - 37908*x^2 + 14580*x^3 - 9720*x^4 + 6 
804*x^5 - 1980*x^6 + 864*x^7 - 140*x^8 - 20*x^9 + 24*x^10 - 20*x^11 + 4*x^ 
12 + E^2*(-648*x^4 - 180*x^6 + 36*x^7 - 8*x^8 - 4*x^9 + 4*x^10) + (17496*x 
^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8 - 36*x^10 + 12*x^11 
 + E^2*(72*x^6 + 4*x^8 + 4*x^9))*Log[x] + (-1944*x^4 - 540*x^6 + 108*x^7 - 
 24*x^8 - 12*x^9 + 12*x^10)*Log[x]^2 + (72*x^6 + 4*x^8 + 4*x^9)*Log[x]^3)) 
/x^9,x]
 

output

$Aborted
 

3.30.55.3.1 Defintions of rubi rules used

rule 25

Int[-(Fx_), x_Symbol] :> Simp[Identity[-1]   Int[Fx, x], x]
 

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 7239

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl 
erIntegrandQ[v, u, x]]
 

rule 7293

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v] 
]
 

3.30.55.4 Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(248\) vs. \(2(27)=54\).

Time = 203.01 (sec) , antiderivative size = 249, normalized size of antiderivative = 8.30

method	result	size
parallelrisch	\({\mathrm e}^{\frac {x^{8} \ln \left (x \right )^{4}+\left (4 x^{9}-8 x^{8}-36 x^{6}\right ) \ln \left (x \right )^{3}+\left (2 x^{8} {\mathrm e}^{2}+6 x^{10}-24 x^{9}+24 x^{8}-108 x^{7}+216 x^{6}+486 x^{4}\right ) \ln \left (x \right )^{2}+\left (\left (4 x^{9}-8 x^{8}-36 x^{6}\right ) {\mathrm e}^{2}+4 x^{11}-24 x^{10}+48 x^{9}-140 x^{8}+432 x^{7}-432 x^{6}+972 x^{5}-1944 x^{4}-2916 x^{2}\right ) \ln \left (x \right )+x^{8} {\mathrm e}^{5}+x^{8} {\mathrm e}^{4}+\left (2 x^{10}-8 x^{9}+8 x^{8}-36 x^{7}+72 x^{6}+162 x^{4}\right ) {\mathrm e}^{2}+x^{12}-8 x^{11}+24 x^{10}-68 x^{9}+232 x^{8}-432 x^{7}+774 x^{6}-1944 x^{5}+1944 x^{4}-2916 x^{3}+5832 x^{2}+6561}{x^{8}}}\)	\(249\)
risch	\(\frac {x^{-8 \,{\mathrm e}^{2}} x^{-\frac {432}{x^{2}}} x^{48 x} x^{\frac {972}{x^{3}}} x^{\frac {432}{x}} x^{4 \,{\mathrm e}^{2} x} x^{4 x^{3}} x^{-24 x^{2}} x^{-\frac {2916}{x^{6}}} x^{-\frac {1944}{x^{4}}} x^{-\frac {36 \,{\mathrm e}^{2}}{x^{2}}} {\mathrm e}^{\frac {6561+8 x^{8} {\mathrm e}^{2}-8 x^{8} \ln \left (x \right )^{3}-24 x^{9} \ln \left (x \right )^{2}+2 \,{\mathrm e}^{2} x^{10}-8 \,{\mathrm e}^{2} x^{9}+4 x^{9} \ln \left (x \right )^{3}+6 x^{10} \ln \left (x \right )^{2}-108 x^{7} \ln \left (x \right )^{2}+72 x^{6} {\mathrm e}^{2}+24 x^{8} \ln \left (x \right )^{2}+216 x^{6} \ln \left (x \right )^{2}-36 x^{6} \ln \left (x \right )^{3}+x^{8} {\mathrm e}^{4}+486 x^{4} \ln \left (x \right )^{2}+x^{8} {\mathrm e}^{5}+162 x^{4} {\mathrm e}^{2}+x^{8} \ln \left (x \right )^{4}-8 x^{11}+x^{12}+24 x^{10}-68 x^{9}-432 x^{7}+232 x^{8}+1944 x^{4}-2916 x^{3}+5832 x^{2}+774 x^{6}-1944 x^{5}+2 \,{\mathrm e}^{2} \ln \left (x \right )^{2} x^{8}-36 x^{7} {\mathrm e}^{2}}{x^{8}}}}{x^{140}}\)	\(295\)

input

int(((4*x^9+4*x^8+72*x^6)*ln(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-540*x^6-1 
944*x^4)*ln(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x^8-648*x 
^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*ln(x)+(4*x^10-4*x^9-8*x^8+36*x^7- 
180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864*x^7-1980 
*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*ln(x)^4+(4*x^9- 
8*x^8-36*x^6)*ln(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^7+216*x^6+4 
86*x^4)*ln(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48*x^9-140*x^8 
+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*ln(x)+x^8*exp(5)+x^8*exp(2)^2+ 
(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11+24*x^10-68*x 
^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^2+6561)/x^8)/ 
x^9,x,method=_RETURNVERBOSE)
 

output

exp((x^8*ln(x)^4+(4*x^9-8*x^8-36*x^6)*ln(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+ 
24*x^8-108*x^7+216*x^6+486*x^4)*ln(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^1 
1-24*x^10+48*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*ln(x)+ 
x^8*exp(5)+x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+ 
x^12-8*x^11+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916* 
x^3+5832*x^2+6561)/x^8)
 

3.30.55.5 Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 241 vs. \(2 (23) = 46\).

Time = 3.21 (sec) , antiderivative size = 241, normalized size of antiderivative = 8.03 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=e^{\left (\frac {x^{12} + x^{8} \log \left (x\right )^{4} - 8 \, x^{11} + 24 \, x^{10} - 68 \, x^{9} + x^{8} e^{5} + x^{8} e^{4} + 232 \, x^{8} - 432 \, x^{7} + 774 \, x^{6} - 1944 \, x^{5} + 1944 \, x^{4} + 4 \, {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} \log \left (x\right )^{3} - 2916 \, x^{3} + 2 \, {\left (3 \, x^{10} - 12 \, x^{9} + x^{8} e^{2} + 12 \, x^{8} - 54 \, x^{7} + 108 \, x^{6} + 243 \, x^{4}\right )} \log \left (x\right )^{2} + 5832 \, x^{2} + 2 \, {\left (x^{10} - 4 \, x^{9} + 4 \, x^{8} - 18 \, x^{7} + 36 \, x^{6} + 81 \, x^{4}\right )} e^{2} + 4 \, {\left (x^{11} - 6 \, x^{10} + 12 \, x^{9} - 35 \, x^{8} + 108 \, x^{7} - 108 \, x^{6} + 243 \, x^{5} - 486 \, x^{4} - 729 \, x^{2} + {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} e^{2}\right )} \log \left (x\right ) + 6561}{x^{8}}\right )} \]

input

integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-54 
0*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x 
^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*x^ 
8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864 
*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*log(x) 
^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^ 
7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48 
*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+ 
x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11 
+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^ 
2+6561)/x^8)/x^9,x, algorithm=\
 

output

e^((x^12 + x^8*log(x)^4 - 8*x^11 + 24*x^10 - 68*x^9 + x^8*e^5 + x^8*e^4 + 
232*x^8 - 432*x^7 + 774*x^6 - 1944*x^5 + 1944*x^4 + 4*(x^9 - 2*x^8 - 9*x^6 
)*log(x)^3 - 2916*x^3 + 2*(3*x^10 - 12*x^9 + x^8*e^2 + 12*x^8 - 54*x^7 + 1 
08*x^6 + 243*x^4)*log(x)^2 + 5832*x^2 + 2*(x^10 - 4*x^9 + 4*x^8 - 18*x^7 + 
 36*x^6 + 81*x^4)*e^2 + 4*(x^11 - 6*x^10 + 12*x^9 - 35*x^8 + 108*x^7 - 108 
*x^6 + 243*x^5 - 486*x^4 - 729*x^2 + (x^9 - 2*x^8 - 9*x^6)*e^2)*log(x) + 6 
561)/x^8)
 

3.30.55.6 Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 248 vs. \(2 (24) = 48\).

Time = 2.88 (sec) , antiderivative size = 248, normalized size of antiderivative = 8.27 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=e^{\frac {x^{12} - 8 x^{11} + 24 x^{10} - 68 x^{9} + x^{8} \log {\left (x \right )}^{4} + x^{8} e^{4} + x^{8} e^{5} + 232 x^{8} - 432 x^{7} + 774 x^{6} - 1944 x^{5} + 1944 x^{4} - 2916 x^{3} + 5832 x^{2} + \left (4 x^{9} - 8 x^{8} - 36 x^{6}\right ) \log {\left (x \right )}^{3} + \left (2 x^{10} - 8 x^{9} + 8 x^{8} - 36 x^{7} + 72 x^{6} + 162 x^{4}\right ) e^{2} + \left (6 x^{10} - 24 x^{9} + 2 x^{8} e^{2} + 24 x^{8} - 108 x^{7} + 216 x^{6} + 486 x^{4}\right ) \log {\left (x \right )}^{2} + \left (4 x^{11} - 24 x^{10} + 48 x^{9} - 140 x^{8} + 432 x^{7} - 432 x^{6} + 972 x^{5} - 1944 x^{4} - 2916 x^{2} + \left (4 x^{9} - 8 x^{8} - 36 x^{6}\right ) e^{2}\right ) \log {\left (x \right )} + 6561}{x^{8}}} \]

input

integrate(((4*x**9+4*x**8+72*x**6)*ln(x)**3+(12*x**10-12*x**9-24*x**8+108* 
x**7-540*x**6-1944*x**4)*ln(x)**2+((4*x**9+4*x**8+72*x**6)*exp(2)+12*x**11 
-36*x**10+48*x**8-648*x**7+1296*x**6-2916*x**5+8748*x**4+17496*x**2)*ln(x) 
+(4*x**10-4*x**9-8*x**8+36*x**7-180*x**6-648*x**4)*exp(2)+4*x**12-20*x**11 
+24*x**10-20*x**9-140*x**8+864*x**7-1980*x**6+6804*x**5-9720*x**4+14580*x* 
*3-37908*x**2-52488)*exp((x**8*ln(x)**4+(4*x**9-8*x**8-36*x**6)*ln(x)**3+( 
2*x**8*exp(2)+6*x**10-24*x**9+24*x**8-108*x**7+216*x**6+486*x**4)*ln(x)**2 
+((4*x**9-8*x**8-36*x**6)*exp(2)+4*x**11-24*x**10+48*x**9-140*x**8+432*x** 
7-432*x**6+972*x**5-1944*x**4-2916*x**2)*ln(x)+x**8*exp(5)+x**8*exp(2)**2+ 
(2*x**10-8*x**9+8*x**8-36*x**7+72*x**6+162*x**4)*exp(2)+x**12-8*x**11+24*x 
**10-68*x**9+232*x**8-432*x**7+774*x**6-1944*x**5+1944*x**4-2916*x**3+5832 
*x**2+6561)/x**8)/x**9,x)
 

output

exp((x**12 - 8*x**11 + 24*x**10 - 68*x**9 + x**8*log(x)**4 + x**8*exp(4) + 
 x**8*exp(5) + 232*x**8 - 432*x**7 + 774*x**6 - 1944*x**5 + 1944*x**4 - 29 
16*x**3 + 5832*x**2 + (4*x**9 - 8*x**8 - 36*x**6)*log(x)**3 + (2*x**10 - 8 
*x**9 + 8*x**8 - 36*x**7 + 72*x**6 + 162*x**4)*exp(2) + (6*x**10 - 24*x**9 
 + 2*x**8*exp(2) + 24*x**8 - 108*x**7 + 216*x**6 + 486*x**4)*log(x)**2 + ( 
4*x**11 - 24*x**10 + 48*x**9 - 140*x**8 + 432*x**7 - 432*x**6 + 972*x**5 - 
 1944*x**4 - 2916*x**2 + (4*x**9 - 8*x**8 - 36*x**6)*exp(2))*log(x) + 6561 
)/x**8)
 

3.30.55.7 Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 258 vs. \(2 (23) = 46\).

Time = 5.30 (sec) , antiderivative size = 258, normalized size of antiderivative = 8.60 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=\frac {e^{\left (x^{4} + 4 \, x^{3} \log \left (x\right ) + 6 \, x^{2} \log \left (x\right )^{2} + 4 \, x \log \left (x\right )^{3} + \log \left (x\right )^{4} - 8 \, x^{3} + 2 \, x^{2} e^{2} - 24 \, x^{2} \log \left (x\right ) + 4 \, x e^{2} \log \left (x\right ) - 24 \, x \log \left (x\right )^{2} + 2 \, e^{2} \log \left (x\right )^{2} - 8 \, \log \left (x\right )^{3} + 24 \, x^{2} - 8 \, x e^{2} + 48 \, x \log \left (x\right ) - 8 \, e^{2} \log \left (x\right ) + 24 \, \log \left (x\right )^{2} - 68 \, x - \frac {108 \, \log \left (x\right )^{2}}{x} - \frac {36 \, \log \left (x\right )^{3}}{x^{2}} - \frac {36 \, e^{2}}{x} + \frac {432 \, \log \left (x\right )}{x} - \frac {36 \, e^{2} \log \left (x\right )}{x^{2}} + \frac {216 \, \log \left (x\right )^{2}}{x^{2}} - \frac {432}{x} + \frac {72 \, e^{2}}{x^{2}} - \frac {432 \, \log \left (x\right )}{x^{2}} + \frac {774}{x^{2}} + \frac {972 \, \log \left (x\right )}{x^{3}} + \frac {486 \, \log \left (x\right )^{2}}{x^{4}} - \frac {1944}{x^{3}} + \frac {162 \, e^{2}}{x^{4}} - \frac {1944 \, \log \left (x\right )}{x^{4}} + \frac {1944}{x^{4}} - \frac {2916}{x^{5}} - \frac {2916 \, \log \left (x\right )}{x^{6}} + \frac {5832}{x^{6}} + \frac {6561}{x^{8}} + e^{5} + e^{4} + 8 \, e^{2} + 232\right )}}{x^{140}} \]

input

integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-54 
0*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x 
^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*x^ 
8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864 
*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*log(x) 
^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^ 
7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48 
*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+ 
x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11 
+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^ 
2+6561)/x^8)/x^9,x, algorithm=\
 

output

e^(x^4 + 4*x^3*log(x) + 6*x^2*log(x)^2 + 4*x*log(x)^3 + log(x)^4 - 8*x^3 + 
 2*x^2*e^2 - 24*x^2*log(x) + 4*x*e^2*log(x) - 24*x*log(x)^2 + 2*e^2*log(x) 
^2 - 8*log(x)^3 + 24*x^2 - 8*x*e^2 + 48*x*log(x) - 8*e^2*log(x) + 24*log(x 
)^2 - 68*x - 108*log(x)^2/x - 36*log(x)^3/x^2 - 36*e^2/x + 432*log(x)/x - 
36*e^2*log(x)/x^2 + 216*log(x)^2/x^2 - 432/x + 72*e^2/x^2 - 432*log(x)/x^2 
 + 774/x^2 + 972*log(x)/x^3 + 486*log(x)^2/x^4 - 1944/x^3 + 162*e^2/x^4 - 
1944*log(x)/x^4 + 1944/x^4 - 2916/x^5 - 2916*log(x)/x^6 + 5832/x^6 + 6561/ 
x^8 + e^5 + e^4 + 8*e^2 + 232)/x^140
 

3.30.55.8 Giac [F]

\[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=\int { \frac {4 \, {\left (x^{12} - 5 \, x^{11} + 6 \, x^{10} - 5 \, x^{9} - 35 \, x^{8} + 216 \, x^{7} - 495 \, x^{6} + 1701 \, x^{5} - 2430 \, x^{4} + {\left (x^{9} + x^{8} + 18 \, x^{6}\right )} \log \left (x\right )^{3} + 3645 \, x^{3} + 3 \, {\left (x^{10} - x^{9} - 2 \, x^{8} + 9 \, x^{7} - 45 \, x^{6} - 162 \, x^{4}\right )} \log \left (x\right )^{2} - 9477 \, x^{2} + {\left (x^{10} - x^{9} - 2 \, x^{8} + 9 \, x^{7} - 45 \, x^{6} - 162 \, x^{4}\right )} e^{2} + {\left (3 \, x^{11} - 9 \, x^{10} + 12 \, x^{8} - 162 \, x^{7} + 324 \, x^{6} - 729 \, x^{5} + 2187 \, x^{4} + 4374 \, x^{2} + {\left (x^{9} + x^{8} + 18 \, x^{6}\right )} e^{2}\right )} \log \left (x\right ) - 13122\right )} e^{\left (\frac {x^{12} + x^{8} \log \left (x\right )^{4} - 8 \, x^{11} + 24 \, x^{10} - 68 \, x^{9} + x^{8} e^{5} + x^{8} e^{4} + 232 \, x^{8} - 432 \, x^{7} + 774 \, x^{6} - 1944 \, x^{5} + 1944 \, x^{4} + 4 \, {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} \log \left (x\right )^{3} - 2916 \, x^{3} + 2 \, {\left (3 \, x^{10} - 12 \, x^{9} + x^{8} e^{2} + 12 \, x^{8} - 54 \, x^{7} + 108 \, x^{6} + 243 \, x^{4}\right )} \log \left (x\right )^{2} + 5832 \, x^{2} + 2 \, {\left (x^{10} - 4 \, x^{9} + 4 \, x^{8} - 18 \, x^{7} + 36 \, x^{6} + 81 \, x^{4}\right )} e^{2} + 4 \, {\left (x^{11} - 6 \, x^{10} + 12 \, x^{9} - 35 \, x^{8} + 108 \, x^{7} - 108 \, x^{6} + 243 \, x^{5} - 486 \, x^{4} - 729 \, x^{2} + {\left (x^{9} - 2 \, x^{8} - 9 \, x^{6}\right )} e^{2}\right )} \log \left (x\right ) + 6561}{x^{8}}\right )}}{x^{9}} \,d x } \]

input

integrate(((4*x^9+4*x^8+72*x^6)*log(x)^3+(12*x^10-12*x^9-24*x^8+108*x^7-54 
0*x^6-1944*x^4)*log(x)^2+((4*x^9+4*x^8+72*x^6)*exp(2)+12*x^11-36*x^10+48*x 
^8-648*x^7+1296*x^6-2916*x^5+8748*x^4+17496*x^2)*log(x)+(4*x^10-4*x^9-8*x^ 
8+36*x^7-180*x^6-648*x^4)*exp(2)+4*x^12-20*x^11+24*x^10-20*x^9-140*x^8+864 
*x^7-1980*x^6+6804*x^5-9720*x^4+14580*x^3-37908*x^2-52488)*exp((x^8*log(x) 
^4+(4*x^9-8*x^8-36*x^6)*log(x)^3+(2*x^8*exp(2)+6*x^10-24*x^9+24*x^8-108*x^ 
7+216*x^6+486*x^4)*log(x)^2+((4*x^9-8*x^8-36*x^6)*exp(2)+4*x^11-24*x^10+48 
*x^9-140*x^8+432*x^7-432*x^6+972*x^5-1944*x^4-2916*x^2)*log(x)+x^8*exp(5)+ 
x^8*exp(2)^2+(2*x^10-8*x^9+8*x^8-36*x^7+72*x^6+162*x^4)*exp(2)+x^12-8*x^11 
+24*x^10-68*x^9+232*x^8-432*x^7+774*x^6-1944*x^5+1944*x^4-2916*x^3+5832*x^ 
2+6561)/x^8)/x^9,x, algorithm=\
 

output

integrate(4*(x^12 - 5*x^11 + 6*x^10 - 5*x^9 - 35*x^8 + 216*x^7 - 495*x^6 + 
 1701*x^5 - 2430*x^4 + (x^9 + x^8 + 18*x^6)*log(x)^3 + 3645*x^3 + 3*(x^10 
- x^9 - 2*x^8 + 9*x^7 - 45*x^6 - 162*x^4)*log(x)^2 - 9477*x^2 + (x^10 - x^ 
9 - 2*x^8 + 9*x^7 - 45*x^6 - 162*x^4)*e^2 + (3*x^11 - 9*x^10 + 12*x^8 - 16 
2*x^7 + 324*x^6 - 729*x^5 + 2187*x^4 + 4374*x^2 + (x^9 + x^8 + 18*x^6)*e^2 
)*log(x) - 13122)*e^((x^12 + x^8*log(x)^4 - 8*x^11 + 24*x^10 - 68*x^9 + x^ 
8*e^5 + x^8*e^4 + 232*x^8 - 432*x^7 + 774*x^6 - 1944*x^5 + 1944*x^4 + 4*(x 
^9 - 2*x^8 - 9*x^6)*log(x)^3 - 2916*x^3 + 2*(3*x^10 - 12*x^9 + x^8*e^2 + 1 
2*x^8 - 54*x^7 + 108*x^6 + 243*x^4)*log(x)^2 + 5832*x^2 + 2*(x^10 - 4*x^9 
+ 4*x^8 - 18*x^7 + 36*x^6 + 81*x^4)*e^2 + 4*(x^11 - 6*x^10 + 12*x^9 - 35*x 
^8 + 108*x^7 - 108*x^6 + 243*x^5 - 486*x^4 - 729*x^2 + (x^9 - 2*x^8 - 9*x^ 
6)*e^2)*log(x) + 6561)/x^8)/x^9, x)
 

3.30.55.9 Mupad [B] (verification not implemented)

Time = 11.00 (sec) , antiderivative size = 299, normalized size of antiderivative = 9.97 \[ \int \frac {e^{\frac {6561+5832 x^2-2916 x^3+1944 x^4-1944 x^5+774 x^6-432 x^7+232 x^8+e^4 x^8+e^5 x^8-68 x^9+24 x^{10}-8 x^{11}+x^{12}+e^2 \left (162 x^4+72 x^6-36 x^7+8 x^8-8 x^9+2 x^{10}\right )+\left (-2916 x^2-1944 x^4+972 x^5-432 x^6+432 x^7-140 x^8+48 x^9-24 x^{10}+4 x^{11}+e^2 \left (-36 x^6-8 x^8+4 x^9\right )\right ) \log (x)+\left (486 x^4+216 x^6-108 x^7+24 x^8+2 e^2 x^8-24 x^9+6 x^{10}\right ) \log ^2(x)+\left (-36 x^6-8 x^8+4 x^9\right ) \log ^3(x)+x^8 \log ^4(x)}{x^8}} \left (-52488-37908 x^2+14580 x^3-9720 x^4+6804 x^5-1980 x^6+864 x^7-140 x^8-20 x^9+24 x^{10}-20 x^{11}+4 x^{12}+e^2 \left (-648 x^4-180 x^6+36 x^7-8 x^8-4 x^9+4 x^{10}\right )+\left (17496 x^2+8748 x^4-2916 x^5+1296 x^6-648 x^7+48 x^8-36 x^{10}+12 x^{11}+e^2 \left (72 x^6+4 x^8+4 x^9\right )\right ) \log (x)+\left (-1944 x^4-540 x^6+108 x^7-24 x^8-12 x^9+12 x^{10}\right ) \log ^2(x)+\left (72 x^6+4 x^8+4 x^9\right ) \log ^3(x)\right )}{x^9} \, dx=\frac {x^{4\,x^3}\,x^{432/x}\,x^{\frac {972}{x^3}}\,x^{4\,x\,{\mathrm {e}}^2}\,x^{48\,x}\,{\mathrm {e}}^{2\,x^2\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-\frac {36\,{\mathrm {e}}^2}{x}}\,{\mathrm {e}}^{\frac {72\,{\mathrm {e}}^2}{x^2}}\,{\mathrm {e}}^{\frac {162\,{\mathrm {e}}^2}{x^4}}\,{\mathrm {e}}^{-8\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{24\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{8\,{\mathrm {e}}^2}\,{\mathrm {e}}^{-68\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{232}\,{\mathrm {e}}^{2\,{\mathrm {e}}^2\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{4\,x\,{\ln \left (x\right )}^3}\,{\mathrm {e}}^{-24\,x\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-8\,x^3}\,{\mathrm {e}}^{24\,x^2}\,{\mathrm {e}}^{-\frac {432}{x}}\,{\mathrm {e}}^{\frac {774}{x^2}}\,{\mathrm {e}}^{-\frac {1944}{x^3}}\,{\mathrm {e}}^{\frac {1944}{x^4}}\,{\mathrm {e}}^{-\frac {2916}{x^5}}\,{\mathrm {e}}^{\frac {5832}{x^6}}\,{\mathrm {e}}^{\frac {6561}{x^8}}\,{\mathrm {e}}^{-8\,x\,{\mathrm {e}}^2}\,{\mathrm {e}}^{{\ln \left (x\right )}^4}\,{\mathrm {e}}^{{\mathrm {e}}^4}\,{\mathrm {e}}^{{\mathrm {e}}^5}\,{\mathrm {e}}^{6\,x^2\,{\ln \left (x\right )}^2}\,{\mathrm {e}}^{-\frac {36\,{\ln \left (x\right )}^3}{x^2}}\,{\mathrm {e}}^{-\frac {108\,{\ln \left (x\right )}^2}{x}}\,{\mathrm {e}}^{\frac {216\,{\ln \left (x\right )}^2}{x^2}}\,{\mathrm {e}}^{\frac {486\,{\ln \left (x\right )}^2}{x^4}}}{x^{24\,x^2}\,x^{\frac {432}{x^2}}\,x^{\frac {1944}{x^4}}\,x^{\frac {2916}{x^6}}\,x^{\frac {36\,{\mathrm {e}}^2}{x^2}}\,x^{8\,{\mathrm {e}}^2}\,x^{140}} \]

input

int(-(exp((exp(2)*(162*x^4 + 72*x^6 - 36*x^7 + 8*x^8 - 8*x^9 + 2*x^10) - l 
og(x)*(exp(2)*(36*x^6 + 8*x^8 - 4*x^9) + 2916*x^2 + 1944*x^4 - 972*x^5 + 4 
32*x^6 - 432*x^7 + 140*x^8 - 48*x^9 + 24*x^10 - 4*x^11) + x^8*log(x)^4 + x 
^8*exp(4) + x^8*exp(5) - log(x)^3*(36*x^6 + 8*x^8 - 4*x^9) + 5832*x^2 - 29 
16*x^3 + 1944*x^4 - 1944*x^5 + 774*x^6 - 432*x^7 + 232*x^8 - 68*x^9 + 24*x 
^10 - 8*x^11 + x^12 + log(x)^2*(2*x^8*exp(2) + 486*x^4 + 216*x^6 - 108*x^7 
 + 24*x^8 - 24*x^9 + 6*x^10) + 6561)/x^8)*(log(x)^2*(1944*x^4 + 540*x^6 - 
108*x^7 + 24*x^8 + 12*x^9 - 12*x^10) - log(x)*(exp(2)*(72*x^6 + 4*x^8 + 4* 
x^9) + 17496*x^2 + 8748*x^4 - 2916*x^5 + 1296*x^6 - 648*x^7 + 48*x^8 - 36* 
x^10 + 12*x^11) + exp(2)*(648*x^4 + 180*x^6 - 36*x^7 + 8*x^8 + 4*x^9 - 4*x 
^10) - log(x)^3*(72*x^6 + 4*x^8 + 4*x^9) + 37908*x^2 - 14580*x^3 + 9720*x^ 
4 - 6804*x^5 + 1980*x^6 - 864*x^7 + 140*x^8 + 20*x^9 - 24*x^10 + 20*x^11 - 
 4*x^12 + 52488))/x^9,x)
 

output

(x^(4*x^3)*x^(432/x)*x^(972/x^3)*x^(4*x*exp(2))*x^(48*x)*exp(2*x^2*exp(2)) 
*exp(-(36*exp(2))/x)*exp((72*exp(2))/x^2)*exp((162*exp(2))/x^4)*exp(-8*log 
(x)^3)*exp(24*log(x)^2)*exp(8*exp(2))*exp(-68*x)*exp(x^4)*exp(232)*exp(2*e 
xp(2)*log(x)^2)*exp(4*x*log(x)^3)*exp(-24*x*log(x)^2)*exp(-8*x^3)*exp(24*x 
^2)*exp(-432/x)*exp(774/x^2)*exp(-1944/x^3)*exp(1944/x^4)*exp(-2916/x^5)*e 
xp(5832/x^6)*exp(6561/x^8)*exp(-8*x*exp(2))*exp(log(x)^4)*exp(exp(4))*exp( 
exp(5))*exp(6*x^2*log(x)^2)*exp(-(36*log(x)^3)/x^2)*exp(-(108*log(x)^2)/x) 
*exp((216*log(x)^2)/x^2)*exp((486*log(x)^2)/x^4))/(x^(24*x^2)*x^(432/x^2)* 
x^(1944/x^4)*x^(2916/x^6)*x^((36*exp(2))/x^2)*x^(8*exp(2))*x^140)