Integrand size = 238, antiderivative size = 25 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\frac {5}{-3 e+e^{\frac {4 e^x}{9-\log (\log (x))}}+x} \] Output:
5/(x+exp(4*exp(x)/(9-ln(ln(x))))-3*exp(1))
Leaf count is larger than twice the leaf count of optimal. \(55\) vs. \(2(25)=50\).
Time = 0.37 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.20 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=-\frac {5 e^{\frac {4 e^x}{-9+\log (\log (x))}}}{-1+3 e^{1+\frac {4 e^x}{-9+\log (\log (x))}}-e^{\frac {4 e^x}{-9+\log (\log (x))}} x} \] Input:
Integrate[(-405*x*Log[x] + 90*x*Log[x]*Log[Log[x]] - 5*x*Log[x]*Log[Log[x] ]^2 + (-20*E^x - 180*E^x*x*Log[x] + 20*E^x*x*Log[x]*Log[Log[x]])/E^((4*E^x )/(-9 + Log[Log[x]])))/((729*E^2*x - 486*E*x^2 + 81*x^3)*Log[x] + (-162*E^ 2*x + 108*E*x^2 - 18*x^3)*Log[x]*Log[Log[x]] + (9*E^2*x - 6*E*x^2 + x^3)*L og[x]*Log[Log[x]]^2 + (81*x*Log[x] - 18*x*Log[x]*Log[Log[x]] + x*Log[x]*Lo g[Log[x]]^2)/E^((8*E^x)/(-9 + Log[Log[x]])) + ((-486*E*x + 162*x^2)*Log[x] + (108*E*x - 36*x^2)*Log[x]*Log[Log[x]] + (-6*E*x + 2*x^2)*Log[x]*Log[Log [x]]^2)/E^((4*E^x)/(-9 + Log[Log[x]]))),x]
Output:
(-5*E^((4*E^x)/(-9 + Log[Log[x]])))/(-1 + 3*E^(1 + (4*E^x)/(-9 + Log[Log[x ]])) - E^((4*E^x)/(-9 + Log[Log[x]]))*x)
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.
| \(\displaystyle \int \frac {-5 x \log (x) \log ^2(\log (x))+90 x \log (x) \log (\log (x))-405 x \log (x)+e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (\log (x)) \log (x)\right )}{e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (\left (2 x^2-6 e x\right ) \log (x) \log ^2(\log (x))+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (162 x^2-486 e x\right ) \log (x)\right )+\left (x^3-6 e x^2+9 e^2 x\right ) \log (x) \log ^2(\log (x))+\left (-18 x^3+108 e x^2-162 e^2 x\right ) \log (x) \log (\log (x))+\left (81 x^3-486 e x^2+729 e^2 x\right ) \log (x)+e^{-\frac {8 e^x}{\log (\log (x))-9}} \left (x \log (x) \log ^2(\log (x))-18 x \log (x) \log (\log (x))+81 x \log (x)\right )} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {5 e^{\frac {4 e^x}{\log (\log (x))-9}} \left (-4 e^x-x \log (x) (\log (\log (x))-9) \left (-4 e^x+e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )\right )}{x \left (x e^{\frac {4 e^x}{\log (\log (x))-9}}-3 e^{\frac {4 e^x}{\log (\log (x))-9}+1}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 5 \int -\frac {e^{-\frac {4 e^x}{9-\log (\log (x))}} \left (x \log (x) (9-\log (\log (x))) \left (-e^{-\frac {4 e^x}{9-\log (\log (x))}} \log (\log (x))+4 e^x+9 e^{-\frac {4 e^x}{9-\log (\log (x))}}\right )+4 e^x\right )}{x \left (e^{-\frac {4 e^x}{9-\log (\log (x))}} x-3 e^{1-\frac {4 e^x}{9-\log (\log (x))}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -5 \int \frac {e^{-\frac {4 e^x}{9-\log (\log (x))}} \left (x \log (x) (9-\log (\log (x))) \left (-e^{-\frac {4 e^x}{9-\log (\log (x))}} \log (\log (x))+4 e^x+9 e^{-\frac {4 e^x}{9-\log (\log (x))}}\right )+4 e^x\right )}{x \left (e^{-\frac {4 e^x}{9-\log (\log (x))}} x-3 e^{1-\frac {4 e^x}{9-\log (\log (x))}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (-\frac {4 e^{x-\frac {4 e^x}{9-\log (\log (x))}} (-9 x \log (x)+x \log (\log (x)) \log (x)-1)}{x \log (x) (\log (\log (x))-9)^2}-\frac {e^{\frac {8 e^x}{\log (\log (x))-9}-\frac {4 e^x}{9-\log (\log (x))}} (3 e-x) \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}+\frac {e^{\frac {4 e^x}{\log (\log (x))-9}-\frac {4 e^x}{9-\log (\log (x))}} \left (-72 e^x \log (x) x^2+8 e^x \log (x) \log (\log (x)) x^2-8 e^x x+\log (x) \log ^2(\log (x)) x+216 e^{x+1} \log (x) x+81 \log (x) x-24 e^{x+1} \log (x) \log (\log (x)) x-18 \log (x) \log (\log (x)) x+24 e^{x+1}\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right ) \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{\left (-x-e^{-\frac {4 e^x}{\log (\log (x))-9}}+3 e\right )^2 x \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (-\frac {e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (72 e^x \log (x) x^2-8 e^x \log (x) \log (\log (x)) x^2+8 e^x x-3 \log (x) \log ^2(\log (x)) x-216 e^{x+1} \log (x) x-243 \log (x) x+24 e^{x+1} \log (x) \log (\log (x)) x+54 \log (x) \log (\log (x)) x-24 e^{x+1}\right )}{(3 e-x)^3 x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right ) \log (x) (\log (\log (x))-9)^2}-\frac {e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x)^3 x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}-\frac {2 e^{-\frac {4 e^x}{\log (\log (x))-9}} \left (18 e^x \log (x) x^2-2 e^x \log (x) \log (\log (x)) x^2+2 e^x x-\log (x) \log ^2(\log (x)) x-54 e^{x+1} \log (x) x-81 \log (x) x+6 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-6 e^{x+1}\right )}{(3 e-x)^3 x \log (x) (\log (\log (x))-9)^2}+\frac {1}{(3 e-x)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -5 \int \frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (x \log (x) (\log (\log (x))-9) \left (e^{\frac {4 e^x}{\log (\log (x))-9}} \log (\log (x))-4 e^x-9 e^{\frac {4 e^x}{\log (\log (x))-9}}\right )+4 e^x\right )}{x \left (e^{\frac {4 e^x}{\log (\log (x))-9}} x-3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}+1\right )^2 \log (x) (9-\log (\log (x)))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -5 \int \left (\frac {e^{\frac {4 e^x}{\log (\log (x))-9}}}{(3 e-x) \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )}-\frac {e^{\frac {4 e^x}{\log (\log (x))-9}} \left (36 e^x \log (x) x^2-4 e^x \log (x) \log (\log (x)) x^2+4 e^x x-\log (x) \log ^2(\log (x)) x-108 e^{x+1} \log (x) x-81 \log (x) x+12 e^{x+1} \log (x) \log (\log (x)) x+18 \log (x) \log (\log (x)) x-12 e^{x+1}\right )}{(3 e-x) x \left (-e^{\frac {4 e^x}{\log (\log (x))-9}} x+3 e^{1+\frac {4 e^x}{\log (\log (x))-9}}-1\right )^2 \log (x) (\log (\log (x))-9)^2}\right )dx\) |
Input:
Int[(-405*x*Log[x] + 90*x*Log[x]*Log[Log[x]] - 5*x*Log[x]*Log[Log[x]]^2 + (-20*E^x - 180*E^x*x*Log[x] + 20*E^x*x*Log[x]*Log[Log[x]])/E^((4*E^x)/(-9 + Log[Log[x]])))/((729*E^2*x - 486*E*x^2 + 81*x^3)*Log[x] + (-162*E^2*x + 108*E*x^2 - 18*x^3)*Log[x]*Log[Log[x]] + (9*E^2*x - 6*E*x^2 + x^3)*Log[x]* Log[Log[x]]^2 + (81*x*Log[x] - 18*x*Log[x]*Log[Log[x]] + x*Log[x]*Log[Log[ x]]^2)/E^((8*E^x)/(-9 + Log[Log[x]])) + ((-486*E*x + 162*x^2)*Log[x] + (10 8*E*x - 36*x^2)*Log[x]*Log[Log[x]] + (-6*E*x + 2*x^2)*Log[x]*Log[Log[x]]^2 )/E^((4*E^x)/(-9 + Log[Log[x]]))),x]
Output:
$Aborted
Time = 0.09 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08
\[-\frac {5}{3 \,{\mathrm e}-x -{\mathrm e}^{-\frac {4 \,{\mathrm e}^{x}}{\ln \left (\ln \left (x \right )\right )-9}}}\]
Input:
int(((20*x*exp(x)*ln(x)*ln(ln(x))-180*x*exp(x)*ln(x)-20*exp(x))*exp(-4*exp (x)/(ln(ln(x))-9))-5*x*ln(x)*ln(ln(x))^2+90*x*ln(x)*ln(ln(x))-405*x*ln(x)) /((x*ln(x)*ln(ln(x))^2-18*x*ln(x)*ln(ln(x))+81*x*ln(x))*exp(-4*exp(x)/(ln( ln(x))-9))^2+((-6*x*exp(1)+2*x^2)*ln(x)*ln(ln(x))^2+(108*x*exp(1)-36*x^2)* ln(x)*ln(ln(x))+(-486*x*exp(1)+162*x^2)*ln(x))*exp(-4*exp(x)/(ln(ln(x))-9) )+(9*x*exp(1)^2-6*x^2*exp(1)+x^3)*ln(x)*ln(ln(x))^2+(-162*x*exp(1)^2+108*x ^2*exp(1)-18*x^3)*ln(x)*ln(ln(x))+(729*x*exp(1)^2-486*x^2*exp(1)+81*x^3)*l n(x)),x)
Output:
-5/(3*exp(1)-x-exp(-4*exp(x)/(ln(ln(x))-9)))
Time = 0.11 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\frac {5}{x - 3 \, e + e^{\left (-\frac {4 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )}} \] Input:
integrate(((20*x*exp(x)*log(x)*log(log(x))-180*x*exp(x)*log(x)-20*exp(x))* exp(-4*exp(x)/(log(log(x))-9))-5*x*log(x)*log(log(x))^2+90*x*log(x)*log(lo g(x))-405*x*log(x))/((x*log(x)*log(log(x))^2-18*x*log(x)*log(log(x))+81*x* log(x))*exp(-4*exp(x)/(log(log(x))-9))^2+((-6*exp(1)*x+2*x^2)*log(x)*log(l og(x))^2+(108*exp(1)*x-36*x^2)*log(x)*log(log(x))+(-486*exp(1)*x+162*x^2)* log(x))*exp(-4*exp(x)/(log(log(x))-9))+(9*x*exp(1)^2-6*x^2*exp(1)+x^3)*log (x)*log(log(x))^2+(-162*x*exp(1)^2+108*x^2*exp(1)-18*x^3)*log(x)*log(log(x ))+(729*x*exp(1)^2-486*x^2*exp(1)+81*x^3)*log(x)),x, algorithm="fricas")
Output:
5/(x - 3*e + e^(-4*e^x/(log(log(x)) - 9)))
Time = 0.94 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\frac {5}{x - 3 e + e^{- \frac {4 e^{x}}{\log {\left (\log {\left (x \right )} \right )} - 9}}} \] Input:
integrate(((20*x*exp(x)*ln(x)*ln(ln(x))-180*x*exp(x)*ln(x)-20*exp(x))*exp( -4*exp(x)/(ln(ln(x))-9))-5*x*ln(x)*ln(ln(x))**2+90*x*ln(x)*ln(ln(x))-405*x *ln(x))/((x*ln(x)*ln(ln(x))**2-18*x*ln(x)*ln(ln(x))+81*x*ln(x))*exp(-4*exp (x)/(ln(ln(x))-9))**2+((-6*exp(1)*x+2*x**2)*ln(x)*ln(ln(x))**2+(108*exp(1) *x-36*x**2)*ln(x)*ln(ln(x))+(-486*exp(1)*x+162*x**2)*ln(x))*exp(-4*exp(x)/ (ln(ln(x))-9))+(9*x*exp(1)**2-6*x**2*exp(1)+x**3)*ln(x)*ln(ln(x))**2+(-162 *x*exp(1)**2+108*x**2*exp(1)-18*x**3)*ln(x)*ln(ln(x))+(729*x*exp(1)**2-486 *x**2*exp(1)+81*x**3)*ln(x)),x)
Output:
5/(x - 3*E + exp(-4*exp(x)/(log(log(x)) - 9)))
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.48 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\frac {5 \, e^{\left (\frac {4 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )}}{{\left (x - 3 \, e\right )} e^{\left (\frac {4 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )} + 1} \] Input:
integrate(((20*x*exp(x)*log(x)*log(log(x))-180*x*exp(x)*log(x)-20*exp(x))* exp(-4*exp(x)/(log(log(x))-9))-5*x*log(x)*log(log(x))^2+90*x*log(x)*log(lo g(x))-405*x*log(x))/((x*log(x)*log(log(x))^2-18*x*log(x)*log(log(x))+81*x* log(x))*exp(-4*exp(x)/(log(log(x))-9))^2+((-6*exp(1)*x+2*x^2)*log(x)*log(l og(x))^2+(108*exp(1)*x-36*x^2)*log(x)*log(log(x))+(-486*exp(1)*x+162*x^2)* log(x))*exp(-4*exp(x)/(log(log(x))-9))+(9*x*exp(1)^2-6*x^2*exp(1)+x^3)*log (x)*log(log(x))^2+(-162*x*exp(1)^2+108*x^2*exp(1)-18*x^3)*log(x)*log(log(x ))+(729*x*exp(1)^2-486*x^2*exp(1)+81*x^3)*log(x)),x, algorithm="maxima")
Output:
5*e^(4*e^x/(log(log(x)) - 9))/((x - 3*e)*e^(4*e^x/(log(log(x)) - 9)) + 1)
\[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\int { -\frac {5 \, {\left (x \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} - 18 \, x \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 4 \, {\left (x e^{x} \log \left (x\right ) \log \left (\log \left (x\right )\right ) - 9 \, x e^{x} \log \left (x\right ) - e^{x}\right )} e^{\left (-\frac {4 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )} + 81 \, x \log \left (x\right )\right )}}{{\left (x^{3} - 6 \, x^{2} e + 9 \, x e^{2}\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} - 18 \, {\left (x^{3} - 6 \, x^{2} e + 9 \, x e^{2}\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 2 \, {\left ({\left (x^{2} - 3 \, x e\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} - 18 \, {\left (x^{2} - 3 \, x e\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 81 \, {\left (x^{2} - 3 \, x e\right )} \log \left (x\right )\right )} e^{\left (-\frac {4 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )} + {\left (x \log \left (x\right ) \log \left (\log \left (x\right )\right )^{2} - 18 \, x \log \left (x\right ) \log \left (\log \left (x\right )\right ) + 81 \, x \log \left (x\right )\right )} e^{\left (-\frac {8 \, e^{x}}{\log \left (\log \left (x\right )\right ) - 9}\right )} + 81 \, {\left (x^{3} - 6 \, x^{2} e + 9 \, x e^{2}\right )} \log \left (x\right )} \,d x } \] Input:
integrate(((20*x*exp(x)*log(x)*log(log(x))-180*x*exp(x)*log(x)-20*exp(x))* exp(-4*exp(x)/(log(log(x))-9))-5*x*log(x)*log(log(x))^2+90*x*log(x)*log(lo g(x))-405*x*log(x))/((x*log(x)*log(log(x))^2-18*x*log(x)*log(log(x))+81*x* log(x))*exp(-4*exp(x)/(log(log(x))-9))^2+((-6*exp(1)*x+2*x^2)*log(x)*log(l og(x))^2+(108*exp(1)*x-36*x^2)*log(x)*log(log(x))+(-486*exp(1)*x+162*x^2)* log(x))*exp(-4*exp(x)/(log(log(x))-9))+(9*x*exp(1)^2-6*x^2*exp(1)+x^3)*log (x)*log(log(x))^2+(-162*x*exp(1)^2+108*x^2*exp(1)-18*x^3)*log(x)*log(log(x ))+(729*x*exp(1)^2-486*x^2*exp(1)+81*x^3)*log(x)),x, algorithm="giac")
Output:
undef
Time = 3.91 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.88 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=\frac {5}{x-3\,\mathrm {e}+{\mathrm {e}}^{-\frac {4\,{\mathrm {e}}^x}{\ln \left (\ln \left (x\right )\right )-9}}} \] Input:
int(-(exp(-(4*exp(x))/(log(log(x)) - 9))*(20*exp(x) + 180*x*exp(x)*log(x) - 20*x*log(log(x))*exp(x)*log(x)) + 405*x*log(x) - 90*x*log(log(x))*log(x) + 5*x*log(log(x))^2*log(x))/(exp(-(8*exp(x))/(log(log(x)) - 9))*(81*x*log (x) - 18*x*log(log(x))*log(x) + x*log(log(x))^2*log(x)) + log(x)*(729*x*ex p(2) - 486*x^2*exp(1) + 81*x^3) - exp(-(4*exp(x))/(log(log(x)) - 9))*(log( x)*(486*x*exp(1) - 162*x^2) - log(log(x))*log(x)*(108*x*exp(1) - 36*x^2) + log(log(x))^2*log(x)*(6*x*exp(1) - 2*x^2)) - log(log(x))*log(x)*(162*x*ex p(2) - 108*x^2*exp(1) + 18*x^3) + log(log(x))^2*log(x)*(9*x*exp(2) - 6*x^2 *exp(1) + x^3)),x)
Output:
5/(x - 3*exp(1) + exp(-(4*exp(x))/(log(log(x)) - 9)))
Time = 0.27 (sec) , antiderivative size = 54, normalized size of antiderivative = 2.16 \[ \int \frac {-405 x \log (x)+90 x \log (x) \log (\log (x))-5 x \log (x) \log ^2(\log (x))+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (-20 e^x-180 e^x x \log (x)+20 e^x x \log (x) \log (\log (x))\right )}{\left (729 e^2 x-486 e x^2+81 x^3\right ) \log (x)+\left (-162 e^2 x+108 e x^2-18 x^3\right ) \log (x) \log (\log (x))+\left (9 e^2 x-6 e x^2+x^3\right ) \log (x) \log ^2(\log (x))+e^{-\frac {8 e^x}{-9+\log (\log (x))}} \left (81 x \log (x)-18 x \log (x) \log (\log (x))+x \log (x) \log ^2(\log (x))\right )+e^{-\frac {4 e^x}{-9+\log (\log (x))}} \left (\left (-486 e x+162 x^2\right ) \log (x)+\left (108 e x-36 x^2\right ) \log (x) \log (\log (x))+\left (-6 e x+2 x^2\right ) \log (x) \log ^2(\log (x))\right )} \, dx=-\frac {5 e^{\frac {4 e^{x}}{\mathrm {log}\left (\mathrm {log}\left (x \right )\right )-9}}}{3 e^{\frac {4 e^{x}}{\mathrm {log}\left (\mathrm {log}\left (x \right )\right )-9}} e -e^{\frac {4 e^{x}}{\mathrm {log}\left (\mathrm {log}\left (x \right )\right )-9}} x -1} \] Input:
int(((20*x*exp(x)*log(x)*log(log(x))-180*x*exp(x)*log(x)-20*exp(x))*exp(-4 *exp(x)/(log(log(x))-9))-5*x*log(x)*log(log(x))^2+90*x*log(x)*log(log(x))- 405*x*log(x))/((x*log(x)*log(log(x))^2-18*x*log(x)*log(log(x))+81*x*log(x) )*exp(-4*exp(x)/(log(log(x))-9))^2+((-6*exp(1)*x+2*x^2)*log(x)*log(log(x)) ^2+(108*exp(1)*x-36*x^2)*log(x)*log(log(x))+(-486*exp(1)*x+162*x^2)*log(x) )*exp(-4*exp(x)/(log(log(x))-9))+(9*x*exp(1)^2-6*x^2*exp(1)+x^3)*log(x)*lo g(log(x))^2+(-162*x*exp(1)^2+108*x^2*exp(1)-18*x^3)*log(x)*log(log(x))+(72 9*x*exp(1)^2-486*x^2*exp(1)+81*x^3)*log(x)),x)
Output:
( - 5*e**((4*e**x)/(log(log(x)) - 9)))/(3*e**((4*e**x)/(log(log(x)) - 9))* e - e**((4*e**x)/(log(log(x)) - 9))*x - 1)