\(\int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} (-6 x-2 x^2) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} ((3+3 x) \log (x)+(3 x+3 x^2) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) (2+(-1-2 x) \log (x)+(-3 x-2 x^2) \log ^2(x))}{\log (x)})}{(-27 x^2-27 x^3-9 x^4-x^5) \log (x)+(-27 x^3-27 x^4-9 x^5-x^6) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 (x^2 \log (x)+x^3 \log ^2(x))}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 ((-9 x^2-3 x^3) \log (x)+(-9 x^3-3 x^4) \log ^2(x))}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) ((27 x^2+18 x^3+3 x^4) \log (x)+(27 x^3+18 x^4+3 x^5) \log ^2(x))}{\log (x)}} \, dx\) [601]

Optimal result

Integrand size = 322, antiderivative size = 24 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=e^{\frac {1}{x \left (3+x-e^{5+x} \left (x+\frac {1}{\log (x)}\right )\right )^2}} \]

[Out]

exp(1/x/(3-exp(x+ln(1/ln(x)+x)+5)+x)^2)

Rubi [F]

\[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=\int \frac {\exp \left (\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}\right ) \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx \]

[In]

Int[(E^(9*x + 6*x^2 + x^3 + (E^(5 + x)*(-6*x - 2*x^2)*(1 + x*Log[x]))/Log[x] + (E^(10 + 2*x)*x*(1 + x*Log[x])^
2)/Log[x]^2)^(-1)*((3 + 3*x)*Log[x] + (3*x + 3*x^2)*Log[x]^2 + (E^(5 + x)*(1 + x*Log[x])*(2 + (-1 - 2*x)*Log[x
] + (-3*x - 2*x^2)*Log[x]^2))/Log[x]))/((-27*x^2 - 27*x^3 - 9*x^4 - x^5)*Log[x] + (-27*x^3 - 27*x^4 - 9*x^5 -
x^6)*Log[x]^2 + (E^(15 + 3*x)*(1 + x*Log[x])^3*(x^2*Log[x] + x^3*Log[x]^2))/Log[x]^3 + (E^(10 + 2*x)*(1 + x*Lo
g[x])^2*((-9*x^2 - 3*x^3)*Log[x] + (-9*x^3 - 3*x^4)*Log[x]^2))/Log[x]^2 + (E^(5 + x)*(1 + x*Log[x])*((27*x^2 +
18*x^3 + 3*x^4)*Log[x] + (27*x^3 + 18*x^4 + 3*x^5)*Log[x]^2))/Log[x]),x]

[Out]

6*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^2)/(x^2*(1 + x*Log[x])*
(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^3), x] + 2*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3
+ (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^2)/(x*(1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*L
og[x])^3), x] - 2*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^3)/((1
+ x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^3), x] - 4*Defer[Int][(E^(Log[x]^2/(x*(E^(5
+ x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^3)/(x*(1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E
^(5 + x)*x*Log[x])^3), x] - 6*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Lo
g[x]^4)/((1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^3), x] - 6*Defer[Int][(E^(Log[x
]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^4)/(x*(1 + x*Log[x])*(E^(5 + x) - 3*Log[x] -
x*Log[x] + E^(5 + x)*x*Log[x])^3), x] - 2*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Lo
g[x])^2))*x*Log[x]^4)/((1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^3), x] + 2*Defer[
Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x])/(x^2*(1 + x*Log[x])*(E^(5 + x)
- 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^2), x] - Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5
+ x))*x)*Log[x])^2))*Log[x]^2)/(x^2*(1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^2),
x] - 2*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^2)/(x*(1 + x*Log[
x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^2), x] - 2*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) +
(-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^3)/((1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x
*Log[x])^2), x] - 3*Defer[Int][(E^(Log[x]^2/(x*(E^(5 + x) + (-3 + (-1 + E^(5 + x))*x)*Log[x])^2))*Log[x]^3)/(x
*(1 + x*Log[x])*(E^(5 + x) - 3*Log[x] - x*Log[x] + E^(5 + x)*x*Log[x])^2), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log (x) \left (2 e^{5+x}-e^{5+x} (1+2 x) \log (x)-\left (-3+3 \left (-1+e^{5+x}\right ) x+2 e^{5+x} x^2\right ) \log ^2(x)\right )}{x^2 \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^3} \, dx \\ & = \int \left (-\frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log (x) \left (-2+\log (x)+2 x \log (x)+3 x \log ^2(x)+2 x^2 \log ^2(x)\right )}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}-\frac {2 \exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^2(x) \left (-3-x+2 x \log (x)+x^2 \log (x)+3 x \log ^2(x)+3 x^2 \log ^2(x)+x^3 \log ^2(x)\right )}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^2(x) \left (-3-x+2 x \log (x)+x^2 \log (x)+3 x \log ^2(x)+3 x^2 \log ^2(x)+x^3 \log ^2(x)\right )}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx\right )-\int \frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log (x) \left (-2+\log (x)+2 x \log (x)+3 x \log ^2(x)+2 x^2 \log ^2(x)\right )}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx \\ & = -\left (2 \int \frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^2(x) \left (-3-x+x (2+x) \log (x)+x \left (3+3 x+x^2\right ) \log ^2(x)\right )}{x^2 (1+x \log (x)) \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^3} \, dx\right )-\int \left (-\frac {2 \exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log (x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}+\frac {\exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^2(x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}+\frac {2 \exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^2(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}+\frac {2 \exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^3(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}+\frac {3 \exp \left (\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}\right ) \log ^3(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2}\right ) \, dx \\ & = 2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log (x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-2 \int \left (-\frac {3 e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}-\frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}+\frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}+\frac {2 e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}+\frac {3 e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^4(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}+\frac {3 e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^4(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}+\frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} x \log ^4(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3}\right ) \, dx-3 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-\int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx \\ & = 2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} x \log ^4(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx+2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log (x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-2 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-3 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx-4 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^3(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx+6 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx-6 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^4(x)}{(1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx-6 \int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^4(x)}{x (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^3} \, dx-\int \frac {e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \log ^2(x)}{x^2 (1+x \log (x)) \left (e^{5+x}-3 \log (x)-x \log (x)+e^{5+x} x \log (x)\right )^2} \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.37 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=e^{\frac {\log ^2(x)}{x \left (e^{5+x}+\left (-3+\left (-1+e^{5+x}\right ) x\right ) \log (x)\right )^2}} \]

[In]

Integrate[(E^(9*x + 6*x^2 + x^3 + (E^(5 + x)*(-6*x - 2*x^2)*(1 + x*Log[x]))/Log[x] + (E^(10 + 2*x)*x*(1 + x*Lo
g[x])^2)/Log[x]^2)^(-1)*((3 + 3*x)*Log[x] + (3*x + 3*x^2)*Log[x]^2 + (E^(5 + x)*(1 + x*Log[x])*(2 + (-1 - 2*x)
*Log[x] + (-3*x - 2*x^2)*Log[x]^2))/Log[x]))/((-27*x^2 - 27*x^3 - 9*x^4 - x^5)*Log[x] + (-27*x^3 - 27*x^4 - 9*
x^5 - x^6)*Log[x]^2 + (E^(15 + 3*x)*(1 + x*Log[x])^3*(x^2*Log[x] + x^3*Log[x]^2))/Log[x]^3 + (E^(10 + 2*x)*(1
+ x*Log[x])^2*((-9*x^2 - 3*x^3)*Log[x] + (-9*x^3 - 3*x^4)*Log[x]^2))/Log[x]^2 + (E^(5 + x)*(1 + x*Log[x])*((27
*x^2 + 18*x^3 + 3*x^4)*Log[x] + (27*x^3 + 18*x^4 + 3*x^5)*Log[x]^2))/Log[x]),x]

[Out]

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

Maple [C] (warning: unable to verify)

Result contains higher order function than in optimal. Order 9 vs. order 3.

Time = 0.07 (sec) , antiderivative size = 578, normalized size of antiderivative = 24.08

\[\text {Expression too large to display}\]

[In]

int((((-2*x^2-3*x)*ln(x)^2+(-1-2*x)*ln(x)+2)*exp(ln((x*ln(x)+1)/ln(x))+5+x)+(3*x^2+3*x)*ln(x)^2+(3*x+3)*ln(x))
*exp(1/(x*exp(ln((x*ln(x)+1)/ln(x))+5+x)^2+(-2*x^2-6*x)*exp(ln((x*ln(x)+1)/ln(x))+5+x)+x^3+6*x^2+9*x))/((x^3*l
n(x)^2+x^2*ln(x))*exp(ln((x*ln(x)+1)/ln(x))+5+x)^3+((-3*x^4-9*x^3)*ln(x)^2+(-3*x^3-9*x^2)*ln(x))*exp(ln((x*ln(
x)+1)/ln(x))+5+x)^2+((3*x^5+18*x^4+27*x^3)*ln(x)^2+(3*x^4+18*x^3+27*x^2)*ln(x))*exp(ln((x*ln(x)+1)/ln(x))+5+x)
+(-x^6-9*x^5-27*x^4-27*x^3)*ln(x)^2+(-x^5-9*x^4-27*x^3-27*x^2)*ln(x)),x)

[Out]

exp(ln(x)^2/x/(-2*ln(x)^2*exp(5+x)*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^3)*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(
x)+1))^2*csgn(I/ln(x)))*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I*(x*ln(x)+1)))*exp(-1/2*I*Pi*csgn(I/ln(
x)*(x*ln(x)+1))*csgn(I/ln(x))*csgn(I*(x*ln(x)+1)))*x^2-6*ln(x)^2*exp(5+x)*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+
1))^3)*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I/ln(x)))*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I
*(x*ln(x)+1)))*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))*csgn(I/ln(x))*csgn(I*(x*ln(x)+1)))*x-2*ln(x)*exp(5+x)*e
xp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^3)*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I/ln(x)))*exp(1/2*I*Pi
*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I*(x*ln(x)+1)))*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))*csgn(I/ln(x))*csgn(I
*(x*ln(x)+1)))*x-6*exp(5+x)*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^3)*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^
2*csgn(I/ln(x)))*exp(1/2*I*Pi*csgn(I/ln(x)*(x*ln(x)+1))^2*csgn(I*(x*ln(x)+1)))*exp(-1/2*I*Pi*csgn(I/ln(x)*(x*l
n(x)+1))*csgn(I/ln(x))*csgn(I*(x*ln(x)+1)))*ln(x)+ln(x)^2*exp(2*x+10)*x^2+x^2*ln(x)^2+6*x*ln(x)^2+2*ln(x)*exp(
2*x+10)*x+9*ln(x)^2+exp(2*x+10)))

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (23) = 46\).

Time = 0.25 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.58 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=e^{\left (\frac {1}{x^{3} + 6 \, x^{2} + x e^{\left (2 \, x + 2 \, \log \left (\frac {x \log \left (x\right ) + 1}{\log \left (x\right )}\right ) + 10\right )} - 2 \, {\left (x^{2} + 3 \, x\right )} e^{\left (x + \log \left (\frac {x \log \left (x\right ) + 1}{\log \left (x\right )}\right ) + 5\right )} + 9 \, x}\right )} \]

[In]

integrate((((-2*x^2-3*x)*log(x)^2+(-1-2*x)*log(x)+2)*exp(log((x*log(x)+1)/log(x))+5+x)+(3*x^2+3*x)*log(x)^2+(3
*x+3)*log(x))*exp(1/(x*exp(log((x*log(x)+1)/log(x))+5+x)^2+(-2*x^2-6*x)*exp(log((x*log(x)+1)/log(x))+5+x)+x^3+
6*x^2+9*x))/((x^3*log(x)^2+x^2*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^3+((-3*x^4-9*x^3)*log(x)^2+(-3*x^3-9*
x^2)*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^2+((3*x^5+18*x^4+27*x^3)*log(x)^2+(3*x^4+18*x^3+27*x^2)*log(x))
*exp(log((x*log(x)+1)/log(x))+5+x)+(-x^6-9*x^5-27*x^4-27*x^3)*log(x)^2+(-x^5-9*x^4-27*x^3-27*x^2)*log(x)),x, a
lgorithm="fricas")

[Out]

e^(1/(x^3 + 6*x^2 + x*e^(2*x + 2*log((x*log(x) + 1)/log(x)) + 10) - 2*(x^2 + 3*x)*e^(x + log((x*log(x) + 1)/lo
g(x)) + 5) + 9*x))

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (20) = 40\).

Time = 3.38 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.54 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=e^{\frac {1}{x^{3} + 6 x^{2} + \frac {x \left (x \log {\left (x \right )} + 1\right )^{2} e^{2 x + 10}}{\log {\left (x \right )}^{2}} + 9 x + \frac {\left (- 2 x^{2} - 6 x\right ) \left (x \log {\left (x \right )} + 1\right ) e^{x + 5}}{\log {\left (x \right )}}}} \]

[In]

integrate((((-2*x**2-3*x)*ln(x)**2+(-1-2*x)*ln(x)+2)*exp(ln((x*ln(x)+1)/ln(x))+5+x)+(3*x**2+3*x)*ln(x)**2+(3*x
+3)*ln(x))*exp(1/(x*exp(ln((x*ln(x)+1)/ln(x))+5+x)**2+(-2*x**2-6*x)*exp(ln((x*ln(x)+1)/ln(x))+5+x)+x**3+6*x**2
+9*x))/((x**3*ln(x)**2+x**2*ln(x))*exp(ln((x*ln(x)+1)/ln(x))+5+x)**3+((-3*x**4-9*x**3)*ln(x)**2+(-3*x**3-9*x**
2)*ln(x))*exp(ln((x*ln(x)+1)/ln(x))+5+x)**2+((3*x**5+18*x**4+27*x**3)*ln(x)**2+(3*x**4+18*x**3+27*x**2)*ln(x))
*exp(ln((x*ln(x)+1)/ln(x))+5+x)+(-x**6-9*x**5-27*x**4-27*x**3)*ln(x)**2+(-x**5-9*x**4-27*x**3-27*x**2)*ln(x)),
x)

[Out]

exp(1/(x**3 + 6*x**2 + x*(x*log(x) + 1)**2*exp(2*x + 10)/log(x)**2 + 9*x + (-2*x**2 - 6*x)*(x*log(x) + 1)*exp(
x + 5)/log(x)))

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 500 vs. \(2 (23) = 46\).

Time = 4.96 (sec) , antiderivative size = 500, normalized size of antiderivative = 20.83 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=e^{\left (\frac {e^{\left (x + 5\right )} \log \left (x\right )^{3}}{3 \, {\left (x^{2} e^{\left (2 \, x + 10\right )} + x^{2} - 2 \, {\left (x^{2} e^{5} + 3 \, x e^{5}\right )} e^{x} + 6 \, x + 9\right )} \log \left (x\right )^{3} - {\left (x^{2} e^{\left (3 \, x + 15\right )} - 2 \, {\left (x^{2} e^{10} + 6 \, x e^{10}\right )} e^{\left (2 \, x\right )} + {\left (x^{2} e^{5} + 12 \, x e^{5} + 27 \, e^{5}\right )} e^{x}\right )} \log \left (x\right )^{2} + {\left ({\left (2 \, x e^{10} + 9 \, e^{10}\right )} e^{\left (2 \, x\right )} - 2 \, x e^{\left (3 \, x + 15\right )}\right )} \log \left (x\right ) - e^{\left (3 \, x + 15\right )}} - \frac {e^{\left (x + 5\right )} \log \left (x\right )^{3}}{9 \, {\left (x e^{\left (x + 5\right )} - x - 3\right )} \log \left (x\right )^{3} - 3 \, {\left (2 \, x e^{\left (2 \, x + 10\right )} - {\left (2 \, x e^{5} + 9 \, e^{5}\right )} e^{x}\right )} \log \left (x\right )^{2} - {\left ({\left (x e^{10} + 9 \, e^{10}\right )} e^{\left (2 \, x\right )} - x e^{\left (3 \, x + 15\right )}\right )} \log \left (x\right ) + e^{\left (3 \, x + 15\right )}} - \frac {\log \left (x\right )^{3}}{3 \, {\left (x^{2} e^{\left (2 \, x + 10\right )} + x^{2} - 2 \, {\left (x^{2} e^{5} + 3 \, x e^{5}\right )} e^{x} + 6 \, x + 9\right )} \log \left (x\right )^{3} - {\left (x^{2} e^{\left (3 \, x + 15\right )} - 2 \, {\left (x^{2} e^{10} + 6 \, x e^{10}\right )} e^{\left (2 \, x\right )} + {\left (x^{2} e^{5} + 12 \, x e^{5} + 27 \, e^{5}\right )} e^{x}\right )} \log \left (x\right )^{2} + {\left ({\left (2 \, x e^{10} + 9 \, e^{10}\right )} e^{\left (2 \, x\right )} - 2 \, x e^{\left (3 \, x + 15\right )}\right )} \log \left (x\right ) - e^{\left (3 \, x + 15\right )}} + \frac {\log \left (x\right )^{3}}{9 \, {\left (x e^{\left (x + 5\right )} - x - 3\right )} \log \left (x\right )^{3} - 3 \, {\left (2 \, x e^{\left (2 \, x + 10\right )} - {\left (2 \, x e^{5} + 9 \, e^{5}\right )} e^{x}\right )} \log \left (x\right )^{2} - {\left ({\left (x e^{10} + 9 \, e^{10}\right )} e^{\left (2 \, x\right )} - x e^{\left (3 \, x + 15\right )}\right )} \log \left (x\right ) + e^{\left (3 \, x + 15\right )}} - \frac {\log \left (x\right )^{2}}{6 \, x e^{\left (x + 5\right )} \log \left (x\right ) - 9 \, x \log \left (x\right )^{2} - x e^{\left (2 \, x + 10\right )}}\right )} \]

[In]

integrate((((-2*x^2-3*x)*log(x)^2+(-1-2*x)*log(x)+2)*exp(log((x*log(x)+1)/log(x))+5+x)+(3*x^2+3*x)*log(x)^2+(3
*x+3)*log(x))*exp(1/(x*exp(log((x*log(x)+1)/log(x))+5+x)^2+(-2*x^2-6*x)*exp(log((x*log(x)+1)/log(x))+5+x)+x^3+
6*x^2+9*x))/((x^3*log(x)^2+x^2*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^3+((-3*x^4-9*x^3)*log(x)^2+(-3*x^3-9*
x^2)*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^2+((3*x^5+18*x^4+27*x^3)*log(x)^2+(3*x^4+18*x^3+27*x^2)*log(x))
*exp(log((x*log(x)+1)/log(x))+5+x)+(-x^6-9*x^5-27*x^4-27*x^3)*log(x)^2+(-x^5-9*x^4-27*x^3-27*x^2)*log(x)),x, a
lgorithm="maxima")

[Out]

e^(e^(x + 5)*log(x)^3/(3*(x^2*e^(2*x + 10) + x^2 - 2*(x^2*e^5 + 3*x*e^5)*e^x + 6*x + 9)*log(x)^3 - (x^2*e^(3*x
+ 15) - 2*(x^2*e^10 + 6*x*e^10)*e^(2*x) + (x^2*e^5 + 12*x*e^5 + 27*e^5)*e^x)*log(x)^2 + ((2*x*e^10 + 9*e^10)*
e^(2*x) - 2*x*e^(3*x + 15))*log(x) - e^(3*x + 15)) - e^(x + 5)*log(x)^3/(9*(x*e^(x + 5) - x - 3)*log(x)^3 - 3*
(2*x*e^(2*x + 10) - (2*x*e^5 + 9*e^5)*e^x)*log(x)^2 - ((x*e^10 + 9*e^10)*e^(2*x) - x*e^(3*x + 15))*log(x) + e^
(3*x + 15)) - log(x)^3/(3*(x^2*e^(2*x + 10) + x^2 - 2*(x^2*e^5 + 3*x*e^5)*e^x + 6*x + 9)*log(x)^3 - (x^2*e^(3*
x + 15) - 2*(x^2*e^10 + 6*x*e^10)*e^(2*x) + (x^2*e^5 + 12*x*e^5 + 27*e^5)*e^x)*log(x)^2 + ((2*x*e^10 + 9*e^10)
*e^(2*x) - 2*x*e^(3*x + 15))*log(x) - e^(3*x + 15)) + log(x)^3/(9*(x*e^(x + 5) - x - 3)*log(x)^3 - 3*(2*x*e^(2
*x + 10) - (2*x*e^5 + 9*e^5)*e^x)*log(x)^2 - ((x*e^10 + 9*e^10)*e^(2*x) - x*e^(3*x + 15))*log(x) + e^(3*x + 15
)) - log(x)^2/(6*x*e^(x + 5)*log(x) - 9*x*log(x)^2 - x*e^(2*x + 10)))

Giac [F(-2)]

Exception generated. \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx=\text {Exception raised: TypeError} \]

[In]

integrate((((-2*x^2-3*x)*log(x)^2+(-1-2*x)*log(x)+2)*exp(log((x*log(x)+1)/log(x))+5+x)+(3*x^2+3*x)*log(x)^2+(3
*x+3)*log(x))*exp(1/(x*exp(log((x*log(x)+1)/log(x))+5+x)^2+(-2*x^2-6*x)*exp(log((x*log(x)+1)/log(x))+5+x)+x^3+
6*x^2+9*x))/((x^3*log(x)^2+x^2*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^3+((-3*x^4-9*x^3)*log(x)^2+(-3*x^3-9*
x^2)*log(x))*exp(log((x*log(x)+1)/log(x))+5+x)^2+((3*x^5+18*x^4+27*x^3)*log(x)^2+(3*x^4+18*x^3+27*x^2)*log(x))
*exp(log((x*log(x)+1)/log(x))+5+x)+(-x^6-9*x^5-27*x^4-27*x^3)*log(x)^2+(-x^5-9*x^4-27*x^3-27*x^2)*log(x)),x, a
lgorithm="giac")

[Out]

Exception raised: TypeError >> an error occurred running a Giac command:INPUT:sage2:=int(sage0,sageVARx):;OUTP
UT:Not invertible Error: Bad Argument Value

Mupad [B] (verification not implemented)

Time = 10.49 (sec) , antiderivative size = 94, normalized size of antiderivative = 3.92 \[ \int \frac {e^{\frac {1}{9 x+6 x^2+x^3+\frac {e^{5+x} \left (-6 x-2 x^2\right ) (1+x \log (x))}{\log (x)}+\frac {e^{10+2 x} x (1+x \log (x))^2}{\log ^2(x)}}} \left ((3+3 x) \log (x)+\left (3 x+3 x^2\right ) \log ^2(x)+\frac {e^{5+x} (1+x \log (x)) \left (2+(-1-2 x) \log (x)+\left (-3 x-2 x^2\right ) \log ^2(x)\right )}{\log (x)}\right )}{\left (-27 x^2-27 x^3-9 x^4-x^5\right ) \log (x)+\left (-27 x^3-27 x^4-9 x^5-x^6\right ) \log ^2(x)+\frac {e^{15+3 x} (1+x \log (x))^3 \left (x^2 \log (x)+x^3 \log ^2(x)\right )}{\log ^3(x)}+\frac {e^{10+2 x} (1+x \log (x))^2 \left (\left (-9 x^2-3 x^3\right ) \log (x)+\left (-9 x^3-3 x^4\right ) \log ^2(x)\right )}{\log ^2(x)}+\frac {e^{5+x} (1+x \log (x)) \left (\left (27 x^2+18 x^3+3 x^4\right ) \log (x)+\left (27 x^3+18 x^4+3 x^5\right ) \log ^2(x)\right )}{\log (x)}} \, dx={\mathrm {e}}^{\frac {1}{9\,x-6\,x^2\,{\mathrm {e}}^{x+5}-2\,x^3\,{\mathrm {e}}^{x+5}+x^3\,{\mathrm {e}}^{2\,x+10}+6\,x^2+x^3+\frac {2\,x^2\,{\mathrm {e}}^{2\,x+10}}{\ln \left (x\right )}-\frac {6\,x\,{\mathrm {e}}^{x+5}}{\ln \left (x\right )}+\frac {x\,{\mathrm {e}}^{2\,x+10}}{{\ln \left (x\right )}^2}-\frac {2\,x^2\,{\mathrm {e}}^{x+5}}{\ln \left (x\right )}}} \]

[In]

int(-(exp(1/(9*x - exp(x + log((x*log(x) + 1)/log(x)) + 5)*(6*x + 2*x^2) + 6*x^2 + x^3 + x*exp(2*x + 2*log((x*
log(x) + 1)/log(x)) + 10)))*(log(x)^2*(3*x + 3*x^2) + log(x)*(3*x + 3) - exp(x + log((x*log(x) + 1)/log(x)) +
5)*(log(x)^2*(3*x + 2*x^2) + log(x)*(2*x + 1) - 2)))/(log(x)*(27*x^2 + 27*x^3 + 9*x^4 + x^5) - exp(x + log((x*
log(x) + 1)/log(x)) + 5)*(log(x)*(27*x^2 + 18*x^3 + 3*x^4) + log(x)^2*(27*x^3 + 18*x^4 + 3*x^5)) + exp(2*x + 2
*log((x*log(x) + 1)/log(x)) + 10)*(log(x)*(9*x^2 + 3*x^3) + log(x)^2*(9*x^3 + 3*x^4)) - exp(3*x + 3*log((x*log
(x) + 1)/log(x)) + 15)*(x^2*log(x) + x^3*log(x)^2) + log(x)^2*(27*x^3 + 27*x^4 + 9*x^5 + x^6)),x)

[Out]

exp(1/(9*x - 6*x^2*exp(x + 5) - 2*x^3*exp(x + 5) + x^3*exp(2*x + 10) + 6*x^2 + x^3 + (2*x^2*exp(2*x + 10))/log
(x) - (6*x*exp(x + 5))/log(x) + (x*exp(2*x + 10))/log(x)^2 - (2*x^2*exp(x + 5))/log(x)))