\(\int \frac {e^{28+x-2 x^2+(-24+6 x) \log (\frac {\log (x)}{5})+(4-x) \log ^2(\frac {\log (x)}{5})} (-24+6 x+(x-4 x^2) \log (x)+(8-2 x+6 x \log (x)) \log (\frac {\log (x)}{5})-x \log (x) \log ^2(\frac {\log (x)}{5}))}{x \log (x)} \, dx\) [7712]

Optimal result

Integrand size = 93, antiderivative size = 24 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=e^{(4-x) \left (-2+2 x+\left (-3+\log \left (\frac {\log (x)}{5}\right )\right )^2\right )} \]

[Out]

exp((-x+4)*(2*x-2+(ln(1/5*ln(x))-3)^2))

Rubi [F]

\[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=\int \frac {\exp \left (28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )\right ) \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx \]

[In]

Int[(E^(28 + x - 2*x^2 + (-24 + 6*x)*Log[Log[x]/5] + (4 - x)*Log[Log[x]/5]^2)*(-24 + 6*x + (x - 4*x^2)*Log[x]
+ (8 - 2*x + 6*x*Log[x])*Log[Log[x]/5] - x*Log[x]*Log[Log[x]/5]^2))/(x*Log[x]),x]

[Out]

Defer[Int][E^(-((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2))), x] - 4*Defer[Int][x/E^((-4 + x)*(7 +
2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2)), x] + 6*Defer[Int][1/(E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[
Log[x]/5]^2))*Log[x]), x] - 24*Defer[Int][1/(E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2))*x*Log[
x]), x] + 6*Defer[Int][Log[Log[x]/5]/E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2)), x] - 2*Defer[
Int][Log[Log[x]/5]/(E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2))*Log[x]), x] + 8*Defer[Int][Log[
Log[x]/5]/(E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2))*x*Log[x]), x] - Defer[Int][Log[Log[x]/5]
^2/E^((-4 + x)*(7 + 2*x - 6*Log[Log[x]/5] + Log[Log[x]/5]^2)), x]

Rubi steps \begin{align*} \text {integral}& = \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx \\ & = \int \left (\frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \left (-24+6 x+x \log (x)-4 x^2 \log (x)\right )}{x \log (x)}+\frac {2 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) (4-x+3 x \log (x)) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)}-\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right )\right ) \, dx \\ & = 2 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) (4-x+3 x \log (x)) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)} \, dx+\int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \left (-24+6 x+x \log (x)-4 x^2 \log (x)\right )}{x \log (x)} \, dx-\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right ) \, dx \\ & = 2 \int \left (3 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )-\frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{\log (x)}+\frac {4 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)}\right ) \, dx+\int \left (\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right )-4 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) x+\frac {6 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) (-4+x)}{x \log (x)}\right ) \, dx-\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{\log (x)} \, dx\right )-4 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) x \, dx+6 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) (-4+x)}{x \log (x)} \, dx+6 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right ) \, dx+8 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)} \, dx+\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \, dx-\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{\log (x)} \, dx\right )-4 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) x \, dx+6 \int \left (\frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right )}{\log (x)}-\frac {4 \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right )}{x \log (x)}\right ) \, dx+6 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right ) \, dx+8 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)} \, dx+\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \, dx-\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right ) \, dx \\ & = -\left (2 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{\log (x)} \, dx\right )-4 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) x \, dx+6 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right )}{\log (x)} \, dx+6 \int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right ) \, dx+8 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log \left (\frac {\log (x)}{5}\right )}{x \log (x)} \, dx-24 \int \frac {\exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right )}{x \log (x)} \, dx+\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \, dx-\int \exp \left (-\left ((-4+x) \left (7+2 x-6 \log \left (\frac {\log (x)}{5}\right )+\log ^2\left (\frac {\log (x)}{5}\right )\right )\right )\right ) \log ^2\left (\frac {\log (x)}{5}\right ) \, dx \\ \end{align*}

Mathematica [F]

\[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=\int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx \]

[In]

Integrate[(E^(28 + x - 2*x^2 + (-24 + 6*x)*Log[Log[x]/5] + (4 - x)*Log[Log[x]/5]^2)*(-24 + 6*x + (x - 4*x^2)*L
og[x] + (8 - 2*x + 6*x*Log[x])*Log[Log[x]/5] - x*Log[x]*Log[Log[x]/5]^2))/(x*Log[x]),x]

[Out]

Integrate[(E^(28 + x - 2*x^2 + (-24 + 6*x)*Log[Log[x]/5] + (4 - x)*Log[Log[x]/5]^2)*(-24 + 6*x + (x - 4*x^2)*L
og[x] + (8 - 2*x + 6*x*Log[x])*Log[Log[x]/5] - x*Log[x]*Log[Log[x]/5]^2))/(x*Log[x]), x]

Maple [A] (verified)

Time = 0.24 (sec) , antiderivative size = 30, normalized size of antiderivative = 1.25

method	result	size
risch	\(\left (\frac {\ln \left (x \right )}{5}\right )^{6 x -24} {\mathrm e}^{-\left (x -4\right ) \left (\ln \left (\frac {\ln \left (x \right )}{5}\right )^{2}+2 x +7\right )}\)	\(30\)
parallelrisch	\({\mathrm e}^{\left (-x +4\right ) \ln \left (\frac {\ln \left (x \right )}{5}\right )^{2}+\left (6 x -24\right ) \ln \left (\frac {\ln \left (x \right )}{5}\right )-2 x^{2}+x +28}\)	\(34\)

[In]

int((-x*ln(x)*ln(1/5*ln(x))^2+(6*x*ln(x)-2*x+8)*ln(1/5*ln(x))+(-4*x^2+x)*ln(x)+6*x-24)*exp((-x+4)*ln(1/5*ln(x)
)^2+(6*x-24)*ln(1/5*ln(x))-2*x^2+x+28)/x/ln(x),x,method=_RETURNVERBOSE)

[Out]

(1/5*ln(x))^(6*x-24)*exp(-(x-4)*(ln(1/5*ln(x))^2+2*x+7))

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.29 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=e^{\left (-{\left (x - 4\right )} \log \left (\frac {1}{5} \, \log \left (x\right )\right )^{2} - 2 \, x^{2} + 6 \, {\left (x - 4\right )} \log \left (\frac {1}{5} \, \log \left (x\right )\right ) + x + 28\right )} \]

[In]

integrate((-x*log(x)*log(1/5*log(x))^2+(6*x*log(x)-2*x+8)*log(1/5*log(x))+(-4*x^2+x)*log(x)+6*x-24)*exp((-x+4)
*log(1/5*log(x))^2+(6*x-24)*log(1/5*log(x))-2*x^2+x+28)/x/log(x),x, algorithm="fricas")

[Out]

e^(-(x - 4)*log(1/5*log(x))^2 - 2*x^2 + 6*(x - 4)*log(1/5*log(x)) + x + 28)

Sympy [A] (verification not implemented)

Time = 0.37 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=e^{- 2 x^{2} + x + \left (4 - x\right ) \log {\left (\frac {\log {\left (x \right )}}{5} \right )}^{2} + \left (6 x - 24\right ) \log {\left (\frac {\log {\left (x \right )}}{5} \right )} + 28} \]

[In]

integrate((-x*ln(x)*ln(1/5*ln(x))**2+(6*x*ln(x)-2*x+8)*ln(1/5*ln(x))+(-4*x**2+x)*ln(x)+6*x-24)*exp((-x+4)*ln(1
/5*ln(x))**2+(6*x-24)*ln(1/5*ln(x))-2*x**2+x+28)/x/ln(x),x)

[Out]

exp(-2*x**2 + x + (4 - x)*log(log(x)/5)**2 + (6*x - 24)*log(log(x)/5) + 28)

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 69 vs. \(2 (20) = 40\).

Time = 0.46 (sec) , antiderivative size = 69, normalized size of antiderivative = 2.88 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=\frac {59604644775390625 \, e^{\left (-x \log \left (5\right )^{2} + 2 \, x \log \left (5\right ) \log \left (\log \left (x\right )\right ) - x \log \left (\log \left (x\right )\right )^{2} - 2 \, x^{2} - 6 \, x \log \left (5\right ) + 4 \, \log \left (5\right )^{2} + 6 \, x \log \left (\log \left (x\right )\right ) - 8 \, \log \left (5\right ) \log \left (\log \left (x\right )\right ) + 4 \, \log \left (\log \left (x\right )\right )^{2} + x + 28\right )}}{\log \left (x\right )^{24}} \]

[In]

integrate((-x*log(x)*log(1/5*log(x))^2+(6*x*log(x)-2*x+8)*log(1/5*log(x))+(-4*x^2+x)*log(x)+6*x-24)*exp((-x+4)
*log(1/5*log(x))^2+(6*x-24)*log(1/5*log(x))-2*x^2+x+28)/x/log(x),x, algorithm="maxima")

[Out]

59604644775390625*e^(-x*log(5)^2 + 2*x*log(5)*log(log(x)) - x*log(log(x))^2 - 2*x^2 - 6*x*log(5) + 4*log(5)^2
+ 6*x*log(log(x)) - 8*log(5)*log(log(x)) + 4*log(log(x))^2 + x + 28)/log(x)^24

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 43 vs. \(2 (20) = 40\).

Time = 2.99 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=e^{\left (-x \log \left (\frac {1}{5} \, \log \left (x\right )\right )^{2} - 2 \, x^{2} + 6 \, x \log \left (\frac {1}{5} \, \log \left (x\right )\right ) + 4 \, \log \left (\frac {1}{5} \, \log \left (x\right )\right )^{2} + x - 24 \, \log \left (\frac {1}{5} \, \log \left (x\right )\right ) + 28\right )} \]

[In]

integrate((-x*log(x)*log(1/5*log(x))^2+(6*x*log(x)-2*x+8)*log(1/5*log(x))+(-4*x^2+x)*log(x)+6*x-24)*exp((-x+4)
*log(1/5*log(x))^2+(6*x-24)*log(1/5*log(x))-2*x^2+x+28)/x/log(x),x, algorithm="giac")

[Out]

e^(-x*log(1/5*log(x))^2 - 2*x^2 + 6*x*log(1/5*log(x)) + 4*log(1/5*log(x))^2 + x - 24*log(1/5*log(x)) + 28)

Mupad [B] (verification not implemented)

Time = 13.61 (sec) , antiderivative size = 78, normalized size of antiderivative = 3.25 \[ \int \frac {e^{28+x-2 x^2+(-24+6 x) \log \left (\frac {\log (x)}{5}\right )+(4-x) \log ^2\left (\frac {\log (x)}{5}\right )} \left (-24+6 x+\left (x-4 x^2\right ) \log (x)+(8-2 x+6 x \log (x)) \log \left (\frac {\log (x)}{5}\right )-x \log (x) \log ^2\left (\frac {\log (x)}{5}\right )\right )}{x \log (x)} \, dx=\frac {59604644775390625\,{\mathrm {e}}^{-x\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{28}\,{\mathrm {e}}^{4\,{\ln \left (\ln \left (x\right )\right )}^2}\,{\mathrm {e}}^{4\,{\ln \left (5\right )}^2}\,{\mathrm {e}}^{-2\,x^2}\,{\mathrm {e}}^x\,{\mathrm {e}}^{-x\,{\ln \left (\ln \left (x\right )\right )}^2}\,{\ln \left (x\right )}^{6\,x}\,{\ln \left (x\right )}^{2\,x\,\ln \left (5\right )}}{5^{6\,x}\,{\ln \left (x\right )}^{8\,\ln \left (5\right )}\,{\ln \left (x\right )}^{24}} \]

[In]

int((exp(x + log(log(x)/5)*(6*x - 24) - log(log(x)/5)^2*(x - 4) - 2*x^2 + 28)*(6*x + log(log(x)/5)*(6*x*log(x)
- 2*x + 8) + log(x)*(x - 4*x^2) - x*log(log(x)/5)^2*log(x) - 24))/(x*log(x)),x)

[Out]

(59604644775390625*exp(-x*log(5)^2)*exp(28)*exp(4*log(log(x))^2)*exp(4*log(5)^2)*exp(-2*x^2)*exp(x)*exp(-x*log
(log(x))^2)*log(x)^(6*x)*log(x)^(2*x*log(5)))/(5^(6*x)*log(x)^(8*log(5))*log(x)^24)