\(\int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} (-24 x+(24+168 x-48 x^2) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx\) [3309]

Optimal result

Integrand size = 61, antiderivative size = 24 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=24 e^{-(3-x)^2-x (-1+\log (\log (\log (x))))} x \]

[Out]

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

Rubi [F]

\[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=\int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx \]

[In]

Int[(E^(-9 + 7*x - x^2 - x*Log[Log[Log[x]]])*(-24*x + (24 + 168*x - 48*x^2)*Log[x]*Log[Log[x]] - 24*x*Log[x]*L
og[Log[x]]*Log[Log[Log[x]]]))/(Log[x]*Log[Log[x]]),x]

[Out]

24*Defer[Int][E^(-9 + 7*x - x^2 - x*Log[Log[Log[x]]]), x] + 168*Defer[Int][E^(-9 + 7*x - x^2 - x*Log[Log[Log[x
]]])*x, x] - 48*Defer[Int][E^(-9 + 7*x - x^2 - x*Log[Log[Log[x]]])*x^2, x] - 24*Defer[Int][(E^(-9 + 7*x - x^2
- x*Log[Log[Log[x]]])*x)/(Log[x]*Log[Log[x]]), x] - 24*Defer[Int][E^(-9 + 7*x - x^2 - x*Log[Log[Log[x]]])*x*Lo
g[Log[Log[x]]], x]

Rubi steps \begin{align*} \text {integral}& = \int \left (-\frac {24 e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (x-\log (x) \log (\log (x))-7 x \log (x) \log (\log (x))+2 x^2 \log (x) \log (\log (x))\right )}{\log (x) \log (\log (x))}-24 e^{-9+7 x-x^2-x \log (\log (\log (x)))} x \log (\log (\log (x)))\right ) \, dx \\ & = -\left (24 \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (x-\log (x) \log (\log (x))-7 x \log (x) \log (\log (x))+2 x^2 \log (x) \log (\log (x))\right )}{\log (x) \log (\log (x))} \, dx\right )-24 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} x \log (\log (\log (x))) \, dx \\ & = -\left (24 \int \left (-e^{-9+7 x-x^2-x \log (\log (\log (x)))}-7 e^{-9+7 x-x^2-x \log (\log (\log (x)))} x+2 e^{-9+7 x-x^2-x \log (\log (\log (x)))} x^2+\frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} x}{\log (x) \log (\log (x))}\right ) \, dx\right )-24 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} x \log (\log (\log (x))) \, dx \\ & = 24 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} \, dx-24 \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} x}{\log (x) \log (\log (x))} \, dx-24 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} x \log (\log (\log (x))) \, dx-48 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} x^2 \, dx+168 \int e^{-9+7 x-x^2-x \log (\log (\log (x)))} x \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.36 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=24 e^{-9+7 x-x^2} x \log ^{-x}(\log (x)) \]

[In]

Integrate[(E^(-9 + 7*x - x^2 - x*Log[Log[Log[x]]])*(-24*x + (24 + 168*x - 48*x^2)*Log[x]*Log[Log[x]] - 24*x*Lo
g[x]*Log[Log[x]]*Log[Log[Log[x]]]))/(Log[x]*Log[Log[x]]),x]

[Out]

(24*E^(-9 + 7*x - x^2)*x)/Log[Log[x]]^x

Maple [A] (verified)

Time = 3.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88

method	result	size
parallelrisch	\(24 x \,{\mathrm e}^{-x \ln \left (\ln \left (\ln \left (x \right )\right )\right )-x^{2}+7 x -9}\)	\(21\)
risch	\(24 x \ln \left (\ln \left (x \right )\right )^{-x} {\mathrm e}^{-x^{2}+7 x -9}\)	\(22\)

[In]

int((-24*x*ln(x)*ln(ln(x))*ln(ln(ln(x)))+(-48*x^2+168*x+24)*ln(x)*ln(ln(x))-24*x)/ln(x)/ln(ln(x))/exp(x*ln(ln(
ln(x)))+x^2-7*x+9),x,method=_RETURNVERBOSE)

[Out]

24*x/exp(x*ln(ln(ln(x)))+x^2-7*x+9)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=24 \, x e^{\left (-x^{2} - x \log \left (\log \left (\log \left (x\right )\right )\right ) + 7 \, x - 9\right )} \]

[In]

integrate((-24*x*log(x)*log(log(x))*log(log(log(x)))+(-48*x^2+168*x+24)*log(x)*log(log(x))-24*x)/log(x)/log(lo
g(x))/exp(x*log(log(log(x)))+x^2-7*x+9),x, algorithm="fricas")

[Out]

24*x*e^(-x^2 - x*log(log(log(x))) + 7*x - 9)

Sympy [A] (verification not implemented)

Time = 9.61 (sec) , antiderivative size = 20, normalized size of antiderivative = 0.83 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=24 x e^{- x^{2} - x \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )} + 7 x - 9} \]

[In]

integrate((-24*x*ln(x)*ln(ln(x))*ln(ln(ln(x)))+(-48*x**2+168*x+24)*ln(x)*ln(ln(x))-24*x)/ln(x)/ln(ln(x))/exp(x
*ln(ln(ln(x)))+x**2-7*x+9),x)

[Out]

24*x*exp(-x**2 - x*log(log(log(x))) + 7*x - 9)

Maxima [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 21, normalized size of antiderivative = 0.88 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=24 \, x e^{\left (-x^{2} - x \log \left (\log \left (\log \left (x\right )\right )\right ) + 7 \, x - 9\right )} \]

[In]

integrate((-24*x*log(x)*log(log(x))*log(log(log(x)))+(-48*x^2+168*x+24)*log(x)*log(log(x))-24*x)/log(x)/log(lo
g(x))/exp(x*log(log(log(x)))+x^2-7*x+9),x, algorithm="maxima")

[Out]

24*x*e^(-x^2 - x*log(log(log(x))) + 7*x - 9)

Giac [F]

\[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=\int { -\frac {24 \, {\left (x \log \left (x\right ) \log \left (\log \left (x\right )\right ) \log \left (\log \left (\log \left (x\right )\right )\right ) + {\left (2 \, x^{2} - 7 \, x - 1\right )} \log \left (x\right ) \log \left (\log \left (x\right )\right ) + x\right )} e^{\left (-x^{2} - x \log \left (\log \left (\log \left (x\right )\right )\right ) + 7 \, x - 9\right )}}{\log \left (x\right ) \log \left (\log \left (x\right )\right )} \,d x } \]

[In]

integrate((-24*x*log(x)*log(log(x))*log(log(log(x)))+(-48*x^2+168*x+24)*log(x)*log(log(x))-24*x)/log(x)/log(lo
g(x))/exp(x*log(log(log(x)))+x^2-7*x+9),x, algorithm="giac")

[Out]

undef

Mupad [B] (verification not implemented)

Time = 9.11 (sec) , antiderivative size = 22, normalized size of antiderivative = 0.92 \[ \int \frac {e^{-9+7 x-x^2-x \log (\log (\log (x)))} \left (-24 x+\left (24+168 x-48 x^2\right ) \log (x) \log (\log (x))-24 x \log (x) \log (\log (x)) \log (\log (\log (x)))\right )}{\log (x) \log (\log (x))} \, dx=\frac {24\,x\,{\mathrm {e}}^{7\,x}\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^{-x^2}}{{\ln \left (\ln \left (x\right )\right )}^x} \]

[In]

int(-(exp(7*x - x*log(log(log(x))) - x^2 - 9)*(24*x - log(log(x))*log(x)*(168*x - 48*x^2 + 24) + 24*x*log(log(
x))*log(log(log(x)))*log(x)))/(log(log(x))*log(x)),x)

[Out]

(24*x*exp(7*x)*exp(-9)*exp(-x^2))/log(log(x))^x