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

Optimal. Leaf size=24 \[ 24 e^{-(3-x)^2-x (-1+\log (\log (\log (x))))} x \]

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Rubi [F]  time = 1.42, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \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 \end {gather*}

Verification is not applicable to the result.

[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 {gather*} \begin {aligned} \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 {aligned} \end {gather*}

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Mathematica [A]  time = 0.36, size = 22, normalized size = 0.92 \begin {gather*} 24 e^{-9+7 x-x^2} x \log ^{-x}(\log (x)) \end {gather*}

Antiderivative was successfully verified.

[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

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fricas [A]  time = 0.59, size = 21, normalized size = 0.88 \begin {gather*} 24 \, x e^{\left (-x^{2} - x \log \left (\log \left (\log \relax (x)\right )\right ) + 7 \, x - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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giac [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \mathit {undef} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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maple [A]  time = 0.03, size = 22, normalized size = 0.92

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

Verification of antiderivative is not currently implemented for this CAS.

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

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maxima [A]  time = 0.72, size = 21, normalized size = 0.88 \begin {gather*} 24 \, x e^{\left (-x^{2} - x \log \left (\log \left (\log \relax (x)\right )\right ) + 7 \, x - 9\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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mupad [B]  time = 2.24, size = 22, normalized size = 0.92 \begin {gather*} \frac {24\,x\,{\mathrm {e}}^{7\,x}\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^{-x^2}}{{\ln \left (\ln \relax (x)\right )}^x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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

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sympy [A]  time = 16.05, size = 20, normalized size = 0.83 \begin {gather*} 24 x e^{- x^{2} - x \log {\left (\log {\left (\log {\relax (x )} \right )} \right )} + 7 x - 9} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[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)

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