3.73.79 \(\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2+(2 x+e^{3+x} x+x^2) \log (\log (\log (x)))} (2+e^{3+x}+x+(-3+e^{3+x} (-2-2 x)-4 x) \log (x) \log (\log (x))+(2+2 x+e^{3+x} (1+x)) \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx\)

Optimal. Leaf size=28 \[ e^{-7+x-\left (2 x+x \left (e^{3+x}+x\right )\right ) (2-\log (\log (\log (x))))} \]

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Rubi [F]  time = 37.35, 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 {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) \left (2+e^{3+x}+x+\left (-3+e^{3+x} (-2-2 x)-4 x\right ) \log (x) \log (\log (x))+\left (2+2 x+e^{3+x} (1+x)\right ) \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^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2 + (2*x + E^(3 + x)*x + x^2)*Log[Log[Log[x]]])*(2 + E^(3 + x) + x + (-
3 + E^(3 + x)*(-2 - 2*x) - 4*x)*Log[x]*Log[Log[x]] + (2 + 2*x + E^(3 + x)*(1 + x))*Log[x]*Log[Log[x]]*Log[Log[
Log[x]]]))/(Log[x]*Log[Log[x]]),x]

[Out]

2*Defer[Int][(E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*Log[Log[x]]^(-1 + (2 + E^(3 + x))*x + x^2))/Log[x], x] + De
fer[Int][Log[Log[x]]^(-1 + (2 + E^(3 + x))*x + x^2)/(E^(2*(2 + x + E^(3 + x)*x + x^2))*Log[x]), x] + Defer[Int
][(E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*x*Log[Log[x]]^(-1 + (2 + E^(3 + x))*x + x^2))/Log[x], x] - 3*Defer[Int
][E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*Log[Log[x]]^((2 + E^(3 + x))*x + x^2), x] - 2*Defer[Int][Log[Log[x]]^((
2 + E^(3 + x))*x + x^2)/E^(2*(2 + x + E^(3 + x)*x + x^2)), x] - 4*Defer[Int][E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x
^2)*x*Log[Log[x]]^((2 + E^(3 + x))*x + x^2), x] - 2*Defer[Int][(x*Log[Log[x]]^((2 + E^(3 + x))*x + x^2))/E^(2*
(2 + x + E^(3 + x)*x + x^2)), x] + 2*Defer[Int][E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*Log[Log[x]]^((2 + E^(3 +
x))*x + x^2)*Log[Log[Log[x]]], x] + Defer[Int][(Log[Log[x]]^((2 + E^(3 + x))*x + x^2)*Log[Log[Log[x]]])/E^(2*(
2 + x + E^(3 + x)*x + x^2)), x] + 2*Defer[Int][E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*x*Log[Log[x]]^((2 + E^(3 +
x))*x + x^2)*Log[Log[Log[x]]], x] + Defer[Int][(x*Log[Log[x]]^((2 + E^(3 + x))*x + x^2)*Log[Log[Log[x]]])/E^(
2*(2 + x + E^(3 + x)*x + x^2)), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {\exp \left (-4-2 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x))+\log (x) \log (\log (x)) \log (\log (\log (x)))+x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))}+\frac {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2 x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))}\right ) \, dx\\ &=\int \frac {\exp \left (-4-2 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x))+\log (x) \log (\log (x)) \log (\log (\log (x)))+x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx+\int \frac {\exp \left (-7-3 x-2 e^{3+x} x-2 x^2+\left (2 x+e^{3+x} x+x^2\right ) \log (\log (\log (x)))\right ) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x))+2 \log (x) \log (\log (x)) \log (\log (\log (x)))+2 x \log (x) \log (\log (x)) \log (\log (\log (x))))}{\log (x) \log (\log (x))} \, dx\\ &=\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1+(1+x) \log (x) \log (\log (x)) (-2+\log (\log (\log (x)))))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x+\log (x) \log (\log (x)) (-3-4 x+2 (1+x) \log (\log (\log (x)))))}{\log (x)} \, dx\\ &=\int \left (\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x)))}{\log (x)}+2 e^{-7-3 x-2 e^{3+x} x-2 x^2} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx+\int \left (\frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x)))}{\log (x)}+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx\\ &=2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (2+x-3 \log (x) \log (\log (x))-4 x \log (x) \log (\log (x)))}{\log (x)} \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 \log (x) \log (\log (x))-2 x \log (x) \log (\log (x)))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \left (e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))+e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x)) (1-2 (1+x) \log (x) \log (\log (x)))}{\log (x)} \, dx+\int \left (\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} (2+x) \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}-e^{-7-3 x-2 e^{3+x} x-2 x^2} (3+4 x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int \left (e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x)))\right ) \, dx\\ &=2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} (2+x) \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-\int e^{-7-3 x-2 e^{3+x} x-2 x^2} (3+4 x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \left (\frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}-2 e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=-\left (2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} (1+x) \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx\right )+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \left (\frac {2 e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}+\frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)}\right ) \, dx-\int \left (3 e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))+4 e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-2 \int \left (e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))+e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x))\right ) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx-3 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-4 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ &=2 \int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx-2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-2 \int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+2 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx-3 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx-4 \int e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \, dx+\int \frac {e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int \frac {e^{-7-3 x-2 e^{3+x} x-2 x^2} x \log ^{-1+\left (2+e^{3+x}\right ) x+x^2}(\log (x))}{\log (x)} \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx+\int e^{-2 \left (2+x+e^{3+x} x+x^2\right )} x \log ^{\left (2+e^{3+x}\right ) x+x^2}(\log (x)) \log (\log (\log (x))) \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.23, size = 35, normalized size = 1.25 \begin {gather*} e^{-7-3 x-2 e^{3+x} x-2 x^2} \log ^{x \left (2+e^{3+x}+x\right )}(\log (x)) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2 + (2*x + E^(3 + x)*x + x^2)*Log[Log[Log[x]]])*(2 + E^(3 + x) +
x + (-3 + E^(3 + x)*(-2 - 2*x) - 4*x)*Log[x]*Log[Log[x]] + (2 + 2*x + E^(3 + x)*(1 + x))*Log[x]*Log[Log[x]]*Lo
g[Log[Log[x]]]))/(Log[x]*Log[Log[x]]),x]

[Out]

E^(-7 - 3*x - 2*E^(3 + x)*x - 2*x^2)*Log[Log[x]]^(x*(2 + E^(3 + x) + x))

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fricas [A]  time = 1.49, size = 36, normalized size = 1.29 \begin {gather*} e^{\left (-2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + {\left (x^{2} + x e^{\left (x + 3\right )} + 2 \, x\right )} \log \left (\log \left (\log \relax (x)\right )\right ) - 3 \, x - 7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2*x-2)*exp(3+x)-4*x-3)*log(x)*log(log
(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, a
lgorithm="fricas")

[Out]

e^(-2*x^2 - 2*x*e^(x + 3) + (x^2 + x*e^(x + 3) + 2*x)*log(log(log(x))) - 3*x - 7)

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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((((x+1)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2*x-2)*exp(3+x)-4*x-3)*log(x)*log(log
(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, a
lgorithm="giac")

[Out]

undef

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maple [A]  time = 0.06, size = 33, normalized size = 1.18

method	result	size
risch	\(\ln \left (\ln \relax (x )\right )^{\left ({\mathrm e}^{3+x}+x +2\right ) x} {\mathrm e}^{-7-2 \,{\mathrm e}^{3+x} x -2 x^{2}-3 x}\)	\(33\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((x+1)*exp(3+x)+2*x+2)*ln(x)*ln(ln(x))*ln(ln(ln(x)))+((-2*x-2)*exp(3+x)-4*x-3)*ln(x)*ln(ln(x))+exp(3+x)+2
+x)*exp((exp(3+x)*x+x^2+2*x)*ln(ln(ln(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/ln(x)/ln(ln(x)),x,method=_RETURNVERBOSE)

[Out]

ln(ln(x))^((exp(3+x)+x+2)*x)*exp(-7-2*exp(3+x)*x-2*x^2-3*x)

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maxima [A]  time = 0.51, size = 43, normalized size = 1.54 \begin {gather*} e^{\left (x^{2} \log \left (\log \left (\log \relax (x)\right )\right ) + x e^{\left (x + 3\right )} \log \left (\log \left (\log \relax (x)\right )\right ) - 2 \, x^{2} - 2 \, x e^{\left (x + 3\right )} + 2 \, x \log \left (\log \left (\log \relax (x)\right )\right ) - 3 \, x - 7\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*exp(3+x)+2*x+2)*log(x)*log(log(x))*log(log(log(x)))+((-2*x-2)*exp(3+x)-4*x-3)*log(x)*log(log
(x))+exp(3+x)+2+x)*exp((exp(3+x)*x+x^2+2*x)*log(log(log(x)))-2*exp(3+x)*x-2*x^2-3*x-7)/log(x)/log(log(x)),x, a
lgorithm="maxima")

[Out]

e^(x^2*log(log(log(x))) + x*e^(x + 3)*log(log(log(x))) - 2*x^2 - 2*x*e^(x + 3) + 2*x*log(log(log(x))) - 3*x -
7)

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mupad [B]  time = 4.44, size = 38, normalized size = 1.36 \begin {gather*} {\ln \left (\ln \relax (x)\right )}^{2\,x+x^2+x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-3\,x}\,{\mathrm {e}}^{-7}\,{\mathrm {e}}^{-2\,x\,{\mathrm {e}}^3\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-2\,x^2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((exp(log(log(log(x)))*(2*x + x*exp(x + 3) + x^2) - 2*x*exp(x + 3) - 3*x - 2*x^2 - 7)*(x + exp(x + 3) - log
(log(x))*log(x)*(4*x + exp(x + 3)*(2*x + 2) + 3) + log(log(x))*log(log(log(x)))*log(x)*(2*x + exp(x + 3)*(x +
1) + 2) + 2))/(log(log(x))*log(x)),x)

[Out]

log(log(x))^(2*x + x^2 + x*exp(3)*exp(x))*exp(-3*x)*exp(-7)*exp(-2*x*exp(3)*exp(x))*exp(-2*x^2)

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sympy [A]  time = 20.40, size = 39, normalized size = 1.39 \begin {gather*} e^{- 2 x^{2} - 2 x e^{x + 3} - 3 x + \left (x^{2} + x e^{x + 3} + 2 x\right ) \log {\left (\log {\left (\log {\relax (x )} \right )} \right )} - 7} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((x+1)*exp(3+x)+2*x+2)*ln(x)*ln(ln(x))*ln(ln(ln(x)))+((-2*x-2)*exp(3+x)-4*x-3)*ln(x)*ln(ln(x))+exp(
3+x)+2+x)*exp((exp(3+x)*x+x**2+2*x)*ln(ln(ln(x)))-2*exp(3+x)*x-2*x**2-3*x-7)/ln(x)/ln(ln(x)),x)

[Out]

exp(-2*x**2 - 2*x*exp(x + 3) - 3*x + (x**2 + x*exp(x + 3) + 2*x)*log(log(log(x))) - 7)

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