3.61.79 \(\int \frac {-x+\log (\log (5))+e^{e^{e^{3+e^x}+\log ^2(\frac {-x+\log (\log (5))}{\log (\log (5))})}} (x-\log (\log (5))+e^{e^{3+e^x}+\log ^2(\frac {-x+\log (\log (5))}{\log (\log (5))})} (e^{3+e^x} (e^x x^2-e^x x \log (\log (5)))+2 x \log (\frac {-x+\log (\log (5))}{\log (\log (5))})))}{-x+\log (\log (5))} \, dx\)

Optimal. Leaf size=30 \[ x-e^{e^{e^{3+e^x}+\log ^2\left (1-\frac {x}{\log (\log (5))}\right )}} x \]

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Rubi [F]  time = 5.20, 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 {-x+\log (\log (5))+\exp \left (e^{e^{3+e^x}+\log ^2\left (\frac {-x+\log (\log (5))}{\log (\log (5))}\right )}\right ) \left (x-\log (\log (5))+e^{e^{3+e^x}+\log ^2\left (\frac {-x+\log (\log (5))}{\log (\log (5))}\right )} \left (e^{3+e^x} \left (e^x x^2-e^x x \log (\log (5))\right )+2 x \log \left (\frac {-x+\log (\log (5))}{\log (\log (5))}\right )\right )\right )}{-x+\log (\log (5))} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

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

Rubi steps

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

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Mathematica [A]  time = 0.30, size = 30, normalized size = 1.00 \begin {gather*} x-e^{e^{e^{3+e^x}+\log ^2\left (1-\frac {x}{\log (\log (5))}\right )}} x \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

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

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fricas [A]  time = 0.59, size = 30, normalized size = 1.00 \begin {gather*} -x e^{\left (e^{\left (\log \left (-\frac {x - \log \left (\log \relax (5)\right )}{\log \left (\log \relax (5)\right )}\right )^{2} + e^{\left (e^{x} + 3\right )}\right )}\right )} + x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*log((log(log(5))-x)/log(log(5)))+(-x*exp(x)*log(log(5))+exp(x)*x^2)*exp(3+exp(x)))*exp(log((l
og(log(5))-x)/log(log(5)))^2+exp(3+exp(x)))-log(log(5))+x)*exp(exp(log((log(log(5))-x)/log(log(5)))^2+exp(3+ex
p(x))))+log(log(5))-x)/(log(log(5))-x),x, algorithm="fricas")

[Out]

-x*e^(e^(log(-(x - log(log(5)))/log(log(5)))^2 + e^(e^x + 3))) + x

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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((((2*x*log((log(log(5))-x)/log(log(5)))+(-x*exp(x)*log(log(5))+exp(x)*x^2)*exp(3+exp(x)))*exp(log((l
og(log(5))-x)/log(log(5)))^2+exp(3+exp(x)))-log(log(5))+x)*exp(exp(log((log(log(5))-x)/log(log(5)))^2+exp(3+ex
p(x))))+log(log(5))-x)/(log(log(5))-x),x, algorithm="giac")

[Out]

undef

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maple [A]  time = 0.42, size = 30, normalized size = 1.00

method	result	size
risch	\(-{\mathrm e}^{{\mathrm e}^{\ln \left (\frac {\ln \left (\ln \relax (5)\right )-x}{\ln \left (\ln \relax (5)\right )}\right )^{2}+{\mathrm e}^{3+{\mathrm e}^{x}}}} x +x\)	\(30\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((((2*x*ln((ln(ln(5))-x)/ln(ln(5)))+(-x*exp(x)*ln(ln(5))+exp(x)*x^2)*exp(3+exp(x)))*exp(ln((ln(ln(5))-x)/ln
(ln(5)))^2+exp(3+exp(x)))-ln(ln(5))+x)*exp(exp(ln((ln(ln(5))-x)/ln(ln(5)))^2+exp(3+exp(x))))+ln(ln(5))-x)/(ln(
ln(5))-x),x,method=_RETURNVERBOSE)

[Out]

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

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maxima [F]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} x - \int \frac {{\left ({\left (2 \, x e^{\left (\log \left (\log \left (\log \relax (5)\right )\right )^{2}\right )} \log \left (-x + \log \left (\log \relax (5)\right )\right ) - 2 \, x e^{\left (\log \left (\log \left (\log \relax (5)\right )\right )^{2}\right )} \log \left (\log \left (\log \relax (5)\right )\right ) + {\left (x^{2} e^{\left (\log \left (\log \left (\log \relax (5)\right )\right )^{2} + 3\right )} - x e^{\left (\log \left (\log \left (\log \relax (5)\right )\right )^{2} + 3\right )} \log \left (\log \relax (5)\right )\right )} e^{\left (x + e^{x}\right )}\right )} e^{\left (\log \left (-x + \log \left (\log \relax (5)\right )\right )^{2} + e^{\left (e^{x} + 3\right )}\right )} + {\left (x - \log \left (\log \relax (5)\right )\right )} e^{\left (2 \, \log \left (-x + \log \left (\log \relax (5)\right )\right ) \log \left (\log \left (\log \relax (5)\right )\right )\right )}\right )} e^{\left (-2 \, \log \left (-x + \log \left (\log \relax (5)\right )\right ) \log \left (\log \left (\log \relax (5)\right )\right ) + e^{\left (\log \left (-x + \log \left (\log \relax (5)\right )\right )^{2} - 2 \, \log \left (-x + \log \left (\log \relax (5)\right )\right ) \log \left (\log \left (\log \relax (5)\right )\right ) + \log \left (\log \left (\log \relax (5)\right )\right )^{2} + e^{\left (e^{x} + 3\right )}\right )}\right )}}{x - \log \left (\log \relax (5)\right )}\,{d x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*log((log(log(5))-x)/log(log(5)))+(-x*exp(x)*log(log(5))+exp(x)*x^2)*exp(3+exp(x)))*exp(log((l
og(log(5))-x)/log(log(5)))^2+exp(3+exp(x)))-log(log(5))+x)*exp(exp(log((log(log(5))-x)/log(log(5)))^2+exp(3+ex
p(x))))+log(log(5))-x)/(log(log(5))-x),x, algorithm="maxima")

[Out]

x - integrate(((2*x*e^(log(log(log(5)))^2)*log(-x + log(log(5))) - 2*x*e^(log(log(log(5)))^2)*log(log(log(5)))
+ (x^2*e^(log(log(log(5)))^2 + 3) - x*e^(log(log(log(5)))^2 + 3)*log(log(5)))*e^(x + e^x))*e^(log(-x + log(lo
g(5)))^2 + e^(e^x + 3)) + (x - log(log(5)))*e^(2*log(-x + log(log(5)))*log(log(log(5)))))*e^(-2*log(-x + log(l
og(5)))*log(log(log(5))) + e^(log(-x + log(log(5)))^2 - 2*log(-x + log(log(5)))*log(log(log(5))) + log(log(log
(5)))^2 + e^(e^x + 3)))/(x - log(log(5))), x)

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mupad [B]  time = 0.42, size = 48, normalized size = 1.60 \begin {gather*} -x\,\left ({\mathrm {e}}^{\frac {{\mathrm {e}}^{{\ln \left (\ln \left (\ln \relax (5)\right )\right )}^2}\,{\mathrm {e}}^{{\ln \left (\ln \left (\ln \relax (5)\right )-x\right )}^2}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^3}}{{\left (\ln \left (\ln \relax (5)\right )-x\right )}^{2\,\ln \left (\ln \left (\ln \relax (5)\right )\right )}}}-1\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(log(log(5)) - x + exp(exp(exp(exp(x) + 3) + log(-(x - log(log(5)))/log(log(5)))^2))*(x - log(log(5)) + e
xp(exp(exp(x) + 3) + log(-(x - log(log(5)))/log(log(5)))^2)*(exp(exp(x) + 3)*(x^2*exp(x) - x*exp(x)*log(log(5)
)) + 2*x*log(-(x - log(log(5)))/log(log(5))))))/(x - log(log(5))),x)

[Out]

-x*(exp((exp(log(log(log(5)))^2)*exp(log(log(log(5)) - x)^2)*exp(exp(exp(x))*exp(3)))/(log(log(5)) - x)^(2*log
(log(log(5))))) - 1)

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sympy [F(-1)]  time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate((((2*x*ln((ln(ln(5))-x)/ln(ln(5)))+(-x*exp(x)*ln(ln(5))+exp(x)*x**2)*exp(3+exp(x)))*exp(ln((ln(ln(5)
)-x)/ln(ln(5)))**2+exp(3+exp(x)))-ln(ln(5))+x)*exp(exp(ln((ln(ln(5))-x)/ln(ln(5)))**2+exp(3+exp(x))))+ln(ln(5)
)-x)/(ln(ln(5))-x),x)

[Out]

Timed out

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