3.61.17 \(\int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log (x^2)-6 e^{e^x+x} x \log (x^2) \log (\log (x^2))+((3 x-3 x \log (3)) \log (x^2)+3 e^{e^x} \log (x^2) \log (\log (x^2))) \log (x-x \log (3)+e^{e^x} \log (\log (x^2)))}{((x-x \log (3)) \log (x^2)+e^{e^x} \log (x^2) \log (\log (x^2))) \log ^3(x-x \log (3)+e^{e^x} \log (\log (x^2)))} \, dx\)

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

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Rubi [F]  time = 6.20, 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 {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\left ((x-x \log (3)) \log \left (x^2\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx \end {gather*}

Verification is not applicable to the result.

[In]

Int[(-12*E^E^x + (-6*x + 6*x*Log[3])*Log[x^2] - 6*E^(E^x + x)*x*Log[x^2]*Log[Log[x^2]] + ((3*x - 3*x*Log[3])*L
og[x^2] + 3*E^E^x*Log[x^2]*Log[Log[x^2]])*Log[x - x*Log[3] + E^E^x*Log[Log[x^2]]])/(((x - x*Log[3])*Log[x^2] +
E^E^x*Log[x^2]*Log[Log[x^2]])*Log[x - x*Log[3] + E^E^x*Log[Log[x^2]]]^3),x]

[Out]

-12*Defer[Int][1/(Log[x^2]*Log[Log[x^2]]*Log[x*(1 - Log[3]) + E^E^x*Log[Log[x^2]]]^3), x] + 6*(1 - Log[3])*Def
er[Int][x/((-(x*(1 - Log[3])) - E^E^x*Log[Log[x^2]])*Log[x*(1 - Log[3]) + E^E^x*Log[Log[x^2]]]^3), x] + 6*Defe
r[Int][(E^(E^x + x)*x*Log[Log[x^2]])/((-(x*(1 - Log[3])) - E^E^x*Log[Log[x^2]])*Log[x*(1 - Log[3]) + E^E^x*Log
[Log[x^2]]]^3), x] + 12*(1 - Log[3])*Defer[Int][x/(Log[x^2]*Log[Log[x^2]]*(x*(1 - Log[3]) + E^E^x*Log[Log[x^2]
])*Log[x*(1 - Log[3]) + E^E^x*Log[Log[x^2]]]^3), x] + 3*Defer[Int][Log[x*(1 - Log[3]) + E^E^x*Log[Log[x^2]]]^(
-2), x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {-12 e^{e^x}+(-6 x+6 x \log (3)) \log \left (x^2\right )-6 e^{e^x+x} x \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )+\left ((3 x-3 x \log (3)) \log \left (x^2\right )+3 e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx\\ &=\int \left (\frac {6 e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {3 \left (-4 e^{e^x}-2 x (1-\log (3)) \log \left (x^2\right )+x (1-\log (3)) \log \left (x^2\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx\\ &=3 \int \frac {-4 e^{e^x}-2 x (1-\log (3)) \log \left (x^2\right )+x (1-\log (3)) \log \left (x^2\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )+e^{e^x} \log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx\\ &=3 \int \left (\frac {2 x (1-\log (3)) \left (2-\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {-4+\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx\\ &=3 \int \frac {-4+\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log \left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \frac {x \left (2-\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right )\right )}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx\\ &=3 \int \left (-\frac {4}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {1}{\log ^2\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \left (\frac {x}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}+\frac {2 x}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )}\right ) \, dx\\ &=3 \int \frac {1}{\log ^2\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+6 \int \frac {e^{e^x+x} x \log \left (\log \left (x^2\right )\right )}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx-12 \int \frac {1}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(6 (1-\log (3))) \int \frac {x}{\left (-x (1-\log (3))-e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx+(12 (1-\log (3))) \int \frac {x}{\log \left (x^2\right ) \log \left (\log \left (x^2\right )\right ) \left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right ) \log ^3\left (x (1-\log (3))+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \, dx\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.17, size = 24, normalized size = 1.00 \begin {gather*} \frac {3 x}{\log ^2\left (x-x \log (3)+e^{e^x} \log \left (\log \left (x^2\right )\right )\right )} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-12*E^E^x + (-6*x + 6*x*Log[3])*Log[x^2] - 6*E^(E^x + x)*x*Log[x^2]*Log[Log[x^2]] + ((3*x - 3*x*Log
[3])*Log[x^2] + 3*E^E^x*Log[x^2]*Log[Log[x^2]])*Log[x - x*Log[3] + E^E^x*Log[Log[x^2]]])/(((x - x*Log[3])*Log[
x^2] + E^E^x*Log[x^2]*Log[Log[x^2]])*Log[x - x*Log[3] + E^E^x*Log[Log[x^2]]]^3),x]

[Out]

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

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fricas [A]  time = 0.72, size = 36, normalized size = 1.50 \begin {gather*} \frac {3 \, x}{\log \left (-{\left ({\left (x \log \relax (3) - x\right )} e^{x} - e^{\left (x + e^{x}\right )} \log \left (\log \left (x^{2}\right )\right )\right )} e^{\left (-x\right )}\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*log(x^2)*exp(exp(x))*log(log(x^2))+(-3*x*log(3)+3*x)*log(x^2))*log(exp(exp(x))*log(log(x^2))-x*l
og(3)+x)-6*x*exp(x)*log(x^2)*exp(exp(x))*log(log(x^2))-12*exp(exp(x))+(6*x*log(3)-6*x)*log(x^2))/(log(x^2)*exp
(exp(x))*log(log(x^2))+(-x*log(3)+x)*log(x^2))/log(exp(exp(x))*log(log(x^2))-x*log(3)+x)^3,x, algorithm="frica
s")

[Out]

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

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giac [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(((3*log(x^2)*exp(exp(x))*log(log(x^2))+(-3*x*log(3)+3*x)*log(x^2))*log(exp(exp(x))*log(log(x^2))-x*l
og(3)+x)-6*x*exp(x)*log(x^2)*exp(exp(x))*log(log(x^2))-12*exp(exp(x))+(6*x*log(3)-6*x)*log(x^2))/(log(x^2)*exp
(exp(x))*log(log(x^2))+(-x*log(3)+x)*log(x^2))/log(exp(exp(x))*log(log(x^2))-x*log(3)+x)^3,x, algorithm="giac"
)

[Out]

Timed out

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maple [C]  time = 1.98, size = 52, normalized size = 2.17

method	result	size
risch	\(\frac {3 x}{\ln \left ({\mathrm e}^{{\mathrm e}^{x}} \ln \left (2 \ln \relax (x )-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \left (-\mathrm {csgn}\left (i x^{2}\right )+\mathrm {csgn}\left (i x \right )\right )^{2}}{2}\right )-x \ln \relax (3)+x \right )^{2}}\)	\(52\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((3*ln(x^2)*exp(exp(x))*ln(ln(x^2))+(-3*x*ln(3)+3*x)*ln(x^2))*ln(exp(exp(x))*ln(ln(x^2))-x*ln(3)+x)-6*x*ex
p(x)*ln(x^2)*exp(exp(x))*ln(ln(x^2))-12*exp(exp(x))+(6*x*ln(3)-6*x)*ln(x^2))/(ln(x^2)*exp(exp(x))*ln(ln(x^2))+
(-x*ln(3)+x)*ln(x^2))/ln(exp(exp(x))*ln(ln(x^2))-x*ln(3)+x)^3,x,method=_RETURNVERBOSE)

[Out]

3*x/ln(exp(exp(x))*ln(2*ln(x)-1/2*I*Pi*csgn(I*x^2)*(-csgn(I*x^2)+csgn(I*x))^2)-x*ln(3)+x)^2

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maxima [A]  time = 0.86, size = 27, normalized size = 1.12 \begin {gather*} \frac {3 \, x}{\log \left (-x {\left (\log \relax (3) - 1\right )} + e^{\left (e^{x}\right )} \log \relax (2) + e^{\left (e^{x}\right )} \log \left (\log \relax (x)\right )\right )^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((3*log(x^2)*exp(exp(x))*log(log(x^2))+(-3*x*log(3)+3*x)*log(x^2))*log(exp(exp(x))*log(log(x^2))-x*l
og(3)+x)-6*x*exp(x)*log(x^2)*exp(exp(x))*log(log(x^2))-12*exp(exp(x))+(6*x*log(3)-6*x)*log(x^2))/(log(x^2)*exp
(exp(x))*log(log(x^2))+(-x*log(3)+x)*log(x^2))/log(exp(exp(x))*log(log(x^2))-x*log(3)+x)^3,x, algorithm="maxim
a")

[Out]

3*x/log(-x*(log(3) - 1) + e^(e^x)*log(2) + e^(e^x)*log(log(x)))^2

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mupad [F]  time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int -\frac {12\,{\mathrm {e}}^{{\mathrm {e}}^x}+\ln \left (x^2\right )\,\left (6\,x-6\,x\,\ln \relax (3)\right )-\ln \left (x-x\,\ln \relax (3)+{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )\,\left (\ln \left (x^2\right )\,\left (3\,x-3\,x\,\ln \relax (3)\right )+3\,\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )+6\,x\,\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^x\,\ln \left (\ln \left (x^2\right )\right )}{{\ln \left (x-x\,\ln \relax (3)+{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )}^3\,\left (\ln \left (x^2\right )\,\left (x-x\,\ln \relax (3)\right )+\ln \left (x^2\right )\,{\mathrm {e}}^{{\mathrm {e}}^x}\,\ln \left (\ln \left (x^2\right )\right )\right )} \,d x \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(12*exp(exp(x)) + log(x^2)*(6*x - 6*x*log(3)) - log(x - x*log(3) + exp(exp(x))*log(log(x^2)))*(log(x^2)*(
3*x - 3*x*log(3)) + 3*log(x^2)*exp(exp(x))*log(log(x^2))) + 6*x*log(x^2)*exp(exp(x))*exp(x)*log(log(x^2)))/(lo
g(x - x*log(3) + exp(exp(x))*log(log(x^2)))^3*(log(x^2)*(x - x*log(3)) + log(x^2)*exp(exp(x))*log(log(x^2)))),
x)

[Out]

int(-(12*exp(exp(x)) + log(x^2)*(6*x - 6*x*log(3)) - log(x - x*log(3) + exp(exp(x))*log(log(x^2)))*(log(x^2)*(
3*x - 3*x*log(3)) + 3*log(x^2)*exp(exp(x))*log(log(x^2))) + 6*x*log(x^2)*exp(exp(x))*exp(x)*log(log(x^2)))/(lo
g(x - x*log(3) + exp(exp(x))*log(log(x^2)))^3*(log(x^2)*(x - x*log(3)) + log(x^2)*exp(exp(x))*log(log(x^2)))),
x)

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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(((3*ln(x**2)*exp(exp(x))*ln(ln(x**2))+(-3*x*ln(3)+3*x)*ln(x**2))*ln(exp(exp(x))*ln(ln(x**2))-x*ln(3)
+x)-6*x*exp(x)*ln(x**2)*exp(exp(x))*ln(ln(x**2))-12*exp(exp(x))+(6*x*ln(3)-6*x)*ln(x**2))/(ln(x**2)*exp(exp(x)
)*ln(ln(x**2))+(-x*ln(3)+x)*ln(x**2))/ln(exp(exp(x))*ln(ln(x**2))-x*ln(3)+x)**3,x)

[Out]

Timed out

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