3.74.67 \(\int \frac {1}{3} \log (3 \log (-6+3 e^{e^{\frac {1}{2} (8+e^3)}})) \, dx\)

Optimal. Leaf size=29 \[ \frac {1}{3} \left (3+x \log \left (3 \log \left (3 \left (-2+e^{e^{4+\frac {e^3}{2}}}\right )\right )\right )\right ) \]

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Rubi [A]  time = 0.01, antiderivative size = 28, normalized size of antiderivative = 0.97, number of steps used = 1, number of rules used = 1, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.040, Rules used = {8} \begin {gather*} \frac {1}{3} x \log \left (3 \log \left (-3 \left (2-e^{e^{4+\frac {e^3}{2}}}\right )\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Int[Log[3*Log[-6 + 3*E^E^((8 + E^3)/2)]]/3,x]

[Out]

(x*Log[3*Log[-3*(2 - E^E^(4 + E^3/2))]])/3

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

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

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Mathematica [A]  time = 0.00, size = 26, normalized size = 0.90 \begin {gather*} \frac {1}{3} x \log \left (3 \log \left (-6+3 e^{e^{\frac {1}{2} \left (8+e^3\right )}}\right )\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[Log[3*Log[-6 + 3*E^E^((8 + E^3)/2)]]/3,x]

[Out]

(x*Log[3*Log[-6 + 3*E^E^((8 + E^3)/2)]])/3

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fricas [A]  time = 0.70, size = 19, normalized size = 0.66 \begin {gather*} \frac {1}{3} \, x \log \left (3 \, \log \left (3 \, e^{\left (e^{\left (\frac {1}{2} \, e^{3} + 4\right )}\right )} - 6\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*log(3*log(3*exp(exp(1/2*exp(3)+4))-6)),x, algorithm="fricas")

[Out]

1/3*x*log(3*log(3*e^(e^(1/2*e^3 + 4)) - 6))

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giac [A]  time = 0.19, size = 19, normalized size = 0.66 \begin {gather*} \frac {1}{3} \, x \log \left (3 \, \log \left (3 \, e^{\left (e^{\left (\frac {1}{2} \, e^{3} + 4\right )}\right )} - 6\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*log(3*log(3*exp(exp(1/2*exp(3)+4))-6)),x, algorithm="giac")

[Out]

1/3*x*log(3*log(3*e^(e^(1/2*e^3 + 4)) - 6))

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maple [A]  time = 0.04, size = 20, normalized size = 0.69

method	result	size
default	\(\frac {x \ln \left (3 \ln \left (3 \,{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{3}}{2}+4}}-6\right )\right )}{3}\)	\(20\)
norman	\(\left (\frac {\ln \relax (3)}{3}+\frac {\ln \left (\ln \relax (3)+\ln \left ({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{3}}{2}+4}}-2\right )\right )}{3}\right ) x\)	\(25\)
risch	\(\frac {x \ln \relax (3)}{3}+\frac {x \ln \left (\ln \relax (3)+\ln \left ({\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{3}}{2}+4}}-2\right )\right )}{3}\)	\(25\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/3*ln(3*ln(3*exp(exp(1/2*exp(3)+4))-6)),x,method=_RETURNVERBOSE)

[Out]

1/3*x*ln(3*ln(3*exp(exp(1/2*exp(3)+4))-6))

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maxima [A]  time = 0.36, size = 19, normalized size = 0.66 \begin {gather*} \frac {1}{3} \, x \log \left (3 \, \log \left (3 \, e^{\left (e^{\left (\frac {1}{2} \, e^{3} + 4\right )}\right )} - 6\right )\right ) \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*log(3*log(3*exp(exp(1/2*exp(3)+4))-6)),x, algorithm="maxima")

[Out]

1/3*x*log(3*log(3*e^(e^(1/2*e^3 + 4)) - 6))

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mupad [B]  time = 0.00, size = 19, normalized size = 0.66 \begin {gather*} \frac {x\,\ln \left (3\,\ln \left (3\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^3}{2}+4}}-6\right )\right )}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(3*log(3*exp(exp(exp(3)/2 + 4)) - 6))/3,x)

[Out]

(x*log(3*log(3*exp(exp(exp(3)/2 + 4)) - 6)))/3

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sympy [A]  time = 0.06, size = 20, normalized size = 0.69 \begin {gather*} \frac {x \log {\left (3 \log {\left (-6 + 3 e^{e^{4 + \frac {e^{3}}{2}}} \right )} \right )}}{3} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/3*ln(3*ln(3*exp(exp(1/2*exp(3)+4))-6)),x)

[Out]

x*log(3*log(-6 + 3*exp(exp(4 + exp(3)/2))))/3

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