3.19.51 \(\int \frac {1}{8 \log (\log (\log (6)))} \, dx\) [1851]

Optimal. Leaf size=13 \[ 6+\frac {x}{8 \log (\log (\log (6)))} \]

[Out]

1/8*x/ln(ln(ln(6)))+6

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Rubi [A]
time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.85, number of steps used = 1, number of rules used = 1, integrand size = 10, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {8} \begin {gather*} \frac {x}{8 \log (\log (\log (6)))} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(8*Log[Log[Log[6]]]),x]

[Out]

x/(8*Log[Log[Log[6]]])

Rule 8

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{8 \log (\log (\log (6)))}\\ \end {aligned} \end {gather*}

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Mathematica [A]
time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} \frac {x}{8 \log (\log (\log (6)))} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1/(8*Log[Log[Log[6]]]),x]

[Out]

x/(8*Log[Log[Log[6]]])

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Maple [A]
time = 0.06, size = 10, normalized size = 0.77

method	result	size
default	\(\frac {x}{8 \ln \left (\ln \left (\ln \left (6\right )\right )\right )}\)	\(10\)
norman	\(\frac {x}{8 \ln \left (\ln \left (\ln \left (6\right )\right )\right )}\)	\(10\)
risch	\(\frac {x}{8 \ln \left (\ln \left (\ln \left (2\right )+\ln \left (3\right )\right )\right )}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/8/ln(ln(ln(6))),x,method=_RETURNVERBOSE)

[Out]

1/8*x/ln(ln(ln(6)))

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Maxima [A]
time = 0.27, size = 9, normalized size = 0.69 \begin {gather*} \frac {x}{8 \, \log \left (\log \left (\log \left (6\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8/log(log(log(6))),x, algorithm="maxima")

[Out]

1/8*x/log(log(log(6)))

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Fricas [A]
time = 0.36, size = 9, normalized size = 0.69 \begin {gather*} \frac {x}{8 \, \log \left (\log \left (\log \left (6\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8/log(log(log(6))),x, algorithm="fricas")

[Out]

1/8*x/log(log(log(6)))

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Sympy [A]
time = 0.00, size = 8, normalized size = 0.62 \begin {gather*} \frac {x}{8 \log {\left (\log {\left (\log {\left (6 \right )} \right )} \right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8/ln(ln(ln(6))),x)

[Out]

x/(8*log(log(log(6))))

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Giac [A]
time = 0.39, size = 9, normalized size = 0.69 \begin {gather*} \frac {x}{8 \, \log \left (\log \left (\log \left (6\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/8/log(log(log(6))),x, algorithm="giac")

[Out]

1/8*x/log(log(log(6)))

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Mupad [B]
time = 0.00, size = 9, normalized size = 0.69 \begin {gather*} \frac {x}{8\,\ln \left (\ln \left (\ln \left (6\right )\right )\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/(8*log(log(log(6)))),x)

[Out]

x/(8*log(log(log(6))))

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