3.75 \(\int \log (\log (\log (\log (x)))) \, dx\)

Optimal. Leaf size=8 \[ \text {Int}(\log (\log (\log (\log (x)))),x) \]

[Out]

CannotIntegrate(ln(ln(ln(ln(x)))),x)

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Rubi [A]  time = 0.01, 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 = {} \[ \int \log (\log (\log (\log (x)))) \, dx \]

Verification is Not applicable to the result.

[In]

Int[Log[Log[Log[Log[x]]]],x]

[Out]

Defer[Int][Log[Log[Log[Log[x]]]], x]

Rubi steps

\begin {align*} \int \log (\log (\log (\log (x)))) \, dx &=\int \log (\log (\log (\log (x)))) \, dx\\ \end {align*}

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Mathematica [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \log (\log (\log (\log (x)))) \, dx \]

Verification is Not applicable to the result.

[In]

Integrate[Log[Log[Log[Log[x]]]],x]

[Out]

Integrate[Log[Log[Log[Log[x]]]], x]

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fricas [A]  time = 0.44, size = 0, normalized size = 0.00 \[ {\rm integral}\left (\log \left (\log \left (\log \left (\log \relax (x)\right )\right )\right ), x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(log(log(x)))),x, algorithm="fricas")

[Out]

integral(log(log(log(log(x)))), x)

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giac [A]  time = 0.00, size = 0, normalized size = 0.00 \[ \int \log \left (\log \left (\log \left (\log \relax (x)\right )\right )\right )\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(log(log(x)))),x, algorithm="giac")

[Out]

integrate(log(log(log(log(x)))), x)

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maple [A]  time = 0.03, size = 0, normalized size = 0.00 \[ \int \ln \left (\ln \left (\ln \left (\ln \relax (x )\right )\right )\right )\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(ln(ln(ln(ln(x)))),x)

[Out]

int(ln(ln(ln(ln(x)))),x)

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maxima [A]  time = 0.00, size = 0, normalized size = 0.00 \[ x \log \left (\log \left (\log \left (\log \relax (x)\right )\right )\right ) - \int \frac {1}{\log \relax (x) \log \left (\log \relax (x)\right ) \log \left (\log \left (\log \relax (x)\right )\right )}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(log(log(x)))),x, algorithm="maxima")

[Out]

x*log(log(log(log(x)))) - integrate(1/(log(x)*log(log(x))*log(log(log(x)))), x)

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mupad [A]  time = 0.00, size = -1, normalized size = -0.12 \[ \int \ln \left (\ln \left (\ln \left (\ln \relax (x)\right )\right )\right ) \,d x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(log(log(log(log(x)))),x)

[Out]

int(log(log(log(log(x)))), x)

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sympy [A]  time = 0.00, size = 0, normalized size = 0.00 \[ x \log {\left (\log {\left (\log {\left (\log {\relax (x )} \right )} \right )} \right )} - \int \frac {1}{\log {\relax (x )} \log {\left (\log {\relax (x )} \right )} \log {\left (\log {\left (\log {\relax (x )} \right )} \right )}}\, dx \]

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(ln(ln(ln(ln(x)))),x)

[Out]

x*log(log(log(log(x)))) - Integral(1/(log(x)*log(log(x))*log(log(log(x)))), x)

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