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

Optimal. Leaf size=7 \[ \text{CannotIntegrate}(\log (\log (\log (\log (x)))),x) \]

[Out]

Defer[Int][Log[Log[Log[Log[x]]]], x]

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Rubi [A]  time = 0.0058479, antiderivative size = 0, normalized size of antiderivative = 0., number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0., 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*}

Mathematica [A]  time = 0.0363875, size = 0, normalized size = 0. \[ \int \log (\log (\log (\log (x)))) \, dx \]

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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Maple [A]  time = 0.014, size = 0, normalized size = 0. \begin{align*} \int \ln \left ( \ln \left ( \ln \left ( \ln \left ( x \right ) \right ) \right ) \right ) \, dx \end{align*}

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., size = 0, normalized size = 0. \begin{align*} x \log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right ) - \int \frac{1}{\log \left (x\right ) \log \left (\log \left (x\right )\right ) \log \left (\log \left (\log \left (x\right )\right )\right )}\,{d x} \end{align*}

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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Fricas [A]  time = 0., size = 0, normalized size = 0. \begin{align*}{\rm integral}\left (\log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right ), x\right ) \end{align*}

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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Sympy [A]  time = 0., size = 0, normalized size = 0. \begin{align*} x \log{\left (\log{\left (\log{\left (\log{\left (x \right )} \right )} \right )} \right )} - \int \frac{1}{\log{\left (x \right )} \log{\left (\log{\left (x \right )} \right )} \log{\left (\log{\left (\log{\left (x \right )} \right )} \right )}}\, dx \end{align*}

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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Giac [A]  time = 0., size = 0, normalized size = 0. \begin{align*} \int \log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right )\,{d x} \end{align*}

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)