3.1.75 \(\int \log (\log (\log (\log (x)))) \, dx\) [75]

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

[Out]

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

________________________________________________________________________________________

Rubi [A]
time = 0.00, 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 \log (\log (\log (\log (x)))) \, dx \end {gather*}

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 = 0.03, size = 0, normalized size = 0.00 \begin {gather*} \int \log (\log (\log (\log (x)))) \, dx \end {gather*}

Verification is not applicable to the result.

[In]

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

[Out]

Integrate[Log[Log[Log[Log[x]]]], x]

________________________________________________________________________________________

Mathics [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {cought exception: maximum recursion depth exceeded in comparison} \end {gather*}

Warning: Unable to verify antiderivative.

[In]

mathics('Integrate[Log[Log[Log[Log[x]]]],x]')

[Out]

cought exception: maximum recursion depth exceeded in comparison

________________________________________________________________________________________

Maple [A]
time = 0.02, size = 0, normalized size = 0.00 \[\int \ln \left (\ln \left (\ln \left (\ln \left (x \right )\right )\right )\right )\, dx\]

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)

________________________________________________________________________________________

Maxima [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Failed to integrate} \end {gather*}

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)

________________________________________________________________________________________

Fricas [A]
time = 0.34, size = 0, normalized size = 0.00 \begin {gather*} \text {could not integrate} \end {gather*}

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)

________________________________________________________________________________________

Sympy [A]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 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 {gather*}

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)

________________________________________________________________________________________

Giac [A] N/A
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Could not integrate} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(log(log(log(log(x)))),x)

[Out]

Could not integrate

________________________________________________________________________________________

Mupad [A]
time = 0.00, size = -1, normalized size = -0.12 \begin {gather*} \int \ln \left (\ln \left (\ln \left (\ln \left (x\right )\right )\right )\right ) \,d x \end {gather*}

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)

________________________________________________________________________________________