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

Optimal result

Integrand size = 5, antiderivative size = 5 \[ \int \log (\log (\log (\log (x)))) \, dx=\text {Int}(\log (\log (\log (\log (x)))),x) \]

[Out]

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

Rubi [N/A]

Not integrable

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 0, number of rules used = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \[ \int \log (\log (\log (\log (x)))) \, dx=\int \log (\log (\log (\log (x)))) \, dx \]

[In]

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

[Out]

Defer[Int][Log[Log[Log[Log[x]]]], x]

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

Mathematica [N/A]

Not integrable

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.40 \[ \int \log (\log (\log (\log (x)))) \, dx=\int \log (\log (\log (\log (x)))) \, dx \]

[In]

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

[Out]

Integrate[Log[Log[Log[Log[x]]]], x]

Maple [N/A]

Not integrable

Time = 0.05 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00

\[\int \ln \left (\ln \left (\ln \left (\ln \left (x \right )\right )\right )\right )d x\]

[In]

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

[Out]

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

Fricas [N/A]

Not integrable

Time = 0.25 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.40 \[ \int \log (\log (\log (\log (x)))) \, dx=\int { \log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right ) \,d x } \]

[In]

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

[Out]

integral(log(log(log(log(x)))), x)

Sympy [N/A]

Not integrable

Time = 3.80 (sec) , antiderivative size = 27, normalized size of antiderivative = 5.40 \[ \int \log (\log (\log (\log (x)))) \, dx=x \log {\left (\log {\left (\log {\left (\log {\left (x \right )} \right )} \right )} \right )} - \int \frac {1}{\log {\left (x \right )} \log {\left (\log {\left (x \right )} \right )} \log {\left (\log {\left (\log {\left (x \right )} \right )} \right )}}\, dx \]

[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)

Maxima [N/A]

Not integrable

Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 5.60 \[ \int \log (\log (\log (\log (x)))) \, dx=\int { \log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right ) \,d x } \]

[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)

Giac [N/A]

Not integrable

Time = 0.27 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.40 \[ \int \log (\log (\log (\log (x)))) \, dx=\int { \log \left (\log \left (\log \left (\log \left (x\right )\right )\right )\right ) \,d x } \]

[In]

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

[Out]

integrate(log(log(log(log(x)))), x)

Mupad [N/A]

Not integrable

Time = 0.58 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.40 \[ \int \log (\log (\log (\log (x)))) \, dx=\int \ln \left (\ln \left (\ln \left (\ln \left (x\right )\right )\right )\right ) \,d x \]

[In]

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

[Out]

int(log(log(log(log(x)))), x)