Optimal. Leaf size=3 \[ \log (\log (x)) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 3, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.250, Rules used = {2302, 29} \[ \log (\log (x)) \]
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 2302
Rubi steps
\begin {align*} \int \frac {1}{x \log (x)} \, dx &=\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=\log (\log (x))\\ \end {align*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 3, normalized size = 1.00 \[ \log (\log (x)) \]
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \[ \int \frac {1}{x \log (x)} \, dx \]
Verification is Not applicable to the result.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.97, size = 3, normalized size = 1.00 \[ \log \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.85, size = 4, normalized size = 1.33 \[ \log \left ({\left | \log \relax (x) \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 4, normalized size = 1.33
method | result | size |
derivativedivides | \(\ln \left (\ln \relax (x )\right )\) | \(4\) |
default | \(\ln \left (\ln \relax (x )\right )\) | \(4\) |
norman | \(\ln \left (\ln \relax (x )\right )\) | \(4\) |
risch | \(\ln \left (\ln \relax (x )\right )\) | \(4\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.42, size = 3, normalized size = 1.00 \[ \log \left (\log \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.18, size = 3, normalized size = 1.00 \[ \ln \left (\ln \relax (x)\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 3, normalized size = 1.00 \[ \log {\left (\log {\relax (x )} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________