Optimal. Leaf size=11 \[ \log \left (\frac {\log (2)}{9 \log (x)}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 5, normalized size of antiderivative = 0.45, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {2302, 29} \begin {gather*} -\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 29
Rule 2302
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=-\log (\log (x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 5, normalized size = 0.45 \begin {gather*} -\log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.66, size = 5, normalized size = 0.45 \begin {gather*} -\log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.22, size = 6, normalized size = 0.55 \begin {gather*} -\log \left ({\left | \log \relax (x) \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 6, normalized size = 0.55
method | result | size |
derivativedivides | \(-\ln \left (\ln \relax (x )\right )\) | \(6\) |
default | \(-\ln \left (\ln \relax (x )\right )\) | \(6\) |
norman | \(-\ln \left (\ln \relax (x )\right )\) | \(6\) |
risch | \(-\ln \left (\ln \relax (x )\right )\) | \(6\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.49, size = 5, normalized size = 0.45 \begin {gather*} -\log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 1.06, size = 5, normalized size = 0.45 \begin {gather*} -\ln \left (\ln \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.08, size = 5, normalized size = 0.45 \begin {gather*} - \log {\left (\log {\relax (x )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________