Optimal. Leaf size=22 \[ e^{-\frac {2}{e^4}} \log \left (\frac {\log (x)}{\left (-\frac {13}{4}-\log (2)\right )^2}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.02, antiderivative size = 11, normalized size of antiderivative = 0.50, number of steps used = 3, number of rules used = 3, integrand size = 15, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {12, 2302, 29} \begin {gather*} e^{-\frac {2}{e^4}} \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 29
Rule 2302
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-\frac {2}{e^4}} \int \frac {1}{x \log (x)} \, dx\\ &=e^{-\frac {2}{e^4}} \operatorname {Subst}\left (\int \frac {1}{x} \, dx,x,\log (x)\right )\\ &=e^{-\frac {2}{e^4}} \log (\log (x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 11, normalized size = 0.50 \begin {gather*} e^{-\frac {2}{e^4}} \log (\log (x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.05, size = 9, normalized size = 0.41 \begin {gather*} e^{\left (-2 \, e^{\left (-4\right )}\right )} \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.23, size = 10, normalized size = 0.45 \begin {gather*} e^{\left (-2 \, e^{\left (-4\right )}\right )} \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 = 0.04, size = 10, normalized size = 0.45
method | result | size |
risch | \({\mathrm e}^{-2 \,{\mathrm e}^{-4}} \ln \left (\ln \relax (x )\right )\) | \(10\) |
norman | \({\mathrm e}^{-2 \,{\mathrm e}^{-4}} \ln \left (\ln \relax (x )\right )\) | \(12\) |
derivativedivides | \({\mathrm e}^{-2 \,{\mathrm e}^{-4}} \ln \left (\ln \relax (x )\right )\) | \(14\) |
default | \({\mathrm e}^{-2 \,{\mathrm e}^{-4}} \ln \left (\ln \relax (x )\right )\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.36, size = 9, normalized size = 0.41 \begin {gather*} e^{\left (-2 \, e^{\left (-4\right )}\right )} \log \left (\log \relax (x)\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 4.84, size = 9, normalized size = 0.41 \begin {gather*} \ln \left (\ln \relax (x)\right )\,{\mathrm {e}}^{-2\,{\mathrm {e}}^{-4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.11, size = 10, normalized size = 0.45 \begin {gather*} \frac {\log {\left (\log {\relax (x )} \right )}}{e^{\frac {2}{e^{4}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________