Optimal. Leaf size=9 \[ \log \left (\frac {x}{\log (3 x)}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 10, normalized size of antiderivative = 1.11, number of steps used = 3, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2365, 43} \begin {gather*} \log (x)-\log (\log (3 x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 43
Rule 2365
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\operatorname {Subst}\left (\int \frac {-1+x}{x} \, dx,x,\log (3 x)\right )\\ &=\operatorname {Subst}\left (\int \left (1-\frac {1}{x}\right ) \, dx,x,\log (3 x)\right )\\ &=\log (x)-\log (\log (3 x))\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.01, size = 10, normalized size = 1.11 \begin {gather*} \log (x)-\log (\log (3 x)) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.00, size = 12, normalized size = 1.33 \begin {gather*} \log \left (3 \, x\right ) - \log \left (\log \left (3 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.25, size = 10, normalized size = 1.11 \begin {gather*} \log \relax (x) - \log \left (\log \left (3 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 11, normalized size = 1.22
method | result | size |
risch | \(\ln \relax (x )-\ln \left (\ln \left (3 x \right )\right )\) | \(11\) |
derivativedivides | \(\ln \left (3 x \right )-\ln \left (\ln \left (3 x \right )\right )\) | \(13\) |
default | \(\ln \left (3 x \right )-\ln \left (\ln \left (3 x \right )\right )\) | \(13\) |
norman | \(\ln \left (3 x \right )-\ln \left (\ln \left (3 x \right )\right )\) | \(13\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 12, normalized size = 1.33 \begin {gather*} \log \left (3 \, x\right ) - \log \left (\log \left (3 \, x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.68, size = 10, normalized size = 1.11 \begin {gather*} \ln \relax (x)-\ln \left (\ln \left (3\,x\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.10, size = 8, normalized size = 0.89 \begin {gather*} \log {\relax (x )} - \log {\left (\log {\left (3 x \right )} \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________