Optimal. Leaf size=15 \[ -3+4 \log ^2(2) \log \left (\frac {\log (3)}{x^2}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.00, antiderivative size = 8, normalized size of antiderivative = 0.53, 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 = {12, 29} \begin {gather*} -8 \log ^2(2) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 12
Rule 29
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (\left (8 \log ^2(2)\right ) \int \frac {1}{x} \, dx\right )\\ &=-8 \log ^2(2) \log (x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 8, normalized size = 0.53 \begin {gather*} -8 \log ^2(2) \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.60, size = 8, normalized size = 0.53 \begin {gather*} -8 \, \log \relax (2)^{2} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.21, size = 9, normalized size = 0.60 \begin {gather*} -8 \, \log \relax (2)^{2} \log \left ({\left | x \right |}\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.03, size = 9, normalized size = 0.60
method | result | size |
default | \(-8 \ln \relax (x ) \ln \relax (2)^{2}\) | \(9\) |
norman | \(-8 \ln \relax (x ) \ln \relax (2)^{2}\) | \(9\) |
risch | \(-8 \ln \relax (x ) \ln \relax (2)^{2}\) | \(9\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 8, normalized size = 0.53 \begin {gather*} -8 \, \log \relax (2)^{2} \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 7.63, size = 8, normalized size = 0.53 \begin {gather*} -8\,{\ln \relax (2)}^2\,\ln \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.05, size = 10, normalized size = 0.67 \begin {gather*} - 8 \log {\relax (2 )}^{2} \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________