Optimal. Leaf size=21 \[ \log \left (\left (-4 x^2+2 x \left (-3+13 x+\log \left (x^2\right )\right )\right )^2\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.03, antiderivative size = 19, normalized size of antiderivative = 0.90, number of steps used = 1, number of rules used = 1, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.034, Rules used = {6684} \begin {gather*} 2 \log \left (-11 x^2-x \log \left (x^2\right )+3 x\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6684
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 \log \left (3 x-11 x^2-x \log \left (x^2\right )\right )\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.11, size = 17, normalized size = 0.81 \begin {gather*} 2 \left (\log (x)+\log \left (3-11 x-\log \left (x^2\right )\right )\right ) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 0.65, size = 17, normalized size = 0.81 \begin {gather*} \log \left (x^{2}\right ) + 2 \, \log \left (11 \, x + \log \left (x^{2}\right ) - 3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.16, size = 17, normalized size = 0.81 \begin {gather*} 2 \, \log \left (11 \, x + \log \left (x^{2}\right ) - 3\right ) + 2 \, \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 18, normalized size = 0.86
method | result | size |
norman | \(2 \ln \relax (x )+2 \ln \left (11 x -3+\ln \left (x^{2}\right )\right )\) | \(18\) |
risch | \(2 \ln \relax (x )+2 \ln \left (11 x -3+\ln \left (x^{2}\right )\right )\) | \(18\) |
default | \(2 \ln \left (x \ln \left (x^{2}\right )+11 x^{2}-3 x \right )\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.35, size = 18, normalized size = 0.86 \begin {gather*} 2 \, \log \left (11 \, x^{2} + x \log \left (x^{2}\right ) - 3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 6.06, size = 17, normalized size = 0.81 \begin {gather*} \ln \left (x^2\right )+2\,\ln \left (11\,x+\ln \left (x^2\right )-3\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.14, size = 17, normalized size = 0.81 \begin {gather*} 2 \log {\relax (x )} + 2 \log {\left (11 x + \log {\left (x^{2} \right )} - 3 \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________