Optimal. Leaf size=13 \[ 8 x^2 \left (x+\frac {x}{\log (3)}\right ) \]
________________________________________________________________________________________
Rubi [A] time = 0.01, antiderivative size = 13, normalized size of antiderivative = 1.00, number of steps used = 3, number of rules used = 3, integrand size = 18, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.167, Rules used = {6, 12, 30} \begin {gather*} \frac {8 x^3 (1+\log (3))}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 6
Rule 12
Rule 30
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {x^2 (24+24 \log (3))}{\log (3)} \, dx\\ &=\frac {(24+24 \log (3)) \int x^2 \, dx}{\log (3)}\\ &=\frac {8 x^3 (1+\log (3))}{\log (3)}\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A] time = 0.00, size = 13, normalized size = 1.00 \begin {gather*} \frac {8 x^3 (1+\log (3))}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
fricas [A] time = 1.01, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
giac [A] time = 0.20, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maple [A] time = 0.02, size = 14, normalized size = 1.08
method | result | size |
gosper | \(\frac {8 x^{3} \left (\ln \relax (3)+1\right )}{\ln \relax (3)}\) | \(14\) |
norman | \(\frac {8 x^{3} \left (\ln \relax (3)+1\right )}{\ln \relax (3)}\) | \(14\) |
risch | \(8 x^{3}+\frac {8 x^{3}}{\ln \relax (3)}\) | \(16\) |
default | \(\frac {8 x^{3} \ln \relax (3)+8 x^{3}}{\ln \relax (3)}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
maxima [A] time = 0.34, size = 16, normalized size = 1.23 \begin {gather*} \frac {8 \, {\left (x^{3} \log \relax (3) + x^{3}\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
mupad [B] time = 0.02, size = 14, normalized size = 1.08 \begin {gather*} \frac {x^3\,\left (8\,\ln \relax (3)+8\right )}{\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
sympy [A] time = 0.06, size = 12, normalized size = 0.92 \begin {gather*} \frac {x^{3} \left (8 + 8 \log {\relax (3 )}\right )}{\log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________