Optimal. Leaf size=23 \[ 3 \left (3+(1-x)^2+2 x+x^2\right ) (-5+\log (3 x)) \]
[Out]
________________________________________________________________________________________
Rubi [A]
time = 0.01, antiderivative size = 19, normalized size of antiderivative = 0.83, number of steps
used = 5, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {14, 2341}
\begin {gather*} -30 x^2+6 x^2 \log (3 x)+12 \log (x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
Rule 14
Rule 2341
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (-\frac {6 \left (-2+9 x^2\right )}{x}+12 x \log (3 x)\right ) \, dx\\ &=-\left (6 \int \frac {-2+9 x^2}{x} \, dx\right )+12 \int x \log (3 x) \, dx\\ &=-3 x^2+6 x^2 \log (3 x)-6 \int \left (-\frac {2}{x}+9 x\right ) \, dx\\ &=-30 x^2+12 \log (x)+6 x^2 \log (3 x)\\ \end {aligned} \end {gather*}
________________________________________________________________________________________
Mathematica [A]
time = 0.01, size = 19, normalized size = 0.83 \begin {gather*} -30 x^2+12 \log (x)+6 x^2 \log (3 x) \end {gather*}
Antiderivative was successfully verified.
[In]
[Out]
________________________________________________________________________________________
Maple [A]
time = 0.27, size = 22, normalized size = 0.96
method | result | size |
risch | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (x \right )\) | \(20\) |
derivativedivides | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
default | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
norman | \(6 x^{2} \ln \left (3 x \right )-30 x^{2}+12 \ln \left (3 x \right )\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Maxima [A]
time = 0.28, size = 19, normalized size = 0.83 \begin {gather*} 6 \, x^{2} \log \left (3 \, x\right ) - 30 \, x^{2} + 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Fricas [A]
time = 0.37, size = 17, normalized size = 0.74 \begin {gather*} -30 \, x^{2} + 6 \, {\left (x^{2} + 2\right )} \log \left (3 \, x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Sympy [A]
time = 0.04, size = 19, normalized size = 0.83 \begin {gather*} 6 x^{2} \log {\left (3 x \right )} - 30 x^{2} + 12 \log {\left (x \right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Giac [A]
time = 0.38, size = 19, normalized size = 0.83 \begin {gather*} 6 \, x^{2} \log \left (3 \, x\right ) - 30 \, x^{2} + 12 \, \log \left (x\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________
Mupad [B]
time = 4.13, size = 24, normalized size = 1.04 \begin {gather*} 12\,\ln \left (x\right )+6\,x^2\,\ln \left (x\right )+6\,x^2\,\ln \left (3\right )-30\,x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
[Out]
________________________________________________________________________________________