Optimal. Leaf size=28 \[ \frac{2 x^3}{27}+\frac{1}{3} x^3 \log ^2(x)-\frac{2}{9} x^3 \log (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0305475, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 8, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.25 \[ \frac{2 x^3}{27}+\frac{1}{3} x^3 \log ^2(x)-\frac{2}{9} x^3 \log (x) \]
Antiderivative was successfully verified.
[In] Int[x^2*Log[x]^2,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.92764, size = 26, normalized size = 0.93 \[ \frac{x^{3} \log{\left (x \right )}^{2}}{3} - \frac{2 x^{3} \log{\left (x \right )}}{9} + \frac{2 x^{3}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x**2*ln(x)**2,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00370572, size = 28, normalized size = 1. \[ \frac{2 x^3}{27}+\frac{1}{3} x^3 \log ^2(x)-\frac{2}{9} x^3 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[x^2*Log[x]^2,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.001, size = 23, normalized size = 0.8 \[{\frac{2\,{x}^{3}}{27}}-{\frac{2\,{x}^{3}\ln \left ( x \right ) }{9}}+{\frac{{x}^{3} \left ( \ln \left ( x \right ) \right ) ^{2}}{3}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x^2*ln(x)^2,x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41614, size = 23, normalized size = 0.82 \[ \frac{1}{27} \,{\left (9 \, \log \left (x\right )^{2} - 6 \, \log \left (x\right ) + 2\right )} x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x)^2,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.20615, size = 30, normalized size = 1.07 \[ \frac{1}{3} \, x^{3} \log \left (x\right )^{2} - \frac{2}{9} \, x^{3} \log \left (x\right ) + \frac{2}{27} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x)^2,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.091174, size = 26, normalized size = 0.93 \[ \frac{x^{3} \log{\left (x \right )}^{2}}{3} - \frac{2 x^{3} \log{\left (x \right )}}{9} + \frac{2 x^{3}}{27} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x**2*ln(x)**2,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.23451, size = 30, normalized size = 1.07 \[ \frac{1}{3} \, x^{3}{\rm ln}\left (x\right )^{2} - \frac{2}{9} \, x^{3}{\rm ln}\left (x\right ) + \frac{2}{27} \, x^{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x^2*log(x)^2,x, algorithm="giac")
[Out]