Optimal. Leaf size=28 \[ \frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x) \]
[Out]
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Rubi [A] time = 0.016315, antiderivative size = 28, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ \frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x) \]
Antiderivative was successfully verified.
[In] Int[x*Log[x]^2,x]
[Out]
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Rubi in Sympy [F] time = 0., size = 0, normalized size = 0. \[ \frac{x^{2} \log{\left (x \right )}^{2}}{2} - \frac{x^{2} \log{\left (x \right )}}{2} + \frac{\int x\, dx}{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x*ln(x)**2,x)
[Out]
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Mathematica [A] time = 0.00186486, size = 28, normalized size = 1. \[ \frac{x^2}{4}+\frac{1}{2} x^2 \log ^2(x)-\frac{1}{2} x^2 \log (x) \]
Antiderivative was successfully verified.
[In] Integrate[x*Log[x]^2,x]
[Out]
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Maple [A] time = 0., size = 23, normalized size = 0.8 \[{\frac{{x}^{2}}{4}}-{\frac{{x}^{2}\ln \left ( x \right ) }{2}}+{\frac{{x}^{2} \left ( \ln \left ( x \right ) \right ) ^{2}}{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x*ln(x)^2,x)
[Out]
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Maxima [A] time = 1.3461, size = 23, normalized size = 0.82 \[ \frac{1}{4} \,{\left (2 \, \log \left (x\right )^{2} - 2 \, \log \left (x\right ) + 1\right )} x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(x)^2,x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.225426, size = 30, normalized size = 1.07 \[ \frac{1}{2} \, x^{2} \log \left (x\right )^{2} - \frac{1}{2} \, x^{2} \log \left (x\right ) + \frac{1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(x)^2,x, algorithm="fricas")
[Out]
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Sympy [A] time = 0.092948, size = 22, normalized size = 0.79 \[ \frac{x^{2} \log{\left (x \right )}^{2}}{2} - \frac{x^{2} \log{\left (x \right )}}{2} + \frac{x^{2}}{4} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*ln(x)**2,x)
[Out]
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GIAC/XCAS [A] time = 0.210396, size = 30, normalized size = 1.07 \[ \frac{1}{2} \, x^{2}{\rm ln}\left (x\right )^{2} - \frac{1}{2} \, x^{2}{\rm ln}\left (x\right ) + \frac{1}{4} \, x^{2} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x*log(x)^2,x, algorithm="giac")
[Out]