Optimal. Leaf size=48 \[ -\frac{1}{9} \sqrt{-9 x^2+12 x-4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{-9 x^2+12 x-4}} \]
[Out]
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Rubi [A] time = 0.0379717, antiderivative size = 48, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 16, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.188 \[ -\frac{1}{9} \sqrt{-9 x^2+12 x-4}-\frac{2 (2-3 x) \log (2-3 x)}{9 \sqrt{-9 x^2+12 x-4}} \]
Antiderivative was successfully verified.
[In] Int[x/Sqrt[-4 + 12*x - 9*x^2],x]
[Out]
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Rubi in Sympy [A] time = 5.08702, size = 44, normalized size = 0.92 \[ - \frac{2 \left (- 9 x + 6\right ) \log{\left (- 3 x + 2 \right )}}{27 \sqrt{- 9 x^{2} + 12 x - 4}} - \frac{\sqrt{- 9 x^{2} + 12 x - 4}}{9} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(x/(-(-2+3*x)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.0191862, size = 35, normalized size = 0.73 \[ \frac{(3 x-2) (3 x+2 \log (2-3 x)-2)}{9 \sqrt{-(2-3 x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[-4 + 12*x - 9*x^2],x]
[Out]
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Maple [A] time = 0.004, size = 31, normalized size = 0.7 \[{\frac{ \left ( -2+3\,x \right ) \left ( 3\,x+2\,\ln \left ( -2+3\,x \right ) \right ) }{9}{\frac{1}{\sqrt{- \left ( -2+3\,x \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(x/(-(-2+3*x)^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.821781, size = 28, normalized size = 0.58 \[ -\frac{1}{9} \, \sqrt{-9 \, x^{2} + 12 \, x - 4} + \frac{2}{9} i \, \log \left (x - \frac{2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-(3*x - 2)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.221141, size = 14, normalized size = 0.29 \[ -\frac{1}{3} i \, x - \frac{2}{9} i \, \log \left (x - \frac{2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-(3*x - 2)^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{x}{\sqrt{- \left (3 x - 2\right )^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/(-(-2+3*x)**2)**(1/2),x)
[Out]
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GIAC/XCAS [F] time = 0., size = 0, normalized size = 0. \[ \mathit{undef} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt(-(3*x - 2)^2),x, algorithm="giac")
[Out]