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 = 0.0378473, 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 = 4.87924, size = 42, normalized size = 0.88 \[ - \frac{2 \left (- 9 x + 6\right ) \log{\left (- 3 x + 2 \right )}}{27 \sqrt{9 x^{2} - 12 x + 4}} + \frac{\sqrt{9 x^{2} - 12 x + 4}}{9} \]
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 = 0.0276005, size = 33, normalized size = 0.69 \[ \frac{(3 x-2) (3 x+2 \log (3 x-2)-2)}{9 \sqrt{(2-3 x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[x/Sqrt[4 - 12*x + 9*x^2],x]
[Out]
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Maple [A] time = 0.006, size = 29, normalized size = 0.6 \[{\frac{ \left ( -2+3\,x \right ) \left ( 3\,x+2\,\ln \left ( -2+3\,x \right ) \right ) }{9}{\frac{1}{\sqrt{ \left ( -2+3\,x \right ) ^{2}}}}} \]
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 = 0.834375, size = 28, normalized size = 0.58 \[ \frac{1}{9} \, \sqrt{9 \, x^{2} - 12 \, x + 4} + \frac{2}{9} \, \log \left (x - \frac{2}{3}\right ) \]
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 = 0.225078, size = 16, normalized size = 0.33 \[ \frac{1}{3} \, x + \frac{2}{9} \, \log \left (3 \, x - 2\right ) \]
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 [A] time = 0.166254, size = 12, normalized size = 0.25 \[ \frac{x}{3} + \frac{2 \log{\left (3 x - 2 \right )}}{9} \]
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 [A] time = 0.20659, size = 34, normalized size = 0.71 \[ \frac{1}{3} \, x{\rm sign}\left (3 \, x - 2\right ) + \frac{2}{9} \,{\rm ln}\left ({\left | 3 \, x - 2 \right |}\right ){\rm sign}\left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(x/sqrt((3*x - 2)^2),x, algorithm="giac")
[Out]