Optimal. Leaf size=48 \[ -\frac{1}{9} \sqrt{-9 x^2-12 x-4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{-9 x^2-12 x-4}} \]
[Out]
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Rubi [A] time = 0.0412039, 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 \[ -\frac{1}{9} \sqrt{-9 x^2-12 x-4}-\frac{2 (3 x+2) \log (3 x+2)}{9 \sqrt{-9 x^2-12 x-4}} \]
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 = 5.20679, size = 48, normalized size = 1. \[ - \frac{2 \left (9 x + 6\right ) \log{\left (3 x + 2 \right )}}{27 \sqrt{- 9 x^{2} - 12 x - 4}} - \frac{\sqrt{- 9 x^{2} - 12 x - 4}}{9} \]
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 = 0.0127721, size = 35, normalized size = 0.73 \[ \frac{(3 x+2) (3 x-2 \log (3 x+2)+2)}{9 \sqrt{-(3 x+2)^2}} \]
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 = 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 = 0.816452, 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 = 0.225857, 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]