Optimal. Leaf size=29 \[ \frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-9 x^2-12 x-4}} \]
[Out]
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Rubi [A] time = 0.0174394, antiderivative size = 29, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-9 x^2-12 x-4}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[-4 - 12*x - 9*x^2],x]
[Out]
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Rubi in Sympy [A] time = 1.88976, size = 27, normalized size = 0.93 \[ \frac{\left (9 x + 6\right ) \log{\left (3 x + 2 \right )}}{9 \sqrt{- 9 x^{2} - 12 x - 4}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(-(2+3*x)**2)**(1/2),x)
[Out]
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Mathematica [A] time = 0.00728601, size = 28, normalized size = 0.97 \[ \frac{(3 x+2) \log (3 x+2)}{3 \sqrt{-(3 x+2)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[-4 - 12*x - 9*x^2],x]
[Out]
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Maple [A] time = 0.003, size = 25, normalized size = 0.9 \[{\frac{ \left ( 2+3\,x \right ) \ln \left ( 2+3\,x \right ) }{3}{\frac{1}{\sqrt{- \left ( 2+3\,x \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(-(2+3*x)^2)^(1/2),x)
[Out]
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Maxima [A] time = 0.795971, size = 8, normalized size = 0.28 \[ \frac{1}{3} i \, \log \left (x + \frac{2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-(3*x + 2)^2),x, algorithm="maxima")
[Out]
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Fricas [A] time = 0.21563, size = 8, normalized size = 0.28 \[ -\frac{1}{3} i \, \log \left (x + \frac{2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-(3*x + 2)^2),x, algorithm="fricas")
[Out]
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Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\sqrt{- \left (3 x + 2\right )^{2}}}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(-(2+3*x)**2)**(1/2),x)
[Out]
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GIAC/XCAS [A] time = 0.21228, size = 35, normalized size = 1.21 \[ \frac{i{\rm ln}\left (-i{\left (3 \, x + 2\right )}{\rm sign}\left (-3 \, x - 2\right )\right )}{3 \,{\rm sign}\left (-3 \, x - 2\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(-(3*x + 2)^2),x, algorithm="giac")
[Out]