Optimal. Leaf size=29 \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.014126, 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 \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{9 x^2-12 x+4}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[4 - 12*x + 9*x^2],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.75393, 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]
_______________________________________________________________________________________
Mathematica [A] time = 0.0180115, size = 26, normalized size = 0.9 \[ -\frac{(2-3 x) \log (2-3 x)}{3 \sqrt{(2-3 x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[4 - 12*x + 9*x^2],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 23, normalized size = 0.8 \[{\frac{ \left ( -2+3\,x \right ) \ln \left ( -2+3\,x \right ) }{3}{\frac{1}{\sqrt{ \left ( -2+3\,x \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/((-2+3*x)^2)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 0.804821, size = 8, normalized size = 0.28 \[ \frac{1}{3} \, \log \left (x - \frac{2}{3}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((3*x - 2)^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.233132, size = 11, normalized size = 0.38 \[ \frac{1}{3} \, \log \left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((3*x - 2)^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.116029, size = 7, normalized size = 0.24 \[ \frac{\log{\left (3 x - 2 \right )}}{3} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((-2+3*x)**2)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.210258, size = 20, normalized size = 0.69 \[ \frac{1}{3} \,{\rm ln}\left ({\left | 3 \, x - 2 \right |}\right ){\rm sign}\left (3 \, x - 2\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt((3*x - 2)^2),x, algorithm="giac")
[Out]