Optimal. Leaf size=12 \[ \log (1-b x)-\log (x) \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0113802, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 3, number of rules used = 3, integrand size = 11, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.273 \[ \log (1-b x)-\log (x) \]
Antiderivative was successfully verified.
[In] Int[1/(x*(-1 + b*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.48967, size = 8, normalized size = 0.67 \[ - \log{\left (x \right )} + \log{\left (- b x + 1 \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/(b*x-1),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00361037, size = 12, normalized size = 1. \[ \log (1-b x)-\log (x) \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*(-1 + b*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.009, size = 12, normalized size = 1. \[ -\ln \left ( x \right ) +\ln \left ( bx-1 \right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/(b*x-1),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.34284, size = 15, normalized size = 1.25 \[ \log \left (b x - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.212492, size = 15, normalized size = 1.25 \[ \log \left (b x - 1\right ) - \log \left (x\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.227036, size = 8, normalized size = 0.67 \[ - \log{\left (x \right )} + \log{\left (x - \frac{1}{b} \right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/(b*x-1),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208412, size = 18, normalized size = 1.5 \[{\rm ln}\left ({\left | b x - 1 \right |}\right ) -{\rm ln}\left ({\left | x \right |}\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/((b*x - 1)*x),x, algorithm="giac")
[Out]