Optimal. Leaf size=71 \[ \frac{\log (x) (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0806786, antiderivative size = 71, normalized size of antiderivative = 1., number of steps used = 4, number of rules used = 4, integrand size = 24, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.167 \[ \frac{\log (x) (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}}-\frac{(a-b x) \log (a-b x)}{a \sqrt{a^2-2 a b x+b^2 x^2}} \]
Antiderivative was successfully verified.
[In] Int[1/(x*Sqrt[a^2 - 2*a*b*x + b^2*x^2]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 15.6807, size = 63, normalized size = 0.89 \[ \frac{\sqrt{a^{2} - 2 a b x + b^{2} x^{2}} \log{\left (x \right )}}{a \left (a - b x\right )} - \frac{\sqrt{a^{2} - 2 a b x + b^{2} x^{2}} \log{\left (a - b x \right )}}{a \left (a - b x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x/((b*x-a)**2)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0342609, size = 34, normalized size = 0.48 \[ \frac{(a-b x) (\log (x)-\log (a-b x))}{a \sqrt{(a-b x)^2}} \]
Antiderivative was successfully verified.
[In] Integrate[1/(x*Sqrt[a^2 - 2*a*b*x + b^2*x^2]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.019, size = 36, normalized size = 0.5 \[{\frac{ \left ( bx-a \right ) \left ( \ln \left ( bx-a \right ) -\ln \left ( x \right ) \right ) }{a}{\frac{1}{\sqrt{ \left ( bx-a \right ) ^{2}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x/((b*x-a)^2)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: ValueError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt((b*x - a)^2)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.221619, size = 23, normalized size = 0.32 \[ \frac{\log \left (b x - a\right ) - \log \left (x\right )}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt((b*x - a)^2)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 0.389651, size = 10, normalized size = 0.14 \[ \frac{- \log{\left (x \right )} + \log{\left (- \frac{a}{b} + x \right )}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x/((b*x-a)**2)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.20665, size = 42, normalized size = 0.59 \[{\left (\frac{{\rm ln}\left ({\left | b x - a \right |}\right )}{a} - \frac{{\rm ln}\left ({\left | x \right |}\right )}{a}\right )}{\rm sign}\left (b x - a\right ) \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt((b*x - a)^2)*x),x, algorithm="giac")
[Out]