Optimal. Leaf size=22 \[ \frac{\sqrt{c x^2} \log (a+b x)}{b x} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0114679, antiderivative size = 22, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1 \[ \frac{\sqrt{c x^2} \log (a+b x)}{b x} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[c*x^2]/(x*(a + b*x)),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 11.8602, size = 17, normalized size = 0.77 \[ \frac{\sqrt{c x^{2}} \log{\left (a + b x \right )}}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((c*x**2)**(1/2)/x/(b*x+a),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00718074, size = 21, normalized size = 0.95 \[ \frac{c x \log (a+b x)}{b \sqrt{c x^2}} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[c*x^2]/(x*(a + b*x)),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.004, size = 21, normalized size = 1. \[{\frac{\ln \left ( bx+a \right ) }{bx}\sqrt{c{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((c*x^2)^(1/2)/x/(b*x+a),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(sqrt(c*x^2)/((b*x + a)*x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.201458, size = 27, normalized size = 1.23 \[ \frac{\sqrt{c x^{2}} \log \left (b x + a\right )}{b x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)/((b*x + a)*x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [F] time = 0., size = 0, normalized size = 0. \[ \int \frac{\sqrt{c x^{2}}}{x \left (a + b x\right )}\, dx \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((c*x**2)**(1/2)/x/(b*x+a),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.208499, size = 38, normalized size = 1.73 \[ \sqrt{c}{\left (\frac{{\rm ln}\left ({\left | b x + a \right |}\right ){\rm sign}\left (x\right )}{b} - \frac{{\rm ln}\left ({\left | a \right |}\right ){\rm sign}\left (x\right )}{b}\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(c*x^2)/((b*x + a)*x),x, algorithm="giac")
[Out]