Optimal. Leaf size=14 \[ -\frac{\sqrt{b x^2}}{x^2} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00675452, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 13, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.154 \[ -\frac{\sqrt{b x^2}}{x^2} \]
Antiderivative was successfully verified.
[In] Int[Sqrt[b*x^2]/x^3,x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.43338, size = 10, normalized size = 0.71 \[ - \frac{b}{\sqrt{b x^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate((b*x**2)**(1/2)/x**3,x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.00349005, size = 14, normalized size = 1. \[ -\frac{\sqrt{b x^2}}{x^2} \]
Antiderivative was successfully verified.
[In] Integrate[Sqrt[b*x^2]/x^3,x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 13, normalized size = 0.9 \[ -{\frac{1}{{x}^{2}}\sqrt{b{x}^{2}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int((b*x^2)^(1/2)/x^3,x)
[Out]
_______________________________________________________________________________________
Maxima [F] time = 0., size = 0, normalized size = 0. \[ \text{Exception raised: RuntimeError} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^3,x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.247893, size = 16, normalized size = 1.14 \[ -\frac{\sqrt{b x^{2}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^3,x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.60944, size = 15, normalized size = 1.07 \[ - \frac{\sqrt{b} \sqrt{x^{2}}}{x^{2}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate((b*x**2)**(1/2)/x**3,x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.212573, size = 14, normalized size = 1. \[ -\frac{\sqrt{b}{\rm sign}\left (x\right )}{x} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(sqrt(b*x^2)/x^3,x, algorithm="giac")
[Out]