Optimal. Leaf size=14 \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.00605984, antiderivative size = 14, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.222 \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
Antiderivative was successfully verified.
[In] Int[1/Sqrt[b/x],x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 1.57558, size = 14, normalized size = 1. \[ \frac{2 x^{2} \sqrt{\frac{b}{x}}}{3 b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(b/x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0029528, size = 14, normalized size = 1. \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]
Antiderivative was successfully verified.
[In] Integrate[1/Sqrt[b/x],x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 11, normalized size = 0.8 \[{\frac{2\,x}{3}{\frac{1}{\sqrt{{\frac{b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(b/x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.41779, size = 14, normalized size = 1. \[ \frac{2 \, x}{3 \, \sqrt{\frac{b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.267758, size = 14, normalized size = 1. \[ \frac{2 \, x}{3 \, \sqrt{\frac{b}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 1.53416, size = 15, normalized size = 1.07 \[ \frac{2 x}{3 \sqrt{b} \sqrt{\frac{1}{x}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(b/x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.220319, size = 20, normalized size = 1.43 \[ \frac{2 \, \sqrt{b x} x}{3 \, b{\rm sign}\left (x\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/sqrt(b/x),x, algorithm="giac")
[Out]