Optimal. Leaf size=16 \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0262674, antiderivative size = 16, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 15, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.067 \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x]*x^2),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 2.21049, size = 12, normalized size = 0.75 \[ - \frac{2 \sqrt{a + \frac{b}{x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/x**2/(a+b/x)**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0136972, size = 16, normalized size = 1. \[ -\frac{2 \sqrt{a+\frac{b}{x}}}{b} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[a + b/x]*x^2),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.007, size = 25, normalized size = 1.6 \[ -2\,{\frac{ax+b}{bx}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/x^2/(a+b/x)^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44046, size = 19, normalized size = 1.19 \[ -\frac{2 \, \sqrt{a + \frac{b}{x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*x^2),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.224532, size = 22, normalized size = 1.38 \[ -\frac{2 \, \sqrt{\frac{a x + b}{x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*x^2),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 2.87512, size = 22, normalized size = 1.38 \[ \begin{cases} - \frac{2 \sqrt{a + \frac{b}{x}}}{b} & \text{for}\: b \neq 0 \\- \frac{1}{\sqrt{a} x} & \text{otherwise} \end{cases} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/x**2/(a+b/x)**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.230186, size = 19, normalized size = 1.19 \[ -\frac{2 \, \sqrt{a + \frac{b}{x}}}{b} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*x^2),x, algorithm="giac")
[Out]