Optimal. Leaf size=21 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a} \]
[Out]
_______________________________________________________________________________________
Rubi [A] time = 0.0247353, antiderivative size = 21, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 17, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.059 \[ \frac{2 \sqrt{x} \sqrt{a+\frac{b}{x}}}{a} \]
Antiderivative was successfully verified.
[In] Int[1/(Sqrt[a + b/x]*Sqrt[x]),x]
[Out]
_______________________________________________________________________________________
Rubi in Sympy [A] time = 3.08494, size = 15, normalized size = 0.71 \[ \frac{2 \sqrt{x} \sqrt{a + \frac{b}{x}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] rubi_integrate(1/(a+b/x)**(1/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
Mathematica [A] time = 0.0276699, size = 23, normalized size = 1.1 \[ \frac{2 \sqrt{x} \sqrt{\frac{a x+b}{x}}}{a} \]
Antiderivative was successfully verified.
[In] Integrate[1/(Sqrt[a + b/x]*Sqrt[x]),x]
[Out]
_______________________________________________________________________________________
Maple [A] time = 0.003, size = 25, normalized size = 1.2 \[ 2\,{\frac{ax+b}{a\sqrt{x}}{\frac{1}{\sqrt{{\frac{ax+b}{x}}}}}} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] int(1/(a+b/x)^(1/2)/x^(1/2),x)
[Out]
_______________________________________________________________________________________
Maxima [A] time = 1.44128, size = 23, normalized size = 1.1 \[ \frac{2 \, \sqrt{a + \frac{b}{x}} \sqrt{x}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*sqrt(x)),x, algorithm="maxima")
[Out]
_______________________________________________________________________________________
Fricas [A] time = 0.229055, size = 26, normalized size = 1.24 \[ \frac{2 \, \sqrt{x} \sqrt{\frac{a x + b}{x}}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*sqrt(x)),x, algorithm="fricas")
[Out]
_______________________________________________________________________________________
Sympy [A] time = 8.94276, size = 17, normalized size = 0.81 \[ \frac{2 \sqrt{b} \sqrt{\frac{a x}{b} + 1}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(a+b/x)**(1/2)/x**(1/2),x)
[Out]
_______________________________________________________________________________________
GIAC/XCAS [A] time = 0.23001, size = 28, normalized size = 1.33 \[ \frac{2 \, \sqrt{a x + b}}{a} - \frac{2 \, \sqrt{b}}{a} \]
Verification of antiderivative is not currently implemented for this CAS.
[In] integrate(1/(sqrt(a + b/x)*sqrt(x)),x, algorithm="giac")
[Out]