3.92 \(\int \frac{1}{\sqrt{\frac{b}{x}}} \, dx\)

Optimal. Leaf size=14 \[ \frac{2 x}{3 \sqrt{\frac{b}{x}}} \]

[Out]

(2*x)/(3*Sqrt[b/x])

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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]

(2*x)/(3*Sqrt[b/x])

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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]

2*x**2*sqrt(b/x)/(3*b)

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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]

(2*x)/(3*Sqrt[b/x])

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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]

2/3*x/(b/x)^(1/2)

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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]

2/3*x/sqrt(b/x)

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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]

2/3*x/sqrt(b/x)

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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]

2*x/(3*sqrt(b)*sqrt(1/x))

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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]

2/3*sqrt(b*x)*x/(b*sign(x))