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

Optimal. Leaf size=12 \[ 2 x \sqrt{\frac{b}{x}} \]

[Out]

2*Sqrt[b/x]*x

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Rubi [A]  time = 0.00703931, antiderivative size = 12, 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 \[ 2 x \sqrt{\frac{b}{x}} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b/x],x]

[Out]

2*Sqrt[b/x]*x

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Rubi in Sympy [A]  time = 1.14967, size = 8, normalized size = 0.67 \[ 2 x \sqrt{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x)**(1/2),x)

[Out]

2*x*sqrt(b/x)

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Mathematica [A]  time = 0.00205493, size = 12, normalized size = 1. \[ 2 x \sqrt{\frac{b}{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b/x],x]

[Out]

2*Sqrt[b/x]*x

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ 2\,x\sqrt{{\frac{b}{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.43619, size = 14, normalized size = 1.17 \[ 2 \, x \sqrt{\frac{b}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x),x, algorithm="maxima")

[Out]

2*x*sqrt(b/x)

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Fricas [A]  time = 0.226164, size = 14, normalized size = 1.17 \[ \frac{2 \, b}{\sqrt{\frac{b}{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x),x, algorithm="fricas")

[Out]

2*b/sqrt(b/x)

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Sympy [A]  time = 0.377444, size = 14, normalized size = 1.17 \[ 2 \sqrt{b} x \sqrt{\frac{1}{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.224363, size = 12, normalized size = 1. \[ 2 \, \sqrt{b x}{\rm sign}\left (x\right ) \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x),x, algorithm="giac")

[Out]

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