3.93 \(\int \frac{1}{\sqrt{\frac{b}{x^2}}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00683868, 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 \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[b/x^2],x]

[Out]

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

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Rubi in Sympy [F]  time = 0., size = 0, normalized size = 0. \[ \frac{x \sqrt{\frac{b}{x^{2}}} \int x\, dx}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b/x**2)**(1/2),x)

[Out]

x*sqrt(b/x**2)*Integral(x, x)/b

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Mathematica [A]  time = 0.0036718, size = 14, normalized size = 1. \[ \frac{x}{2 \sqrt{\frac{b}{x^2}}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[b/x^2],x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{x}{2}{\frac{1}{\sqrt{{\frac{b}{{x}^{2}}}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x^2)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.46196, size = 14, normalized size = 1. \[ \frac{x}{2 \, \sqrt{\frac{b}{x^{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b/x^2),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.250505, size = 20, normalized size = 1.43 \[ \frac{x^{3} \sqrt{\frac{b}{x^{2}}}}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b/x^2),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 1.57395, size = 15, normalized size = 1.07 \[ \frac{x}{2 \sqrt{b} \sqrt{\frac{1}{x^{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x**2)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.221745, size = 16, normalized size = 1.14 \[ \frac{x^{2}}{2 \, \sqrt{b}{\rm sign}\left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b/x^2),x, algorithm="giac")

[Out]

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