3.82 \(\int \sqrt{\frac{b}{x^3}} \, dx\)

Optimal. Leaf size=12 \[ -2 x \sqrt{\frac{b}{x^3}} \]

[Out]

-2*Sqrt[b/x^3]*x

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Rubi [A]  time = 0.00691419, 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 \[ -2 x \sqrt{\frac{b}{x^3}} \]

Antiderivative was successfully verified.

[In]  Int[Sqrt[b/x^3],x]

[Out]

-2*Sqrt[b/x^3]*x

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Rubi in Sympy [A]  time = 1.22009, size = 12, normalized size = 1. \[ - 2 x \sqrt{\frac{b}{x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x**3)**(1/2),x)

[Out]

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

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Mathematica [A]  time = 0.00254706, size = 12, normalized size = 1. \[ -2 x \sqrt{\frac{b}{x^3}} \]

Antiderivative was successfully verified.

[In]  Integrate[Sqrt[b/x^3],x]

[Out]

-2*Sqrt[b/x^3]*x

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ -2\,x\sqrt{{\frac{b}{{x}^{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^3)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.47617, size = 14, normalized size = 1.17 \[ -2 \, x \sqrt{\frac{b}{x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x^3),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.218621, size = 14, normalized size = 1.17 \[ -2 \, x \sqrt{\frac{b}{x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x^3),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 1.23959, size = 17, normalized size = 1.42 \[ - 2 \sqrt{b} x \sqrt{\frac{1}{x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**3)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.228015, size = 11, normalized size = 0.92 \[ -\frac{2 \, b}{\sqrt{b x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(sqrt(b/x^3),x, algorithm="giac")

[Out]

-2*b/sqrt(b*x)