3.89 \(\int \frac{1}{\sqrt{b x^3}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00703099, 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 \[ -\frac{2 x}{\sqrt{b x^3}} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[b*x^3],x]

[Out]

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

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Rubi in Sympy [A]  time = 1.57971, size = 15, normalized size = 1.25 \[ - \frac{2 \sqrt{b x^{3}}}{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.0026245, size = 12, normalized size = 1. \[ -\frac{2 x}{\sqrt{b x^3}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[b*x^3],x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x^3)^(1/2),x)

[Out]

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

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Maxima [A]  time = 1.42588, size = 14, normalized size = 1.17 \[ -\frac{2 \, x}{\sqrt{b x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x^3),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.236745, size = 20, normalized size = 1.67 \[ -\frac{2 \, \sqrt{b x^{3}}}{b x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x^3),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 1.48262, size = 15, normalized size = 1.25 \[ - \frac{2 x}{\sqrt{b} \sqrt{x^{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x**3)**(1/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.226637, size = 15, normalized size = 1.25 \[ -\frac{2}{\sqrt{b x}{\rm sign}\left (x\right )} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/sqrt(b*x^3),x, algorithm="giac")

[Out]

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