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

Optimal. Leaf size=14 \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]

[Out]

(2*x)/(5*Sqrt[b/x^3])

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Rubi [A]  time = 0.00715514, 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 \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]

Antiderivative was successfully verified.

[In]  Int[1/Sqrt[b/x^3],x]

[Out]

(2*x)/(5*Sqrt[b/x^3])

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Rubi in Sympy [A]  time = 1.58655, size = 15, normalized size = 1.07 \[ \frac{2 x^{4} \sqrt{\frac{b}{x^{3}}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2*x**4*sqrt(b/x**3)/(5*b)

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Mathematica [A]  time = 0.00303792, size = 14, normalized size = 1. \[ \frac{2 x}{5 \sqrt{\frac{b}{x^3}}} \]

Antiderivative was successfully verified.

[In]  Integrate[1/Sqrt[b/x^3],x]

[Out]

(2*x)/(5*Sqrt[b/x^3])

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{2\,x}{5}{\frac{1}{\sqrt{{\frac{b}{{x}^{3}}}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x^3)^(1/2),x)

[Out]

2/5*x/(b/x^3)^(1/2)

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Maxima [A]  time = 1.43397, size = 14, normalized size = 1. \[ \frac{2 \, x}{5 \, \sqrt{\frac{b}{x^{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*x/sqrt(b/x^3)

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Fricas [A]  time = 0.257295, size = 20, normalized size = 1.43 \[ \frac{2 \, x^{4} \sqrt{\frac{b}{x^{3}}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*x^4*sqrt(b/x^3)/b

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Sympy [A]  time = 1.59988, size = 17, normalized size = 1.21 \[ \frac{2 x}{5 \sqrt{b} \sqrt{\frac{1}{x^{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x**3)**(1/2),x)

[Out]

2*x/(5*sqrt(b)*sqrt(x**(-3)))

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GIAC/XCAS [A]  time = 0.230453, size = 18, normalized size = 1.29 \[ \frac{2 \, \sqrt{b x} x^{2}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

2/5*sqrt(b*x)*x^2/b