3.122 \(\int \frac{1}{\sqrt [3]{\frac{b}{x^2}}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00650845, 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 \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^2)^(-1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.53033, size = 15, normalized size = 1.07 \[ \frac{3 x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}}{5 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00333646, size = 14, normalized size = 1. \[ \frac{3 x}{5 \sqrt [3]{\frac{b}{x^2}}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^2)^(-1/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x^2)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.43944, size = 14, normalized size = 1. \[ \frac{3 \, x}{5 \, \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^2)^(-1/3),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.21559, size = 20, normalized size = 1.43 \[ \frac{3 \, x^{3} \left (\frac{b}{x^{2}}\right )^{\frac{2}{3}}}{5 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^2)^(-1/3),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 1.54498, size = 17, normalized size = 1.21 \[ \frac{3 x}{5 \sqrt [3]{b} \sqrt [3]{\frac{1}{x^{2}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x**2)**(1/3),x)

[Out]

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

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \frac{1}{\left (\frac{b}{x^{2}}\right )^{\frac{1}{3}}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^2)^(-1/3),x, algorithm="giac")

[Out]

integrate((b/x^2)^(-1/3), x)