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

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

[Out]

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

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Rubi [A]  time = 0.00693723, 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 \[ 3 x \sqrt [3]{\frac{b}{x^2}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^2)^(1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.20164, size = 10, normalized size = 0.83 \[ 3 x \sqrt [3]{\frac{b}{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00208693, size = 12, normalized size = 1. \[ 3 x \sqrt [3]{\frac{b}{x^2}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^2)^(1/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^2)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.43522, size = 14, normalized size = 1.17 \[ 3 \, x \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.24498, size = 14, normalized size = 1.17 \[ 3 \, x \left (\frac{b}{x^{2}}\right )^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.3171, size = 15, normalized size = 1.25 \[ 3 \sqrt [3]{b} x \sqrt [3]{\frac{1}{x^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**2)**(1/3),x)

[Out]

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

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

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)