3.114 \(\int \left (\frac{b}{x^3}\right )^{2/3} \, dx\)

Optimal. Leaf size=12 \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]

[Out]

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

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Rubi [A]  time = 0.00688379, 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 \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]

Antiderivative was successfully verified.

[In]  Int[(b/x^3)^(2/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.2107, size = 10, normalized size = 0.83 \[ - x \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00209269, size = 12, normalized size = 1. \[ x \left (-\left (\frac{b}{x^3}\right )^{2/3}\right ) \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^3)^(2/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^3)^(2/3),x)

[Out]

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

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Maxima [A]  time = 1.44037, size = 14, normalized size = 1.17 \[ -x \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.212811, size = 14, normalized size = 1.17 \[ -x \left (\frac{b}{x^{3}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.69691, size = 15, normalized size = 1.25 \[ - b^{\frac{2}{3}} x \left (\frac{1}{x^{3}}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**3)**(2/3),x)

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

integrate((b/x^3)^(2/3), x)