3.108 \(\int \sqrt [3]{\frac{b}{x^4}} \, dx\)

Optimal. Leaf size=12 \[ -3 x \sqrt [3]{\frac{b}{x^4}} \]

[Out]

-3*(b/x^4)^(1/3)*x

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Rubi [A]  time = 0.00681372, 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 \[ -3 x \sqrt [3]{\frac{b}{x^4}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x^4)^(1/3),x]

[Out]

-3*(b/x^4)^(1/3)*x

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Rubi in Sympy [A]  time = 1.22732, size = 12, normalized size = 1. \[ - 3 x \sqrt [3]{\frac{b}{x^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x**4)**(1/3),x)

[Out]

-3*x*(b/x**4)**(1/3)

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Mathematica [A]  time = 0.00234708, size = 12, normalized size = 1. \[ -3 x \sqrt [3]{\frac{b}{x^4}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x^4)^(1/3),x]

[Out]

-3*(b/x^4)^(1/3)*x

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Maple [A]  time = 0.003, size = 11, normalized size = 0.9 \[ -3\,\sqrt [3]{{\frac{b}{{x}^{4}}}}x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x^4)^(1/3),x)

[Out]

-3*(b/x^4)^(1/3)*x

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Maxima [A]  time = 1.43381, size = 14, normalized size = 1.17 \[ -3 \, x \left (\frac{b}{x^{4}}\right )^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(1/3),x, algorithm="maxima")

[Out]

-3*x*(b/x^4)^(1/3)

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Fricas [A]  time = 0.223739, size = 14, normalized size = 1.17 \[ -3 \, x \left (\frac{b}{x^{4}}\right )^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(1/3),x, algorithm="fricas")

[Out]

-3*x*(b/x^4)^(1/3)

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Sympy [A]  time = 1.40561, size = 17, normalized size = 1.42 \[ - 3 \sqrt [3]{b} x \sqrt [3]{\frac{1}{x^{4}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x**4)**(1/3),x)

[Out]

-3*b**(1/3)*x*(x**(-4))**(1/3)

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GIAC/XCAS [F]  time = 0., size = 0, normalized size = 0. \[ \int \left (\frac{b}{x^{4}}\right )^{\frac{1}{3}}\,{d x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x^4)^(1/3),x, algorithm="giac")

[Out]

integrate((b/x^4)^(1/3), x)