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

Optimal. Leaf size=14 \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]

[Out]

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

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Rubi [A]  time = 0.00652189, 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 \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x)^(-1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.55098, size = 14, normalized size = 1. \[ \frac{3 x^{2} \left (\frac{b}{x}\right )^{\frac{2}{3}}}{4 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00291345, size = 14, normalized size = 1. \[ \frac{3 x}{4 \sqrt [3]{\frac{b}{x}}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x)^(-1/3),x]

[Out]

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

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Maple [A]  time = 0.003, size = 11, normalized size = 0.8 \[{\frac{3\,x}{4}{\frac{1}{\sqrt [3]{{\frac{b}{x}}}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b/x)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.4399, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.216844, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 1.56895, size = 15, normalized size = 1.07 \[ \frac{3 x}{4 \sqrt [3]{b} \sqrt [3]{\frac{1}{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b/x)**(1/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.228809, size = 14, normalized size = 1. \[ \frac{3 \, x}{4 \, \left (\frac{b}{x}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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