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

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

[Out]

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

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Rubi [A]  time = 0.00703803, 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 \[ \frac{3}{2} x \sqrt [3]{\frac{b}{x}} \]

Antiderivative was successfully verified.

[In]  Int[(b/x)^(1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.20638, size = 10, normalized size = 0.71 \[ \frac{3 x \sqrt [3]{\frac{b}{x}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x)**(1/3),x)

[Out]

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

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Mathematica [A]  time = 0.002181, size = 14, normalized size = 1. \[ \frac{3}{2} x \sqrt [3]{\frac{b}{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x)^(1/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.44106, size = 14, normalized size = 1. \[ \frac{3}{2} \, x \left (\frac{b}{x}\right )^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.21905, size = 14, normalized size = 1. \[ \frac{3 \, b}{2 \, \left (\frac{b}{x}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.475068, size = 15, normalized size = 1.07 \[ \frac{3 \sqrt [3]{b} x \sqrt [3]{\frac{1}{x}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x)**(1/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.23422, size = 14, normalized size = 1. \[ \frac{3 \, b}{2 \, \left (\frac{b}{x}\right )^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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