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

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

[Out]

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

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Rubi [A]  time = 0.0071097, 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 \[ 3 x \left (\frac{b}{x}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Int[(b/x)^(2/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.24779, size = 8, normalized size = 0.67 \[ 3 x \left (\frac{b}{x}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((b/x)**(2/3),x)

[Out]

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

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Mathematica [A]  time = 0.00213525, size = 12, normalized size = 1. \[ 3 x \left (\frac{b}{x}\right )^{2/3} \]

Antiderivative was successfully verified.

[In]  Integrate[(b/x)^(2/3),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((b/x)^(2/3),x)

[Out]

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

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Maxima [A]  time = 1.44371, size = 14, normalized size = 1.17 \[ 3 \, x \left (\frac{b}{x}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.21562, size = 14, normalized size = 1.17 \[ \frac{3 \, b}{\left (\frac{b}{x}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.93577, size = 14, normalized size = 1.17 \[ 3 b^{\frac{2}{3}} x \left (\frac{1}{x}\right )^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((b/x)**(2/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.247711, size = 14, normalized size = 1.17 \[ \frac{3 \, b}{\left (\frac{b}{x}\right )^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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