3.127 \(\int \frac{1}{(b x)^{2/3}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00648606, antiderivative size = 12, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143 \[ \frac{3 \sqrt [3]{b x}}{b} \]

Antiderivative was successfully verified.

[In]  Int[(b*x)^(-2/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.33885, size = 8, normalized size = 0.67 \[ \frac{3 \sqrt [3]{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/(b*x)**(2/3),x)

[Out]

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

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Mathematica [A]  time = 0.00224052, size = 10, normalized size = 0.83 \[ \frac{3 x}{(b x)^{2/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(-2/3),x]

[Out]

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

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Maple [A]  time = 0.003, size = 9, normalized size = 0.8 \[ 3\,{\frac{x}{ \left ( bx \right ) ^{2/3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x)^(2/3),x)

[Out]

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

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Maxima [A]  time = 1.43494, size = 14, normalized size = 1.17 \[ \frac{3 \, \left (b x\right )^{\frac{1}{3}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.213626, size = 14, normalized size = 1.17 \[ \frac{3 \, \left (b x\right )^{\frac{1}{3}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.064299, size = 8, normalized size = 0.67 \[ \frac{3 \sqrt [3]{b x}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x)**(2/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.221352, size = 14, normalized size = 1.17 \[ \frac{3 \, \left (b x\right )^{\frac{1}{3}}}{b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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