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

Optimal. Leaf size=14 \[ \frac{3 (b x)^{2/3}}{2 b} \]

[Out]

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

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Rubi [A]  time = 0.00616831, antiderivative size = 14, 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 \[ \frac{3 (b x)^{2/3}}{2 b} \]

Antiderivative was successfully verified.

[In]  Int[(b*x)^(-1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 1.31558, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{2}{3}}}{2 b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Mathematica [A]  time = 0.00249843, size = 12, normalized size = 0.86 \[ \frac{3 x}{2 \sqrt [3]{b x}} \]

Antiderivative was successfully verified.

[In]  Integrate[(b*x)^(-1/3),x]

[Out]

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

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Maple [A]  time = 0.003, size = 9, normalized size = 0.6 \[{\frac{3\,x}{2}{\frac{1}{\sqrt [3]{bx}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/(b*x)^(1/3),x)

[Out]

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

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Maxima [A]  time = 1.43621, size = 14, normalized size = 1. \[ \frac{3 \, \left (b x\right )^{\frac{2}{3}}}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Fricas [A]  time = 0.227519, size = 14, normalized size = 1. \[ \frac{3 \, \left (b x\right )^{\frac{2}{3}}}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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

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Sympy [A]  time = 0.063773, size = 10, normalized size = 0.71 \[ \frac{3 \left (b x\right )^{\frac{2}{3}}}{2 b} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/(b*x)**(1/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.22523, size = 14, normalized size = 1. \[ \frac{3 \, \left (b x\right )^{\frac{2}{3}}}{2 \, b} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

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