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

Optimal. Leaf size=9 \[ \frac{3 x^{2/3}}{2} \]

[Out]

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

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Rubi [A]  time = 0.00312815, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 5, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.2 \[ \frac{3 x^{2/3}}{2} \]

Antiderivative was successfully verified.

[In]  Int[x^(-1/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 0.900272, size = 7, normalized size = 0.78 \[ \frac{3 x^{\frac{2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(1/3),x)

[Out]

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

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Mathematica [A]  time = 0.000877713, size = 9, normalized size = 1. \[ \frac{3 x^{2/3}}{2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-1/3),x]

[Out]

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

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Maple [A]  time = 0.002, size = 6, normalized size = 0.7 \[{\frac{3}{2}{x}^{{\frac{2}{3}}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^(1/3),x)

[Out]

3/2*x^(2/3)

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Maxima [A]  time = 1.33034, size = 7, normalized size = 0.78 \[ \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/2*x^(2/3)

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Fricas [A]  time = 0.194364, size = 7, normalized size = 0.78 \[ \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/2*x^(2/3)

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Sympy [A]  time = 0.029769, size = 7, normalized size = 0.78 \[ \frac{3 x^{\frac{2}{3}}}{2} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(1/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.211061, size = 7, normalized size = 0.78 \[ \frac{3}{2} \, x^{\frac{2}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3/2*x^(2/3)