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

Optimal. Leaf size=7 \[ 3 \sqrt [3]{x} \]

[Out]

3*x^(1/3)

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Rubi [A]  time = 0.00287505, antiderivative size = 7, 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 \[ 3 \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]  Int[x^(-2/3),x]

[Out]

3*x^(1/3)

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Rubi in Sympy [A]  time = 0.918349, size = 5, normalized size = 0.71 \[ 3 \sqrt [3]{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(2/3),x)

[Out]

3*x**(1/3)

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Mathematica [A]  time = 0.000828756, size = 7, normalized size = 1. \[ 3 \sqrt [3]{x} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-2/3),x]

[Out]

3*x^(1/3)

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Maple [A]  time = 0.003, size = 6, normalized size = 0.9 \[ 3\,\sqrt [3]{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^(2/3),x)

[Out]

3*x^(1/3)

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Maxima [A]  time = 1.35407, size = 7, normalized size = 1. \[ 3 \, x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*x^(1/3)

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Fricas [A]  time = 0.193691, size = 7, normalized size = 1. \[ 3 \, x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*x^(1/3)

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Sympy [A]  time = 0.029213, size = 5, normalized size = 0.71 \[ 3 \sqrt [3]{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(2/3),x)

[Out]

3*x**(1/3)

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GIAC/XCAS [A]  time = 0.208479, size = 7, normalized size = 1. \[ 3 \, x^{\frac{1}{3}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

3*x^(1/3)