3.32 \(\int \frac{1}{x^{4/3}} \, dx\)

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

[Out]

-3/x^(1/3)

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Rubi [A]  time = 0.00310671, 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 \[ -\frac{3}{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Int[x^(-4/3),x]

[Out]

-3/x^(1/3)

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Rubi in Sympy [A]  time = 0.916291, size = 7, normalized size = 1. \[ - \frac{3}{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(4/3),x)

[Out]

-3/x**(1/3)

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Mathematica [A]  time = 0.00093371, size = 7, normalized size = 1. \[ -\frac{3}{\sqrt [3]{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-4/3),x]

[Out]

-3/x^(1/3)

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Maple [A]  time = 0.003, size = 6, normalized size = 0.9 \[ -3\,{\frac{1}{\sqrt [3]{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^(4/3),x)

[Out]

-3/x^(1/3)

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Maxima [A]  time = 1.33923, size = 7, normalized size = 1. \[ -\frac{3}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-4/3),x, algorithm="maxima")

[Out]

-3/x^(1/3)

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Fricas [A]  time = 0.193912, size = 7, normalized size = 1. \[ -\frac{3}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-4/3),x, algorithm="fricas")

[Out]

-3/x^(1/3)

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Sympy [A]  time = 0.030737, size = 7, normalized size = 1. \[ - \frac{3}{\sqrt [3]{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(4/3),x)

[Out]

-3/x**(1/3)

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GIAC/XCAS [A]  time = 0.209722, size = 7, normalized size = 1. \[ -\frac{3}{x^{\frac{1}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-4/3),x, algorithm="giac")

[Out]

-3/x^(1/3)