3.33 \(\int \frac{1}{x^{5/3}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00276209, 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 \[ -\frac{3}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]  Int[x^(-5/3),x]

[Out]

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

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Rubi in Sympy [A]  time = 0.924891, size = 8, normalized size = 0.89 \[ - \frac{3}{2 x^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(5/3),x)

[Out]

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

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Mathematica [A]  time = 0.000896592, size = 9, normalized size = 1. \[ -\frac{3}{2 x^{2/3}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-5/3),x]

[Out]

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

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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^(5/3),x)

[Out]

-3/2/x^(2/3)

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Maxima [A]  time = 1.32929, 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^(-5/3),x, algorithm="maxima")

[Out]

-3/2/x^(2/3)

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Fricas [A]  time = 0.196997, 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^(-5/3),x, algorithm="fricas")

[Out]

-3/2/x^(2/3)

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Sympy [A]  time = 0.031208, size = 8, normalized size = 0.89 \[ - \frac{3}{2 x^{\frac{2}{3}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(5/3),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.208849, 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^(-5/3),x, algorithm="giac")

[Out]

-3/2/x^(2/3)