3.25 \(\int \frac{1}{x^{5/2}} \, dx\)

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

[Out]

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

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Rubi [A]  time = 0.00282961, 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 \[ -\frac{2}{3 x^{3/2}} \]

Antiderivative was successfully verified.

[In]  Int[x^(-5/2),x]

[Out]

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

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Rubi in Sympy [A]  time = 0.902821, size = 8, normalized size = 0.89 \[ - \frac{2}{3 x^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(5/2),x)

[Out]

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

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Mathematica [A]  time = 0.000862354, size = 9, normalized size = 1. \[ -\frac{2}{3 x^{3/2}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-5/2),x]

[Out]

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

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

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^(5/2),x)

[Out]

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

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Maxima [A]  time = 1.3336, size = 7, normalized size = 0.78 \[ -\frac{2}{3 \, x^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-5/2),x, algorithm="maxima")

[Out]

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

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Fricas [A]  time = 0.200862, size = 7, normalized size = 0.78 \[ -\frac{2}{3 \, x^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-5/2),x, algorithm="fricas")

[Out]

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

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Sympy [A]  time = 0.030832, size = 8, normalized size = 0.89 \[ - \frac{2}{3 x^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(5/2),x)

[Out]

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

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GIAC/XCAS [A]  time = 0.20353, size = 7, normalized size = 0.78 \[ -\frac{2}{3 \, x^{\frac{3}{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(x^(-5/2),x, algorithm="giac")

[Out]

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