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

Optimal. Leaf size=7 \[ -\frac{2}{\sqrt{x}} \]

[Out]

-2/Sqrt[x]

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Rubi [A]  time = 0.00276689, 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 \[ -\frac{2}{\sqrt{x}} \]

Antiderivative was successfully verified.

[In]  Int[x^(-3/2),x]

[Out]

-2/Sqrt[x]

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Rubi in Sympy [A]  time = 0.908897, size = 7, normalized size = 1. \[ - \frac{2}{\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**(3/2),x)

[Out]

-2/sqrt(x)

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Mathematica [A]  time = 0.000832276, size = 7, normalized size = 1. \[ -\frac{2}{\sqrt{x}} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-3/2),x]

[Out]

-2/Sqrt[x]

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Maple [A]  time = 0.003, size = 6, normalized size = 0.9 \[ -2\,{\frac{1}{\sqrt{x}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^(3/2),x)

[Out]

-2/x^(1/2)

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Maxima [A]  time = 1.34356, size = 7, normalized size = 1. \[ -\frac{2}{\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/sqrt(x)

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Fricas [A]  time = 0.19755, size = 7, normalized size = 1. \[ -\frac{2}{\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/sqrt(x)

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Sympy [A]  time = 0.038551, size = 7, normalized size = 1. \[ - \frac{2}{\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**(3/2),x)

[Out]

-2/sqrt(x)

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GIAC/XCAS [A]  time = 0.207319, size = 7, normalized size = 1. \[ -\frac{2}{\sqrt{x}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-2/sqrt(x)