3.17 \(\int \frac{1}{x^3} \, dx\)

Optimal. Leaf size=7 \[ -\frac{1}{2 x^2} \]

[Out]

-1/(2*x^2)

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Rubi [A]  time = 0.00254099, antiderivative size = 7, normalized size of antiderivative = 1., number of steps used = 1, number of rules used = 1, integrand size = 3, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.333 \[ -\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Int[x^(-3),x]

[Out]

-1/(2*x^2)

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Rubi in Sympy [A]  time = 0.920635, size = 7, normalized size = 1. \[ - \frac{1}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**3,x)

[Out]

-1/(2*x**2)

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Mathematica [A]  time = 0.000229748, size = 7, normalized size = 1. \[ -\frac{1}{2 x^2} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-3),x]

[Out]

-1/(2*x^2)

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Maple [A]  time = 0.001, size = 6, normalized size = 0.9 \[ -{\frac{1}{2\,{x}^{2}}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^3,x)

[Out]

-1/2/x^2

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Maxima [A]  time = 1.3335, size = 7, normalized size = 1. \[ -\frac{1}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/x^2

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Fricas [A]  time = 0.188038, size = 7, normalized size = 1. \[ -\frac{1}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/x^2

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Sympy [A]  time = 0.029585, size = 7, normalized size = 1. \[ - \frac{1}{2 x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**3,x)

[Out]

-1/(2*x**2)

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GIAC/XCAS [A]  time = 0.207198, size = 7, normalized size = 1. \[ -\frac{1}{2 \, x^{2}} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/2/x^2