3.16 \(\int \frac{1}{x^2} \, dx\)

Optimal. Leaf size=5 \[ -\frac{1}{x} \]

[Out]

-x^(-1)

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Rubi [A]  time = 0.00281809, antiderivative size = 5, 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 \[ -\frac{1}{x} \]

Antiderivative was successfully verified.

[In]  Int[x^(-2),x]

[Out]

-x^(-1)

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Rubi in Sympy [A]  time = 0.905092, size = 3, normalized size = 0.6 \[ - \frac{1}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate(1/x**2,x)

[Out]

-1/x

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Mathematica [A]  time = 0.000247027, size = 5, normalized size = 1. \[ -\frac{1}{x} \]

Antiderivative was successfully verified.

[In]  Integrate[x^(-2),x]

[Out]

-x^(-1)

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Maple [A]  time = 0., size = 6, normalized size = 1.2 \[ -{x}^{-1} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int(1/x^2,x)

[Out]

-1/x

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Maxima [A]  time = 1.33171, size = 7, normalized size = 1.4 \[ -\frac{1}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/x

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Fricas [A]  time = 0.201725, size = 7, normalized size = 1.4 \[ -\frac{1}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/x

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Sympy [A]  time = 0.030136, size = 3, normalized size = 0.6 \[ - \frac{1}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(1/x**2,x)

[Out]

-1/x

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GIAC/XCAS [A]  time = 0.211797, size = 7, normalized size = 1.4 \[ -\frac{1}{x} \]

Verification of antiderivative is not currently implemented for this CAS.

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

[Out]

-1/x