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 = 0.0005682, 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, Rules used = {30} \[ -\frac{1}{x} \]

Antiderivative was successfully verified.

[In]

Int[x^(-2),x]

[Out]

-x^(-1)

Rule 30

Int[(x_)^(m_.), x_Symbol] :> Simp[x^(m + 1)/(m + 1), x] /; FreeQ[m, x] && NeQ[m, -1]

Rubi steps

\begin{align*} \int \frac{1}{x^2} \, dx &=-\frac{1}{x}\\ \end{align*}

Mathematica [A]  time = 0.0004322, 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 = 0.001, size = 6, normalized size = 1.2 \begin{align*} -{x}^{-1} \end{align*}

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 = 0.970355, size = 7, normalized size = 1.4 \begin{align*} -\frac{1}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2,x, algorithm="maxima")

[Out]

-1/x

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Fricas [A]  time = 1.45116, size = 8, normalized size = 1.6 \begin{align*} -\frac{1}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2,x, algorithm="fricas")

[Out]

-1/x

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Sympy [A]  time = 0.051356, size = 3, normalized size = 0.6 \begin{align*} - \frac{1}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x**2,x)

[Out]

-1/x

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Giac [A]  time = 1.1073, size = 7, normalized size = 1.4 \begin{align*} -\frac{1}{x} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2,x, algorithm="giac")

[Out]

-1/x