3.1.16 \(\int \frac {1}{x^2} \, dx\) [16]

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

[Out]

-1/x

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Rubi [A]
time = 0.00, antiderivative size = 5, normalized size of antiderivative = 1.00, 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} \begin {gather*} -\frac {1}{x} \end {gather*}

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*}

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Mathematica [A]
time = 0.00, size = 5, normalized size = 1.00 \begin {gather*} -\frac {1}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[x^(-2),x]

[Out]

-x^(-1)

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Maple [A]
time = 0.01, size = 6, normalized size = 1.20

method	result	size
gosper	\(-\frac {1}{x}\)	\(6\)
default	\(-\frac {1}{x}\)	\(6\)
norman	\(-\frac {1}{x}\)	\(6\)
risch	\(-\frac {1}{x}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2,x,method=_RETURNVERBOSE)

[Out]

-1/x

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Maxima [A]
time = 0.30, size = 5, normalized size = 1.00 \begin {gather*} -\frac {1}{x} \end {gather*}

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 = 1.00, size = 5, normalized size = 1.00 \begin {gather*} -\frac {1}{x} \end {gather*}

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 = 0.02, size = 3, normalized size = 0.60 \begin {gather*} - \frac {1}{x} \end {gather*}

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 = 1.78, size = 5, normalized size = 1.00 \begin {gather*} -\frac {1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/x^2,x, algorithm="giac")

[Out]

-1/x

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Mupad [B]
time = 0.03, size = 5, normalized size = 1.00 \begin {gather*} -\frac {1}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/x^2,x)

[Out]

-1/x

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