3.84.69 \(\int -\frac {2}{x^2} \, dx\)

Optimal. Leaf size=24 \[ 2 \left (1+\frac {2}{1+\frac {1}{12} \left (-\frac {17}{4}+e^4\right )}+\frac {1}{x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 5, normalized size of antiderivative = 0.21, number of steps used = 2, number of rules used = 2, integrand size = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \begin {gather*} \frac {2}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-2/x^2,x]

[Out]

2/x

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 30

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

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (2 \int \frac {1}{x^2} \, dx\right )\\ &=\frac {2}{x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 5, normalized size = 0.21 \begin {gather*} \frac {2}{x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-2/x^2,x]

[Out]

2/x

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fricas [A]  time = 0.79, size = 5, normalized size = 0.21 \begin {gather*} \frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/x

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giac [A]  time = 0.20, size = 5, normalized size = 0.21 \begin {gather*} \frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x^2,x, algorithm="giac")

[Out]

2/x

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maple [A]  time = 0.01, size = 6, normalized size = 0.25

method	result	size
gosper	\(\frac {2}{x}\)	\(6\)
default	\(\frac {2}{x}\)	\(6\)
norman	\(\frac {2}{x}\)	\(6\)
risch	\(\frac {2}{x}\)	\(6\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/x

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maxima [A]  time = 0.36, size = 5, normalized size = 0.21 \begin {gather*} \frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

2/x

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mupad [B]  time = 0.01, size = 5, normalized size = 0.21 \begin {gather*} \frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-2/x^2,x)

[Out]

2/x

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sympy [A]  time = 0.05, size = 2, normalized size = 0.08 \begin {gather*} \frac {2}{x} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-2/x**2,x)

[Out]

2/x

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