\(\int -\frac {2}{x^2} \, dx\) [8369]

Optimal result

Integrand size = 5, antiderivative size = 24 \[ \int -\frac {2}{x^2} \, dx=2 \left (1+\frac {2}{1+\frac {1}{12} \left (-\frac {17}{4}+e^4\right )}+\frac {1}{x}\right ) \]

[Out]

2+4/(31/48+1/12*exp(4))+2/x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

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

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

Integrate[-2/x^2,x]

[Out]

2/x

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.25

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

[In]

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

[Out]

2/x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

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

[Out]

2/x

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.08 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

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

[Out]

2/x

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

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

[Out]

2/x

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

integrate(-2/x^2,x, algorithm="giac")

[Out]

2/x

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.21 \[ \int -\frac {2}{x^2} \, dx=\frac {2}{x} \]

[In]

int(-2/x^2,x)

[Out]

2/x