\(\int -2 x \, dx\) [6655]

Optimal result

Integrand size = 3, antiderivative size = 16 \[ \int -2 x \, dx=2-\frac {1}{e^4}+(-2-x) (-2+x) \]

[Out]

2-exp(-2)^2+(-2-x)*(-2+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.667, Rules used = {12, 30} \[ \int -2 x \, dx=-x^2 \]

[In]

Int[-2*x,x]

[Out]

-x^2

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}& = -(2 \int x \, dx) \\ & = -x^2 \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^2 \]

[In]

Integrate[-2*x,x]

[Out]

-x^2

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.38

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

[In]

int(-2*x,x,method=_RETURNVERBOSE)

[Out]

-x^2

Fricas [A] (verification not implemented)

none

Time = 0.66 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]

[In]

integrate(-2*x,x, algorithm="fricas")

[Out]

-x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.19 \[ \int -2 x \, dx=- x^{2} \]

[In]

integrate(-2*x,x)

[Out]

-x**2

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]

[In]

integrate(-2*x,x, algorithm="maxima")

[Out]

-x^2

Giac [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^{2} \]

[In]

integrate(-2*x,x, algorithm="giac")

[Out]

-x^2

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int -2 x \, dx=-x^2 \]

[In]

int(-2*x,x)

[Out]

-x^2