\(\int 2 x \, dx\) [4818]

Optimal result

Integrand size = 3, antiderivative size = 15 \[ \int 2 x \, dx=\frac {8}{5}-\sqrt [5]{5}+e+x^2 \]

[Out]

8/5+x^2+exp(1)-5^(1/5)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20, 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 = 3, normalized size of antiderivative = 0.20 \[ \int 2 x \, dx=x^2 \]

[In]

Integrate[2*x,x]

[Out]

x^2

Maple [A] (verified)

Time = 0.00 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.27

method	result	size
gosper	\(x^{2}\)	\(4\)
default	\(x^{2}\)	\(4\)
norman	\(x^{2}\)	\(4\)
risch	\(x^{2}\)	\(4\)
parallelrisch	\(x^{2}\)	\(4\)

[In]

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

[Out]

x^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20 \[ \int 2 x \, dx=x^{2} \]

[In]

integrate(2*x,x, algorithm="fricas")

[Out]

x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 2, normalized size of antiderivative = 0.13 \[ \int 2 x \, dx=x^{2} \]

[In]

integrate(2*x,x)

[Out]

x**2

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20 \[ \int 2 x \, dx=x^{2} \]

[In]

integrate(2*x,x, algorithm="maxima")

[Out]

x^2

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20 \[ \int 2 x \, dx=x^{2} \]

[In]

integrate(2*x,x, algorithm="giac")

[Out]

x^2

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20 \[ \int 2 x \, dx=x^2 \]

[In]

int(2*x,x)

[Out]

x^2