\(\int \frac {x}{2} \, dx\) [8706]

Optimal result

Integrand size = 5, antiderivative size = 16 \[ \int \frac {x}{2} \, dx=1-e^4+\frac {1}{4} \left (4+x^2\right ) \]

[Out]

2-exp(4)+1/4*x^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.400, Rules used = {12, 30} \[ \int \frac {x}{2} \, dx=\frac {x^2}{4} \]

[In]

Int[x/2,x]

[Out]

x^2/4

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}& = \frac {\int x \, dx}{2} \\ & = \frac {x^2}{4} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.44 \[ \int \frac {x}{2} \, dx=\frac {x^2}{4} \]

[In]

Integrate[x/2,x]

[Out]

x^2/4

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.38

method	result	size
gosper	\(\frac {x^{2}}{4}\)	\(6\)
default	\(\frac {x^{2}}{4}\)	\(6\)
norman	\(\frac {x^{2}}{4}\)	\(6\)
risch	\(\frac {x^{2}}{4}\)	\(6\)
parallelrisch	\(\frac {x^{2}}{4}\)	\(6\)

[In]

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

[Out]

1/4*x^2

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int \frac {x}{2} \, dx=\frac {1}{4} \, x^{2} \]

[In]

integrate(1/2*x,x, algorithm="fricas")

[Out]

1/4*x^2

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.19 \[ \int \frac {x}{2} \, dx=\frac {x^{2}}{4} \]

[In]

integrate(1/2*x,x)

[Out]

x**2/4

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int \frac {x}{2} \, dx=\frac {1}{4} \, x^{2} \]

[In]

integrate(1/2*x,x, algorithm="maxima")

[Out]

1/4*x^2

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int \frac {x}{2} \, dx=\frac {1}{4} \, x^{2} \]

[In]

integrate(1/2*x,x, algorithm="giac")

[Out]

1/4*x^2

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.31 \[ \int \frac {x}{2} \, dx=\frac {x^2}{4} \]

[In]

int(x/2,x)

[Out]

x^2/4