\(\int \frac {18 x}{e} \, dx\) [346]

Optimal result

Integrand size = 6, antiderivative size = 8 \[ \int \frac {18 x}{e} \, dx=\frac {9 x^2}{e} \]

[Out]

9*x^2/exp(1)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 30} \[ \int \frac {18 x}{e} \, dx=\frac {9 x^2}{e} \]

[In]

Int[(18*x)/E,x]

[Out]

(9*x^2)/E

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 {18 \int x \, dx}{e} \\ & = \frac {9 x^2}{e} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00 \[ \int \frac {18 x}{e} \, dx=\frac {9 x^2}{e} \]

[In]

Integrate[(18*x)/E,x]

[Out]

(9*x^2)/E

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 8, normalized size of antiderivative = 1.00

method	result	size
risch	\(9 x^{2} {\mathrm e}^{-1}\)	\(8\)
gosper	\(9 x^{2} {\mathrm e}^{-1}\)	\(10\)
default	\(9 x^{2} {\mathrm e}^{-1}\)	\(10\)
norman	\(9 x^{2} {\mathrm e}^{-1}\)	\(10\)
parallelrisch	\(9 x^{2} {\mathrm e}^{-1}\)	\(10\)

[In]

int(18*x/exp(1),x,method=_RETURNVERBOSE)

[Out]

9*x^2*exp(-1)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {18 x}{e} \, dx=9 \, x^{2} e^{\left (-1\right )} \]

[In]

integrate(18*x/exp(1),x, algorithm="fricas")

[Out]

9*x^2*e^(-1)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {18 x}{e} \, dx=\frac {9 x^{2}}{e} \]

[In]

integrate(18*x/exp(1),x)

[Out]

9*x**2*exp(-1)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {18 x}{e} \, dx=9 \, x^{2} e^{\left (-1\right )} \]

[In]

integrate(18*x/exp(1),x, algorithm="maxima")

[Out]

9*x^2*e^(-1)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {18 x}{e} \, dx=9 \, x^{2} e^{\left (-1\right )} \]

[In]

integrate(18*x/exp(1),x, algorithm="giac")

[Out]

9*x^2*e^(-1)

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.88 \[ \int \frac {18 x}{e} \, dx=9\,x^2\,{\mathrm {e}}^{-1} \]

[In]

int(18*x*exp(-1),x)

[Out]

9*x^2*exp(-1)