3.4.46 \(\int \frac {18 x}{e} \, dx\)

Optimal. Leaf size=8 \[ \frac {9 x^2}{e} \]

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 6, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.333, Rules used = {12, 30} \begin {gather*} \frac {9 x^2}{e} \end {gather*}

Antiderivative was successfully verified.

[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 {gather*} \begin {aligned} \text {integral} &=\frac {18 \int x \, dx}{e}\\ &=\frac {9 x^2}{e}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 8, normalized size = 1.00 \begin {gather*} \frac {9 x^2}{e} \end {gather*}

Antiderivative was successfully verified.

[In]

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

[Out]

(9*x^2)/E

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fricas [A]  time = 0.53, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.32, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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maple [A]  time = 0.02, size = 8, normalized size = 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	\(9 x^{2} {\mathrm e}^{-1}\)	\(10\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

9*x^2*exp(-1)

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maxima [A]  time = 0.49, size = 7, normalized size = 0.88 \begin {gather*} 9 \, x^{2} e^{\left (-1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 0.03, size = 7, normalized size = 0.88 \begin {gather*} 9\,x^2\,{\mathrm {e}}^{-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

9*x^2*exp(-1)

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sympy [A]  time = 0.02, size = 7, normalized size = 0.88 \begin {gather*} \frac {9 x^{2}}{e} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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