3.101.100 \(\int \frac {1}{2 e^2} \, dx\)

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

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Rubi [A]  time = 0.00, antiderivative size = 8, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 7, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {8} \begin {gather*} \frac {x}{2 e^2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[1/(2*E^2),x]

[Out]

x/(2*E^2)

Rule 8

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\frac {x}{2 e^2}\\ \end {aligned} \end {gather*}

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

Antiderivative was successfully verified.

[In]

Integrate[1/(2*E^2),x]

[Out]

x/(2*E^2)

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fricas [A]  time = 0.67, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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giac [A]  time = 0.18, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2/exp(1)^2,x, algorithm="giac")

[Out]

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

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maple [A]  time = 0.01, size = 6, normalized size = 0.75

method	result	size
risch	\(\frac {x \,{\mathrm e}^{-2}}{2}\)	\(6\)
default	\(\frac {x \,{\mathrm e}^{-2}}{2}\)	\(8\)
norman	\(\frac {x \,{\mathrm e}^{-2}}{2}\)	\(8\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(1/2/exp(1)^2,x,method=_RETURNVERBOSE)

[Out]

1/2*x*exp(-2)

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maxima [A]  time = 0.34, size = 5, normalized size = 0.62 \begin {gather*} \frac {1}{2} \, x e^{\left (-2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

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mupad [B]  time = 0.00, size = 5, normalized size = 0.62 \begin {gather*} \frac {x\,{\mathrm {e}}^{-2}}{2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-2)/2,x)

[Out]

(x*exp(-2))/2

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sympy [A]  time = 0.01, size = 5, normalized size = 0.62 \begin {gather*} \frac {x}{2 e^{2}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(1/2/exp(1)**2,x)

[Out]

x*exp(-2)/2

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