3.50.82 \(\int -\frac {e^{2-x}}{81} \, dx\)

Optimal. Leaf size=15 \[ \frac {1}{81} \left (-\frac {10}{3}+e^{2-x}\right ) \]

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Rubi [A]  time = 0.00, antiderivative size = 11, normalized size of antiderivative = 0.73, number of steps used = 2, number of rules used = 2, integrand size = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.182, Rules used = {12, 2194} \begin {gather*} \frac {e^{2-x}}{81} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-1/81*E^(2 - x),x]

[Out]

E^(2 - x)/81

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 2194

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=-\left (\frac {1}{81} \int e^{2-x} \, dx\right )\\ &=\frac {e^{2-x}}{81}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 11, normalized size = 0.73 \begin {gather*} \frac {e^{2-x}}{81} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-1/81*E^(2 - x),x]

[Out]

E^(2 - x)/81

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fricas [A]  time = 0.61, size = 8, normalized size = 0.53 \begin {gather*} \frac {1}{81} \, e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/81*exp(2)/exp(x),x, algorithm="fricas")

[Out]

1/81*e^(-x + 2)

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giac [A]  time = 0.14, size = 8, normalized size = 0.53 \begin {gather*} \frac {1}{81} \, e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/81*exp(2)/exp(x),x, algorithm="giac")

[Out]

1/81*e^(-x + 2)

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maple [A]  time = 0.04, size = 9, normalized size = 0.60

method	result	size
gosper	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-x}}{81}\)	\(9\)
derivativedivides	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-x}}{81}\)	\(9\)
default	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-x}}{81}\)	\(9\)
norman	\(\frac {{\mathrm e}^{2} {\mathrm e}^{-x}}{81}\)	\(9\)
risch	\(\frac {{\mathrm e}^{2-x}}{81}\)	\(9\)
meijerg	\(-\frac {{\mathrm e}^{2} \left (1-{\mathrm e}^{-x}\right )}{81}\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-1/81*exp(2)/exp(x),x,method=_RETURNVERBOSE)

[Out]

1/81*exp(2)/exp(x)

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maxima [A]  time = 0.35, size = 8, normalized size = 0.53 \begin {gather*} \frac {1}{81} \, e^{\left (-x + 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/81*exp(2)/exp(x),x, algorithm="maxima")

[Out]

1/81*e^(-x + 2)

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mupad [B]  time = 0.02, size = 8, normalized size = 0.53 \begin {gather*} \frac {{\mathrm {e}}^{2-x}}{81} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-(exp(-x)*exp(2))/81,x)

[Out]

exp(2 - x)/81

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sympy [A]  time = 0.05, size = 7, normalized size = 0.47 \begin {gather*} \frac {e^{2} e^{- x}}{81} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-1/81*exp(2)/exp(x),x)

[Out]

exp(2)*exp(-x)/81

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