3.5.18 \(\int -e^{-2-x} \, dx\)

Optimal. Leaf size=7 \[ e^{-2-x} \]

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Rubi [A]  time = 0.00, antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2194} \begin {gather*} e^{-x-2} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[-E^(-2 - x),x]

[Out]

E^(-2 - 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} &=e^{-2-x}\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.00, size = 7, normalized size = 1.00 \begin {gather*} e^{-2-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[-E^(-2 - x),x]

[Out]

E^(-2 - x)

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fricas [A]  time = 1.11, size = 6, normalized size = 0.86 \begin {gather*} e^{\left (-x - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(-x-2),x, algorithm="fricas")

[Out]

e^(-x - 2)

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giac [A]  time = 0.31, size = 6, normalized size = 0.86 \begin {gather*} e^{\left (-x - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(-x-2),x, algorithm="giac")

[Out]

e^(-x - 2)

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maple [A]  time = 0.02, size = 7, normalized size = 1.00

method	result	size
gosper	\({\mathrm e}^{-x -2}\)	\(7\)
derivativedivides	\({\mathrm e}^{-x -2}\)	\(7\)
default	\({\mathrm e}^{-x -2}\)	\(7\)
norman	\({\mathrm e}^{-x -2}\)	\(7\)
risch	\({\mathrm e}^{-x -2}\)	\(7\)
meijerg	\(-{\mathrm e}^{-2} \left (1-{\mathrm e}^{-x}\right )\)	\(13\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(-x-2),x,method=_RETURNVERBOSE)

[Out]

exp(-x-2)

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maxima [A]  time = 0.36, size = 6, normalized size = 0.86 \begin {gather*} e^{\left (-x - 2\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(-x-2),x, algorithm="maxima")

[Out]

e^(-x - 2)

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mupad [B]  time = 0.03, size = 6, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{-x-2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(-exp(- x - 2),x)

[Out]

exp(- x - 2)

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sympy [A]  time = 0.07, size = 5, normalized size = 0.71 \begin {gather*} e^{- x - 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(-exp(-x-2),x)

[Out]

exp(-x - 2)

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