3.1.78 \(\int e^{-1-x} \, dx\) [78]

Optimal. Leaf size=9 \[ -e^{-1-x} \]

[Out]

-exp(-1-x)

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Rubi [A]
time = 0.00, antiderivative size = 9, 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 = {2225} \begin {gather*} -e^{-x-1} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[E^(-1 - x),x]

[Out]

-E^(-1 - x)

Rule 2225

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 {align*} \int e^{-1-x} \, dx &=-e^{-1-x}\\ \end {align*}

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Mathematica [A]
time = 0.01, size = 9, normalized size = 1.00 \begin {gather*} -e^{-1-x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[E^(-1 - x),x]

[Out]

-E^(-1 - x)

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Maple [A]
time = 0.01, size = 9, normalized size = 1.00

method	result	size
gosper	\(-{\mathrm e}^{-1-x}\)	\(9\)
derivativedivides	\(-{\mathrm e}^{-1-x}\)	\(9\)
default	\(-{\mathrm e}^{-1-x}\)	\(9\)
norman	\(-{\mathrm e}^{-1-x}\)	\(9\)
risch	\(-{\mathrm e}^{-1-x}\)	\(9\)
meijerg	\({\mathrm e}^{-1} \left (1-{\mathrm e}^{-x}\right )\)	\(12\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(-1-x),x,method=_RETURNVERBOSE)

[Out]

-exp(-1-x)

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Maxima [A]
time = 1.48, size = 8, normalized size = 0.89 \begin {gather*} -e^{\left (-x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-1-x),x, algorithm="maxima")

[Out]

-e^(-x - 1)

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Fricas [A]
time = 0.54, size = 8, normalized size = 0.89 \begin {gather*} -e^{\left (-x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-1-x),x, algorithm="fricas")

[Out]

-e^(-x - 1)

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Sympy [A]
time = 0.02, size = 7, normalized size = 0.78 \begin {gather*} - e^{- x - 1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-1-x),x)

[Out]

-exp(-x - 1)

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Giac [A]
time = 0.43, size = 8, normalized size = 0.89 \begin {gather*} -e^{\left (-x - 1\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(exp(-1-x),x, algorithm="giac")

[Out]

-e^(-x - 1)

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Mupad [B]
time = 0.03, size = 8, normalized size = 0.89 \begin {gather*} -{\mathrm {e}}^{-x-1} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(exp(- x - 1),x)

[Out]

-exp(- x - 1)

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