3.78 \(\int e^{-1-x} \, dx\)

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

[Out]

-E^(-1 - x)

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Rubi [A]  time = 0.003023, antiderivative size = 9, normalized size of antiderivative = 1., 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 = {2194} \[ -e^{-x-1} \]

Antiderivative was successfully verified.

[In]

Int[E^(-1 - x),x]

[Out]

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

Mathematica [A]  time = 0.0025931, size = 9, normalized size = 1. \[ -e^{-x-1} \]

Antiderivative was successfully verified.

[In]

Integrate[E^(-1 - x),x]

[Out]

-E^(-1 - x)

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Maple [A]  time = 0., size = 9, normalized size = 1. \begin{align*} -{{\rm e}^{-1-x}} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-exp(-1-x)

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Maxima [A]  time = 0.935708, size = 11, normalized size = 1.22 \begin{align*} -e^{\left (-x - 1\right )} \end{align*}

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 = 2.0505, size = 18, normalized size = 2. \begin{align*} -e^{\left (-x - 1\right )} \end{align*}

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 = 0.067781, size = 7, normalized size = 0.78 \begin{align*} - e^{- x - 1} \end{align*}

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 = 1.06434, size = 11, normalized size = 1.22 \begin{align*} -e^{\left (-x - 1\right )} \end{align*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

-e^(-x - 1)