\(\int -e^{-2-x} \, dx\) [418]

Optimal result

Integrand size = 9, antiderivative size = 7 \[ \int -e^{-2-x} \, dx=e^{-2-x} \]

[Out]

exp(-2-x)

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.111, Rules used = {2225} \[ \int -e^{-2-x} \, dx=e^{-x-2} \]

[In]

Int[-E^(-2 - x),x]

[Out]

E^(-2 - 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*} \text {integral}& = e^{-2-x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00 \[ \int -e^{-2-x} \, dx=e^{-2-x} \]

[In]

Integrate[-E^(-2 - x),x]

[Out]

E^(-2 - x)

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 1.00

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

[In]

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

[Out]

exp(-2-x)

Fricas [A] (verification not implemented)

none

Time = 0.22 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]

[In]

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

[Out]

e^(-x - 2)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.71 \[ \int -e^{-2-x} \, dx=e^{- x - 2} \]

[In]

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

[Out]

exp(-x - 2)

Maxima [A] (verification not implemented)

none

Time = 0.17 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]

[In]

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

[Out]

e^(-x - 2)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx=e^{\left (-x - 2\right )} \]

[In]

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

[Out]

e^(-x - 2)

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.86 \[ \int -e^{-2-x} \, dx={\mathrm {e}}^{-x-2} \]

[In]

int(-exp(- x - 2),x)

[Out]

exp(- x - 2)