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} $$\begin{array}{c}{e}^{-x-2}\end{array}$$

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

$$\begin{array}{c}\begin{array}{rl}\text{integral}& =e^{-2-x}\end{array}\end{array}$$

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

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 $$\begin{array}{c}{e}^{(-x-2)}\end{array}$$

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 $$\begin{array}{c}{e}^{(-x-2)}\end{array}$$

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	$-{\mathrm{e}}^{-2}(1-{\mathrm{e}}^{-x})$	$13$

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 $$\begin{array}{c}{e}^{(-x-2)}\end{array}$$

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 $$\begin{array}{c}{\mathrm{e}}^{-x-2}\end{array}$$

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 $$\begin{array}{c}{e}^{-x-2}\end{array}$$

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

exp(-x - 2)

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