\(\int (-1-e^{2-x}) \, dx\) [8115]

Optimal result

Integrand size = 11, antiderivative size = 12 \[ \int \left (-1-e^{2-x}\right ) \, dx=-1+e^{2-x}-x \]

[Out]

-1+exp(2-x)-x

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2225} \[ \int \left (-1-e^{2-x}\right ) \, dx=e^{2-x}-x \]

[In]

Int[-1 - E^(2 - x),x]

[Out]

E^(2 - x) - 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}& = -x-\int e^{2-x} \, dx \\ & = e^{2-x}-x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92 \[ \int \left (-1-e^{2-x}\right ) \, dx=e^{2-x}-x \]

[In]

Integrate[-1 - E^(2 - x),x]

[Out]

E^(2 - x) - x

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.92

method	result	size
default	\({\mathrm e}^{2-x}-x\)	\(11\)
norman	\({\mathrm e}^{2-x}-x\)	\(11\)
risch	\({\mathrm e}^{2-x}-x\)	\(11\)
parallelrisch	\({\mathrm e}^{2-x}-x\)	\(11\)
parts	\({\mathrm e}^{2-x}-x\)	\(11\)
derivativedivides	\({\mathrm e}^{2-x}+\ln \left ({\mathrm e}^{2-x}\right )\)	\(15\)

[In]

int(-exp(2-x)-1,x,method=_RETURNVERBOSE)

[Out]

exp(2-x)-x

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-1-e^{2-x}\right ) \, dx=-x + e^{\left (-x + 2\right )} \]

[In]

integrate(-exp(2-x)-1,x, algorithm="fricas")

[Out]

-x + e^(-x + 2)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.42 \[ \int \left (-1-e^{2-x}\right ) \, dx=- x + e^{2 - x} \]

[In]

integrate(-exp(2-x)-1,x)

[Out]

-x + exp(2 - x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-1-e^{2-x}\right ) \, dx=-x + e^{\left (-x + 2\right )} \]

[In]

integrate(-exp(2-x)-1,x, algorithm="maxima")

[Out]

-x + e^(-x + 2)

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-1-e^{2-x}\right ) \, dx=-x + e^{\left (-x + 2\right )} \]

[In]

integrate(-exp(2-x)-1,x, algorithm="giac")

[Out]

-x + e^(-x + 2)

Mupad [B] (verification not implemented)

Time = 0.08 (sec) , antiderivative size = 10, normalized size of antiderivative = 0.83 \[ \int \left (-1-e^{2-x}\right ) \, dx={\mathrm {e}}^{2-x}-x \]

[In]

int(- exp(2 - x) - 1,x)

[Out]

exp(2 - x) - x