\(\int (-1-5 e^x) \, dx\) [4558]

Optimal result

Integrand size = 7, antiderivative size = 10 \[ \int \left (-1-5 e^x\right ) \, dx=4-5 e^x-x \]

[Out]

4-x-5*exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90, number of steps used = 2, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2225} \[ \int \left (-1-5 e^x\right ) \, dx=-x-5 e^x \]

[In]

Int[-1 - 5*E^x,x]

[Out]

-5*E^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-5 \int e^x \, dx \\ & = -5 e^x-x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int \left (-1-5 e^x\right ) \, dx=-5 e^x-x \]

[In]

Integrate[-1 - 5*E^x,x]

[Out]

-5*E^x - x

Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90

method	result	size
default	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
norman	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
risch	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
parallelrisch	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
parts	\(-x -5 \,{\mathrm e}^{x}\)	\(9\)
derivativedivides	\(-5 \,{\mathrm e}^{x}-\ln \left ({\mathrm e}^{x}\right )\)	\(11\)

[In]

int(-5*exp(x)-1,x,method=_RETURNVERBOSE)

[Out]

-x-5*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \left (-1-5 e^x\right ) \, dx=-x - 5 \, e^{x} \]

[In]

integrate(-5*exp(x)-1,x, algorithm="fricas")

[Out]

-x - 5*e^x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.70 \[ \int \left (-1-5 e^x\right ) \, dx=- x - 5 e^{x} \]

[In]

integrate(-5*exp(x)-1,x)

[Out]

-x - 5*exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \left (-1-5 e^x\right ) \, dx=-x - 5 \, e^{x} \]

[In]

integrate(-5*exp(x)-1,x, algorithm="maxima")

[Out]

-x - 5*e^x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \left (-1-5 e^x\right ) \, dx=-x - 5 \, e^{x} \]

[In]

integrate(-5*exp(x)-1,x, algorithm="giac")

[Out]

-x - 5*e^x

Mupad [B] (verification not implemented)

Time = 0.04 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int \left (-1-5 e^x\right ) \, dx=-x-5\,{\mathrm {e}}^x \]

[In]

int(- 5*exp(x) - 1,x)

[Out]

- x - 5*exp(x)