\(\int -5 e^{-x} \, dx\) [1349]

Optimal result

Integrand size = 7, antiderivative size = 9 \[ \int -5 e^{-x} \, dx=-4+5 e^{-x} \]

[Out]

-4+5/exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225} \[ \int -5 e^{-x} \, dx=5 e^{-x} \]

[In]

Int[-5/E^x,x]

[Out]

5/E^x

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, 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}& = -\left (5 \int e^{-x} \, dx\right ) \\ & = 5 e^{-x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78 \[ \int -5 e^{-x} \, dx=5 e^{-x} \]

[In]

Integrate[-5/E^x,x]

[Out]

5/E^x

Maple [A] (verified)

Time = 0.04 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.78

method	result	size
gosper	\(5 \,{\mathrm e}^{-x}\)	\(7\)
derivativedivides	\(5 \,{\mathrm e}^{-x}\)	\(7\)
default	\(5 \,{\mathrm e}^{-x}\)	\(7\)
norman	\(5 \,{\mathrm e}^{-x}\)	\(7\)
risch	\(5 \,{\mathrm e}^{-x}\)	\(7\)
parallelrisch	\(5 \,{\mathrm e}^{-x}\)	\(7\)
meijerg	\(-5+5 \,{\mathrm e}^{-x}\)	\(9\)

[In]

int(-5/exp(x),x,method=_RETURNVERBOSE)

[Out]

5/exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]

[In]

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

[Out]

5*e^(-x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.33 \[ \int -5 e^{-x} \, dx=5 e^{- x} \]

[In]

integrate(-5/exp(x),x)

[Out]

5*exp(-x)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]

[In]

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

[Out]

5*e^(-x)

Giac [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5 \, e^{\left (-x\right )} \]

[In]

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

[Out]

5*e^(-x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.67 \[ \int -5 e^{-x} \, dx=5\,{\mathrm {e}}^{-x} \]

[In]

int(-5*exp(-x),x)

[Out]

5*exp(-x)