\(\int -e^{-x} \, dx\) [6571]

Optimal result

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

[Out]

3/exp(ln(3)+x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.143, Rules used = {2225} \[ \int -e^{-x} \, dx=e^{-x} \]

[In]

Int[-E^(-x),x]

[Out]

E^(-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^{-x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00 \[ \int -e^{-x} \, dx=e^{-x} \]

[In]

Integrate[-E^(-x),x]

[Out]

E^(-x)

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 5, normalized size of antiderivative = 1.00

method	result	size
risch	\({\mathrm e}^{-x}\)	\(5\)
gosper	\({\mathrm e}^{-x}\)	\(10\)
derivativedivides	\({\mathrm e}^{-x}\)	\(10\)
default	\({\mathrm e}^{-x}\)	\(10\)
norman	\({\mathrm e}^{-x}\)	\(10\)
parallelrisch	\({\mathrm e}^{-x}\)	\(10\)

[In]

int(-3/exp(ln(3)+x),x,method=_RETURNVERBOSE)

[Out]

exp(-x)

Fricas [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 11, normalized size of antiderivative = 2.20 \[ \int -e^{-x} \, dx=3 \, e^{\left (-x - \log \left (3\right )\right )} \]

[In]

integrate(-3/exp(log(3)+x),x, algorithm="fricas")

[Out]

3*e^(-x - log(3))

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.60 \[ \int -e^{-x} \, dx=e^{- x} \]

[In]

integrate(-3/exp(ln(3)+x),x)

[Out]

exp(-x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int -e^{-x} \, dx=e^{\left (-x\right )} \]

[In]

integrate(-3/exp(log(3)+x),x, algorithm="maxima")

[Out]

e^(-x)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 11, normalized size of antiderivative = 2.20 \[ \int -e^{-x} \, dx=3 \, e^{\left (-x - \log \left (3\right )\right )} \]

[In]

integrate(-3/exp(log(3)+x),x, algorithm="giac")

[Out]

3*e^(-x - log(3))

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.80 \[ \int -e^{-x} \, dx={\mathrm {e}}^{-x} \]

[In]

int(-3*exp(- x - log(3)),x)

[Out]

exp(-x)