\(\int -e^x \, dx\) [7756]

Optimal result

Integrand size = 5, antiderivative size = 15 \[ \int -e^x \, dx=-e^x+\log ^2(2+e)+\log (\log (3)) \]

[Out]

ln(ln(3))+ln(exp(1)+2)^2-exp(x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, 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 = 0.33 \[ \int -e^x \, dx=-e^x \]

[In]

Integrate[-E^x,x]

[Out]

-E^x

Maple [A] (verified)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.33

method	result	size
gosper	\(-{\mathrm e}^{x}\)	\(5\)
lookup	\(-{\mathrm e}^{x}\)	\(5\)
derivativedivides	\(-{\mathrm e}^{x}\)	\(5\)
default	\(-{\mathrm e}^{x}\)	\(5\)
norman	\(-{\mathrm e}^{x}\)	\(5\)
risch	\(-{\mathrm e}^{x}\)	\(5\)
parallelrisch	\(-{\mathrm e}^{x}\)	\(5\)
parts	\(-{\mathrm e}^{x}\)	\(5\)
meijerg	\(1-{\mathrm e}^{x}\)	\(7\)

[In]

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

[Out]

-exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.40 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.27 \[ \int -e^x \, dx=-e^{x} \]

[In]

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

[Out]

-e^x

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 3, normalized size of antiderivative = 0.20 \[ \int -e^x \, dx=- e^{x} \]

[In]

integrate(-exp(x),x)

[Out]

-exp(x)

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.27 \[ \int -e^x \, dx=-e^{x} \]

[In]

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

[Out]

-e^x

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.27 \[ \int -e^x \, dx=-e^{x} \]

[In]

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

[Out]

-e^x

Mupad [B] (verification not implemented)

Time = 0.01 (sec) , antiderivative size = 4, normalized size of antiderivative = 0.27 \[ \int -e^x \, dx=-{\mathrm {e}}^x \]

[In]

int(-exp(x),x)

[Out]

-exp(x)