\(\int 10 e^{-2 x} \, dx\) [4023]

Optimal result

Integrand size = 7, antiderivative size = 13 \[ \int 10 e^{-2 x} \, dx=-4-5 e^{-2 x}-\log (3) \]

[Out]

-4-ln(3)-5/exp(x)^2

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.286, Rules used = {12, 2225} \[ \int 10 e^{-2 x} \, dx=-5 e^{-2 x} \]

[In]

Int[10/E^(2*x),x]

[Out]

-5/E^(2*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}& = 10 \int e^{-2 x} \, dx \\ & = -5 e^{-2 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54 \[ \int 10 e^{-2 x} \, dx=-5 e^{-2 x} \]

[In]

Integrate[10/E^(2*x),x]

[Out]

-5/E^(2*x)

Maple [A] (verified)

Time = 0.41 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54

method	result	size
gosper	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
derivativedivides	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
default	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
norman	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
risch	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
parallelrisch	\(-5 \,{\mathrm e}^{-2 x}\)	\(7\)
meijerg	\(5-5 \,{\mathrm e}^{-2 x}\)	\(9\)

[In]

int(10/exp(x)^2,x,method=_RETURNVERBOSE)

[Out]

-5/exp(x)^2

Fricas [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int 10 e^{-2 x} \, dx=-5 \, e^{\left (-2 \, x\right )} \]

[In]

integrate(10/exp(x)^2,x, algorithm="fricas")

[Out]

-5*e^(-2*x)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.54 \[ \int 10 e^{-2 x} \, dx=- 5 e^{- 2 x} \]

[In]

integrate(10/exp(x)**2,x)

[Out]

-5*exp(-2*x)

Maxima [A] (verification not implemented)

none

Time = 0.20 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int 10 e^{-2 x} \, dx=-5 \, e^{\left (-2 \, x\right )} \]

[In]

integrate(10/exp(x)^2,x, algorithm="maxima")

[Out]

-5*e^(-2*x)

Giac [A] (verification not implemented)

none

Time = 0.25 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int 10 e^{-2 x} \, dx=-5 \, e^{\left (-2 \, x\right )} \]

[In]

integrate(10/exp(x)^2,x, algorithm="giac")

[Out]

-5*e^(-2*x)

Mupad [B] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.46 \[ \int 10 e^{-2 x} \, dx=-5\,{\mathrm {e}}^{-2\,x} \]

[In]

int(10*exp(-2*x),x)

[Out]

-5*exp(-2*x)