\(\int -8 e^{4-8 x} \, dx\) [2616]

Optimal result

Integrand size = 9, antiderivative size = 14 \[ \int -8 e^{4-8 x} \, dx=e^{\frac {4 \left (x-2 x^2\right )}{x}} \]

[Out]

exp(4*(-2*x^2+x)/x)

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2225} \[ \int -8 e^{4-8 x} \, dx=e^{4-8 x} \]

[In]

Int[-8*E^(4 - 8*x),x]

[Out]

E^(4 - 8*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 (8 \int e^{4-8 x} \, dx\right ) \\ & = e^{4-8 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -8 e^{4-8 x} \, dx=e^{4-8 x} \]

[In]

Integrate[-8*E^(4 - 8*x),x]

[Out]

E^(4 - 8*x)

Maple [A] (verified)

Time = 0.07 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50

method	result	size
gosper	\({\mathrm e}^{-8 x +4}\)	\(7\)
derivativedivides	\({\mathrm e}^{-8 x +4}\)	\(7\)
default	\({\mathrm e}^{-8 x +4}\)	\(7\)
norman	\({\mathrm e}^{-8 x +4}\)	\(7\)
risch	\({\mathrm e}^{-8 x +4}\)	\(7\)
parallelrisch	\({\mathrm e}^{-8 x +4}\)	\(7\)
parts	\({\mathrm e}^{-8 x +4}\)	\(7\)
meijerg	\(-{\mathrm e}^{4} \left (1-{\mathrm e}^{-8 x}\right )\)	\(13\)

[In]

int(-8*exp(-8*x+4),x,method=_RETURNVERBOSE)

[Out]

exp(-8*x+4)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.43 \[ \int -8 e^{4-8 x} \, dx=e^{\left (-8 \, x + 4\right )} \]

[In]

integrate(-8*exp(-8*x+4),x, algorithm="fricas")

[Out]

e^(-8*x + 4)

Sympy [A] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.36 \[ \int -8 e^{4-8 x} \, dx=e^{4 - 8 x} \]

[In]

integrate(-8*exp(-8*x+4),x)

[Out]

exp(4 - 8*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.43 \[ \int -8 e^{4-8 x} \, dx=e^{\left (-8 \, x + 4\right )} \]

[In]

integrate(-8*exp(-8*x+4),x, algorithm="maxima")

[Out]

e^(-8*x + 4)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 6, normalized size of antiderivative = 0.43 \[ \int -8 e^{4-8 x} \, dx=e^{\left (-8 \, x + 4\right )} \]

[In]

integrate(-8*exp(-8*x+4),x, algorithm="giac")

[Out]

e^(-8*x + 4)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 7, normalized size of antiderivative = 0.50 \[ \int -8 e^{4-8 x} \, dx={\mathrm {e}}^{-8\,x}\,{\mathrm {e}}^4 \]

[In]

int(-8*exp(4 - 8*x),x)

[Out]

exp(-8*x)*exp(4)