\(\int 1024 e^{-4+4 x} \, dx\) [8962]

Optimal result

Integrand size = 9, antiderivative size = 9 \[ \int 1024 e^{-4+4 x} \, dx=256 e^{-4+4 x} \]

[Out]

256*exp(x)^4/exp(1)^4

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2225} \[ \int 1024 e^{-4+4 x} \, dx=256 e^{4 x-4} \]

[In]

Int[1024*E^(-4 + 4*x),x]

[Out]

256*E^(-4 + 4*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}& = 1024 \int e^{-4+4 x} \, dx \\ & = 256 e^{-4+4 x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.02 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00 \[ \int 1024 e^{-4+4 x} \, dx=256 e^{-4+4 x} \]

[In]

Integrate[1024*E^(-4 + 4*x),x]

[Out]

256*E^(-4 + 4*x)

Maple [A] (verified)

Time = 0.23 (sec) , antiderivative size = 9, normalized size of antiderivative = 1.00

method	result	size
risch	\(256 \,{\mathrm e}^{-4+4 x}\)	\(9\)
gosper	\(256 \,{\mathrm e}^{4 x} {\mathrm e}^{-4}\)	\(11\)
derivativedivides	\(256 \,{\mathrm e}^{4 x} {\mathrm e}^{-4}\)	\(11\)
default	\(256 \,{\mathrm e}^{4 x} {\mathrm e}^{-4}\)	\(11\)
norman	\(256 \,{\mathrm e}^{4 x} {\mathrm e}^{-4}\)	\(11\)
parallelrisch	\(256 \,{\mathrm e}^{4 x} {\mathrm e}^{-4}\)	\(11\)
meijerg	\(-256 \,{\mathrm e}^{-4} \left (1-{\mathrm e}^{4 x}\right )\)	\(13\)

[In]

int(1024*exp(x)^4/exp(1)^4,x,method=_RETURNVERBOSE)

[Out]

256*exp(-4+4*x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1024 e^{-4+4 x} \, dx=256 \, e^{\left (4 \, x - 4\right )} \]

[In]

integrate(1024*exp(x)^4/exp(1)^4,x, algorithm="fricas")

[Out]

256*e^(4*x - 4)

Sympy [A] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1024 e^{-4+4 x} \, dx=\frac {256 e^{4 x}}{e^{4}} \]

[In]

integrate(1024*exp(x)**4/exp(1)**4,x)

[Out]

256*exp(-4)*exp(4*x)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1024 e^{-4+4 x} \, dx=256 \, e^{\left (4 \, x - 4\right )} \]

[In]

integrate(1024*exp(x)^4/exp(1)^4,x, algorithm="maxima")

[Out]

256*e^(4*x - 4)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1024 e^{-4+4 x} \, dx=256 \, e^{\left (4 \, x - 4\right )} \]

[In]

integrate(1024*exp(x)^4/exp(1)^4,x, algorithm="giac")

[Out]

256*e^(4*x - 4)

Mupad [B] (verification not implemented)

Time = 0.03 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.89 \[ \int 1024 e^{-4+4 x} \, dx=256\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-4} \]

[In]

int(1024*exp(4*x)*exp(-4),x)

[Out]

256*exp(4*x)*exp(-4)