3.90.62 \(\int 1024 e^{-4+4 x} \, dx\)

Optimal. Leaf size=9 \[ 256 e^{-4+4 x} \]

________________________________________________________________________________________

Rubi [A]  time = 0.00, antiderivative size = 9, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 9, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.222, Rules used = {12, 2194} \begin {gather*} 256 e^{4 x-4} \end {gather*}

Antiderivative was successfully verified.

[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 2194

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 {gather*} \begin {aligned} \text {integral} &=1024 \int e^{-4+4 x} \, dx\\ &=256 e^{-4+4 x}\\ \end {aligned} \end {gather*}

________________________________________________________________________________________

Mathematica [A]  time = 0.00, size = 9, normalized size = 1.00 \begin {gather*} 256 e^{-4+4 x} \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[1024*E^(-4 + 4*x),x]

[Out]

256*E^(-4 + 4*x)

________________________________________________________________________________________

fricas [A]  time = 0.49, size = 8, normalized size = 0.89 \begin {gather*} 256 \, e^{\left (4 \, x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

256*e^(4*x - 4)

________________________________________________________________________________________

giac [A]  time = 0.20, size = 8, normalized size = 0.89 \begin {gather*} 256 \, e^{\left (4 \, x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

256*e^(4*x - 4)

________________________________________________________________________________________

maple [A]  time = 0.03, size = 9, normalized size = 1.00

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

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

256*exp(4*x-4)

________________________________________________________________________________________

maxima [A]  time = 0.35, size = 8, normalized size = 0.89 \begin {gather*} 256 \, e^{\left (4 \, x - 4\right )} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

256*e^(4*x - 4)

________________________________________________________________________________________

mupad [B]  time = 0.04, size = 8, normalized size = 0.89 \begin {gather*} 256\,{\mathrm {e}}^{4\,x}\,{\mathrm {e}}^{-4} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________

sympy [A]  time = 0.05, size = 8, normalized size = 0.89 \begin {gather*} \frac {256 e^{4 x}}{e^{4}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

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

[Out]

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

________________________________________________________________________________________