3.30.62 \(\int 1024 e^{-4+4 x} \, dx\) [2962]

3.30.62.1 Optimal result

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

output

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

3.30.62.2 Mathematica [A] (verified)

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

input

Integrate[1024*E^(-4 + 4*x),x]
 

output

256*E^(-4 + 4*x)
 

3.30.62.3 Rubi [A] (verified)

Time = 0.14 (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 = {27, 2624}

Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.

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

\(\Big \downarrow \) 27

\(\displaystyle 1024 \int e^{4 x-4}dx\)

\(\Big \downarrow \) 2624

\(\displaystyle 256 e^{4 x-4}\)

input

Int[1024*E^(-4 + 4*x),x]
 

output

256*E^(-4 + 4*x)
 

3.30.62.3.1 Defintions of rubi rules used

rule 27

Int[(a_)*(Fx_), x_Symbol] :> Simp[a   Int[Fx, x], x] /; FreeQ[a, x] &&  !Ma 
tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
 

rule 2624

Int[((F_)^(v_))^(n_.), x_Symbol] :> Simp[(F^v)^n/(n*Log[F]*D[v, x]), x] /; 
FreeQ[{F, n}, x] && LinearQ[v, x]
 

3.30.62.4 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	\(-256 \,{\mathrm e}^{-4} \left (1-{\mathrm e}^{4 x}\right )\)	\(13\)

input

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

output

256*exp(-4+4*x)
 

3.30.62.5 Fricas [A] (verification not implemented)

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

input

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

output

256*e^(4*x - 4)
 

3.30.62.6 Sympy [A] (verification not implemented)

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

input

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

output

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

3.30.62.7 Maxima [A] (verification not implemented)

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

input

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

output

256*e^(4*x - 4)
 

3.30.62.8 Giac [A] (verification not implemented)

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

input

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

output

256*e^(4*x - 4)
 

3.30.62.9 Mupad [B] (verification not implemented)

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

input

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

output

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