3.18.8 \(\int 18 e^4 \, dx\) [1708]

3.18.8.1 Optimal result

Integrand size = 5, antiderivative size = 6 \[ \int 18 e^4 \, dx=18 e^4 x \]

output

18*x*exp(4)
 

3.18.8.2 Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00 \[ \int 18 e^4 \, dx=18 e^4 x \]

input

Integrate[18*E^4,x]
 

output

18*E^4*x
 

3.18.8.3 Rubi [A] (verified)

Time = 0.12 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.200, Rules used = {24}

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.

\(\displaystyle \int 18 e^4 \, dx\)

\(\Big \downarrow \) 24

\(\displaystyle 18 e^4 x\)

input

Int[18*E^4,x]
 

output

18*E^4*x
 

3.18.8.3.1 Defintions of rubi rules used

rule 24

Int[a_, x_Symbol] :> Simp[a*x, x] /; FreeQ[a, x]
 

3.18.8.4 Maple [A] (verified)

Time = 0.02 (sec) , antiderivative size = 6, normalized size of antiderivative = 1.00

method	result	size
default	\(18 x \,{\mathrm e}^{4}\)	\(6\)
norman	\(18 x \,{\mathrm e}^{4}\)	\(6\)
risch	\(18 x \,{\mathrm e}^{4}\)	\(6\)
parallelrisch	\(18 x \,{\mathrm e}^{4}\)	\(6\)

input

int(18*exp(4),x,method=_RETURNVERBOSE)
 

output

18*x*exp(4)
 

3.18.8.5 Fricas [A] (verification not implemented)

Time = 0.22 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int 18 e^4 \, dx=18 \, x e^{4} \]

input

integrate(18*exp(4),x, algorithm=\
 

output

18*x*e^4
 

3.18.8.6 Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int 18 e^4 \, dx=18 x e^{4} \]

input

integrate(18*exp(4),x)
 

output

18*x*exp(4)
 

3.18.8.7 Maxima [A] (verification not implemented)

Time = 0.20 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int 18 e^4 \, dx=18 \, x e^{4} \]

input

integrate(18*exp(4),x, algorithm=\
 

output

18*x*e^4
 

3.18.8.8 Giac [A] (verification not implemented)

Time = 0.27 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int 18 e^4 \, dx=18 \, x e^{4} \]

input

integrate(18*exp(4),x, algorithm=\
 

output

18*x*e^4
 

3.18.8.9 Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 5, normalized size of antiderivative = 0.83 \[ \int 18 e^4 \, dx=18\,x\,{\mathrm {e}}^4 \]

input

int(18*exp(4),x)
 

output

18*x*exp(4)