\(\int 6 e^{e^3 (20+8 e)} \, dx\) [9398]

Optimal result

Integrand size = 13, antiderivative size = 18 \[ \int 6 e^{e^3 (20+8 e)} \, dx=3+6 e^{\left (8+\frac {20}{e}\right ) e^4} x \]

[Out]

6*x*exp((8+20/exp(1))*exp(4))+3

Rubi [A] (verified)

Time = 0.00 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.83, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {8} \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 e^{4 e^3 (5+2 e)} x \]

[In]

Int[6*E^(E^3*(20 + 8*E)),x]

[Out]

6*E^(4*E^3*(5 + 2*E))*x

Rule 8

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

Rubi steps \begin{align*} \text {integral}& = 6 e^{4 e^3 (5+2 e)} x \\ \end{align*}

Mathematica [A] (verified)

Time = 0.00 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 e^{e^3 (20+8 e)} x \]

[In]

Integrate[6*E^(E^3*(20 + 8*E)),x]

[Out]

6*E^(E^3*(20 + 8*E))*x

Maple [A] (verified)

Time = 0.01 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78

method	result	size
risch	\(6 x \,{\mathrm e}^{8 \,{\mathrm e}^{4}+20 \,{\mathrm e}^{3}}\)	\(14\)
default	\(6 x \,{\mathrm e}^{\left (8 \,{\mathrm e}+20\right ) {\mathrm e}^{4} {\mathrm e}^{-1}}\)	\(18\)
parallelrisch	\(6 x \,{\mathrm e}^{\left (8 \,{\mathrm e}+20\right ) {\mathrm e}^{4} {\mathrm e}^{-1}}\)	\(18\)
norman	\(6 \,{\mathrm e}^{8 \,{\mathrm e}^{4}} {\mathrm e}^{20 \,{\mathrm e}^{3}} x\)	\(19\)

[In]

int(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x,method=_RETURNVERBOSE)

[Out]

6*x*exp(8*exp(4)+20*exp(3))

Fricas [A] (verification not implemented)

none

Time = 0.29 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 \, x e^{\left (8 \, e^{4} + 20 \, e^{3}\right )} \]

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="fricas")

[Out]

6*x*e^(8*e^4 + 20*e^3)

Sympy [A] (verification not implemented)

Time = 0.02 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 x e^{\left (20 + 8 e\right ) e^{3}} \]

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x)

[Out]

6*x*exp((20 + 8*E)*exp(3))

Maxima [A] (verification not implemented)

none

Time = 0.21 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 \, x e^{\left (4 \, {\left (2 \, e + 5\right )} e^{3}\right )} \]

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="maxima")

[Out]

6*x*e^(4*(2*e + 5)*e^3)

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.78 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6 \, x e^{\left (4 \, {\left (2 \, e + 5\right )} e^{3}\right )} \]

[In]

integrate(6*exp((8*exp(1)+20)*exp(4)/exp(1)),x, algorithm="giac")

[Out]

6*x*e^(4*(2*e + 5)*e^3)

Mupad [B] (verification not implemented)

Time = 0.00 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.72 \[ \int 6 e^{e^3 (20+8 e)} \, dx=6\,x\,{\mathrm {e}}^{{\mathrm {e}}^3\,\left (8\,\mathrm {e}+20\right )} \]

[In]

int(6*exp(exp(3)*(8*exp(1) + 20)),x)

[Out]

6*x*exp(exp(3)*(8*exp(1) + 20))