\(\int e^{2+x-8 e^x x} (-8-8 x) \, dx\) [3262]

Optimal result

Integrand size = 17, antiderivative size = 10 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{2-8 e^x x} \]

[Out]

exp(x)*exp(-8*exp(x)*x+2-x)

Rubi [F]

\[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=\int e^{2+x-8 e^x x} (-8-8 x) \, dx \]

[In]

Int[E^(2 + x - 8*E^x*x)*(-8 - 8*x),x]

[Out]

-8*Defer[Int][E^(2 + x - 8*E^x*x), x] - 8*Defer[Int][E^(2 + x - 8*E^x*x)*x, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (-8 e^{2+x-8 e^x x}-8 e^{2+x-8 e^x x} x\right ) \, dx \\ & = -\left (8 \int e^{2+x-8 e^x x} \, dx\right )-8 \int e^{2+x-8 e^x x} x \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.05 (sec) , antiderivative size = 10, normalized size of antiderivative = 1.00 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{2-8 e^x x} \]

[In]

Integrate[E^(2 + x - 8*E^x*x)*(-8 - 8*x),x]

[Out]

E^(2 - 8*E^x*x)

Maple [A] (verified)

Time = 0.81 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90

method	result	size
risch	\({\mathrm e}^{-8 \,{\mathrm e}^{x} x +2}\)	\(9\)
norman	\({\mathrm e}^{x} {\mathrm e}^{-8 \,{\mathrm e}^{x} x +2-x}\)	\(15\)
parallelrisch	\({\mathrm e}^{x} {\mathrm e}^{-8 \,{\mathrm e}^{x} x +2-x}\)	\(15\)

[In]

int((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x,method=_RETURNVERBOSE)

[Out]

exp(-8*exp(x)*x+2)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{\left (-8 \, x e^{x} + 2\right )} \]

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="fricas")

[Out]

e^(-8*x*e^x + 2)

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 14, normalized size of antiderivative = 1.40 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{x} e^{- 8 x e^{x} - x + 2} \]

[In]

integrate((-8*x-8)*exp(x)**2*exp(-8*exp(x)*x+2-x),x)

[Out]

exp(x)*exp(-8*x*exp(x) - x + 2)

Maxima [A] (verification not implemented)

none

Time = 0.23 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{\left (-8 \, x e^{x} + 2\right )} \]

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="maxima")

[Out]

e^(-8*x*e^x + 2)

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 8, normalized size of antiderivative = 0.80 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx=e^{\left (-8 \, x e^{x} + 2\right )} \]

[In]

integrate((-8*x-8)*exp(x)^2*exp(-8*exp(x)*x+2-x),x, algorithm="giac")

[Out]

e^(-8*x*e^x + 2)

Mupad [B] (verification not implemented)

Time = 9.11 (sec) , antiderivative size = 9, normalized size of antiderivative = 0.90 \[ \int e^{2+x-8 e^x x} (-8-8 x) \, dx={\mathrm {e}}^{-8\,x\,{\mathrm {e}}^x}\,{\mathrm {e}}^2 \]

[In]

int(-exp(2*x)*exp(2 - 8*x*exp(x) - x)*(8*x + 8),x)

[Out]

exp(-8*x*exp(x))*exp(2)