\(\int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx\) [7839]

Optimal result

Integrand size = 30, antiderivative size = 15 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{18 e^{-4 \left (-2 x+x^2\right )}} \]

[Out]

exp(9/exp(4*x^2-8*x))^2

Rubi [F]

\[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=\int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx \]

[In]

Int[E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*(144 - 144*x),x]

[Out]

144*Defer[Int][E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2), x] - 144*Defer[Int][E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*
x, x]

Rubi steps \begin{align*} \text {integral}& = \int \left (144 e^{18 e^{8 x-4 x^2}+8 x-4 x^2}-144 e^{18 e^{8 x-4 x^2}+8 x-4 x^2} x\right ) \, dx \\ & = 144 \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} \, dx-144 \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} x \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{18 e^{-4 (-2+x) x}} \]

[In]

Integrate[E^(18*E^(8*x - 4*x^2) + 8*x - 4*x^2)*(144 - 144*x),x]

[Out]

E^(18/E^(4*(-2 + x)*x))

Maple [A] (verified)

Time = 0.08 (sec) , antiderivative size = 11, normalized size of antiderivative = 0.73

method	result	size
risch	\({\mathrm e}^{18 \,{\mathrm e}^{-4 \left (-2+x \right ) x}}\)	\(11\)
norman	\({\mathrm e}^{18 \,{\mathrm e}^{-4 x^{2}+8 x}}\)	\(18\)
parallelrisch	\({\mathrm e}^{18 \,{\mathrm e}^{-4 x^{2}+8 x}}\)	\(18\)

[In]

int((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x,method=_RETURNVERBOSE)

[Out]

exp(18*exp(-4*(-2+x)*x))

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \]

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="fricas")

[Out]

e^(18*e^(-4*x^2 + 8*x))

Sympy [A] (verification not implemented)

Time = 0.09 (sec) , antiderivative size = 12, normalized size of antiderivative = 0.80 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{18 e^{- 4 x^{2} + 8 x}} \]

[In]

integrate((-144*x+144)*exp(9/exp(4*x**2-8*x))**2/exp(4*x**2-8*x),x)

[Out]

exp(18*exp(-4*x**2 + 8*x))

Maxima [A] (verification not implemented)

none

Time = 0.33 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \]

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="maxima")

[Out]

e^(18*e^(-4*x^2 + 8*x))

Giac [A] (verification not implemented)

none

Time = 0.28 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx=e^{\left (18 \, e^{\left (-4 \, x^{2} + 8 \, x\right )}\right )} \]

[In]

integrate((-144*x+144)*exp(9/exp(4*x^2-8*x))^2/exp(4*x^2-8*x),x, algorithm="giac")

[Out]

e^(18*e^(-4*x^2 + 8*x))

Mupad [B] (verification not implemented)

Time = 0.11 (sec) , antiderivative size = 13, normalized size of antiderivative = 0.87 \[ \int e^{18 e^{8 x-4 x^2}+8 x-4 x^2} (144-144 x) \, dx={\mathrm {e}}^{18\,{\mathrm {e}}^{8\,x-4\,x^2}} \]

[In]

int(-exp(18*exp(8*x - 4*x^2))*exp(8*x - 4*x^2)*(144*x - 144),x)

[Out]

exp(18*exp(8*x - 4*x^2))