\(\int e^{e^4-e^{e^x}+x-x^2} (1-e^{e^x+x}-2 x) \, dx\) [999]

Optimal result

Integrand size = 34, antiderivative size = 19 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{e^4-e^{e^x}+x-x^2} \]

[Out]

exp(-exp(exp(x))+exp(4)-x^2+x)

Rubi [A] (verified)

Time = 0.10 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6838} \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{-x^2+x-e^{e^x}+e^4} \]

[In]

Int[E^(E^4 - E^E^x + x - x^2)*(1 - E^(E^x + x) - 2*x),x]

[Out]

E^(E^4 - E^E^x + x - x^2)

Rule 6838

Int[(F_)^(v_)*(u_), x_Symbol] :> With[{q = DerivativeDivides[v, u, x]}, Simp[q*(F^v/Log[F]), x] /;  !FalseQ[q]
] /; FreeQ[F, x]

Rubi steps \begin{align*} \text {integral}& = e^{e^4-e^{e^x}+x-x^2} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.15 (sec) , antiderivative size = 19, normalized size of antiderivative = 1.00 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{e^4-e^{e^x}+x-x^2} \]

[In]

Integrate[E^(E^4 - E^E^x + x - x^2)*(1 - E^(E^x + x) - 2*x),x]

[Out]

E^(E^4 - E^E^x + x - x^2)

Maple [A] (verified)

Time = 0.09 (sec) , antiderivative size = 16, normalized size of antiderivative = 0.84

method	result	size
derivativedivides	\({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\)	\(16\)
default	\({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\)	\(16\)
norman	\({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\)	\(16\)
risch	\({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\)	\(16\)
parallelrisch	\({\mathrm e}^{-{\mathrm e}^{{\mathrm e}^{x}}+{\mathrm e}^{4}-x^{2}+x}\)	\(16\)

[In]

int((-exp(x)*exp(exp(x))+1-2*x)*exp(-exp(exp(x))+exp(4)-x^2+x),x,method=_RETURNVERBOSE)

[Out]

exp(-exp(exp(x))+exp(4)-x^2+x)

Fricas [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.42 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-{\left ({\left (x^{2} - x - e^{4}\right )} e^{x} + e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\right )}\right )} \]

[In]

integrate((-exp(x)*exp(exp(x))+1-2*x)*exp(-exp(exp(x))+exp(4)-x^2+x),x, algorithm="fricas")

[Out]

e^(-((x^2 - x - e^4)*e^x + e^(x + e^x))*e^(-x))

Sympy [A] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 14, normalized size of antiderivative = 0.74 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{- x^{2} + x - e^{e^{x}} + e^{4}} \]

[In]

integrate((-exp(x)*exp(exp(x))+1-2*x)*exp(-exp(exp(x))+exp(4)-x**2+x),x)

[Out]

exp(-x**2 + x - exp(exp(x)) + exp(4))

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-x^{2} + x + e^{4} - e^{\left (e^{x}\right )}\right )} \]

[In]

integrate((-exp(x)*exp(exp(x))+1-2*x)*exp(-exp(exp(x))+exp(4)-x^2+x),x, algorithm="maxima")

[Out]

e^(-x^2 + x + e^4 - e^(e^x))

Giac [A] (verification not implemented)

none

Time = 0.27 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.79 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx=e^{\left (-x^{2} + x + e^{4} - e^{\left (e^{x}\right )}\right )} \]

[In]

integrate((-exp(x)*exp(exp(x))+1-2*x)*exp(-exp(exp(x))+exp(4)-x^2+x),x, algorithm="giac")

[Out]

e^(-x^2 + x + e^4 - e^(e^x))

Mupad [B] (verification not implemented)

Time = 0.15 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.95 \[ \int e^{e^4-e^{e^x}+x-x^2} \left (1-e^{e^x+x}-2 x\right ) \, dx={\mathrm {e}}^{-{\mathrm {e}}^{{\mathrm {e}}^x}}\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^{{\mathrm {e}}^4}\,{\mathrm {e}}^x \]

[In]

int(-exp(x - exp(exp(x)) + exp(4) - x^2)*(2*x + exp(exp(x))*exp(x) - 1),x)

[Out]

exp(-exp(exp(x)))*exp(-x^2)*exp(exp(4))*exp(x)