\(\int (3+e^{2+e^3}+e^x (-1-x)-2 x) \, dx\) [9866]

Optimal result

Integrand size = 21, antiderivative size = 21 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-4+\left (3+e^{2+e^3}-e^x-x\right ) x \]

[Out]

(3+exp(2+exp(3))-x-exp(x))*x-4

Rubi [A] (verified)

Time = 0.01 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.33, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.095, Rules used = {2207, 2225} \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^2+\left (3+e^{2+e^3}\right ) x+e^x-e^x (x+1) \]

[In]

Int[3 + E^(2 + E^3) + E^x*(-1 - x) - 2*x,x]

[Out]

E^x + (3 + E^(2 + E^3))*x - x^2 - E^x*(1 + x)

Rule 2207

Int[((b_.)*(F_)^((g_.)*((e_.) + (f_.)*(x_))))^(n_.)*((c_.) + (d_.)*(x_))^(m_.), x_Symbol] :> Simp[(c + d*x)^m*
((b*F^(g*(e + f*x)))^n/(f*g*n*Log[F])), x] - Dist[d*(m/(f*g*n*Log[F])), Int[(c + d*x)^(m - 1)*(b*F^(g*(e + f*x
)))^n, x], x] /; FreeQ[{F, b, c, d, e, f, g, n}, x] && GtQ[m, 0] && IntegerQ[2*m] &&  !TrueQ[$UseGamma]

Rule 2225

Int[((F_)^((c_.)*((a_.) + (b_.)*(x_))))^(n_.), x_Symbol] :> Simp[(F^(c*(a + b*x)))^n/(b*c*n*Log[F]), x] /; Fre
eQ[{F, a, b, c, n}, x]

Rubi steps \begin{align*} \text {integral}& = \left (3+e^{2+e^3}\right ) x-x^2+\int e^x (-1-x) \, dx \\ & = \left (3+e^{2+e^3}\right ) x-x^2-e^x (1+x)+\int e^x \, dx \\ & = e^x+\left (3+e^{2+e^3}\right ) x-x^2-e^x (1+x) \\ \end{align*}

Mathematica [A] (verified)

Time = 0.01 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.14 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=3 x+e^{2+e^3} x-e^x x-x^2 \]

[In]

Integrate[3 + E^(2 + E^3) + E^x*(-1 - x) - 2*x,x]

[Out]

3*x + E^(2 + E^3)*x - E^x*x - x^2

Maple [A] (verified)

Time = 0.14 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00

method	result	size
parallelrisch	\(-{\mathrm e}^{x} x -x^{2}+\left ({\mathrm e}^{2+{\mathrm e}^{3}}+3\right ) x\)	\(21\)
default	\(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\)	\(22\)
norman	\(\left ({\mathrm e}^{2} {\mathrm e}^{{\mathrm e}^{3}}+3\right ) x -x^{2}-{\mathrm e}^{x} x\)	\(22\)
risch	\(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\)	\(22\)
parts	\(-{\mathrm e}^{x} x +3 x -x^{2}+x \,{\mathrm e}^{2+{\mathrm e}^{3}}\)	\(22\)

[In]

int(exp(2+exp(3))+(-1-x)*exp(x)+3-2*x,x,method=_RETURNVERBOSE)

[Out]

-exp(x)*x-x^2+(exp(2+exp(3))+3)*x

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]

[In]

integrate(exp(2+exp(3))+(-1-x)*exp(x)+3-2*x,x, algorithm="fricas")

[Out]

-x^2 - x*e^x + x*e^(e^3 + 2) + 3*x

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.90 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=- x^{2} - x e^{x} + x \left (3 + e^{2} e^{e^{3}}\right ) \]

[In]

integrate(exp(2+exp(3))+(-1-x)*exp(x)+3-2*x,x)

[Out]

-x**2 - x*exp(x) + x*(3 + exp(2)*exp(exp(3)))

Maxima [A] (verification not implemented)

none

Time = 0.18 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]

[In]

integrate(exp(2+exp(3))+(-1-x)*exp(x)+3-2*x,x, algorithm="maxima")

[Out]

-x^2 - x*e^x + x*e^(e^3 + 2) + 3*x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.00 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x^{2} - x e^{x} + x e^{\left (e^{3} + 2\right )} + 3 \, x \]

[In]

integrate(exp(2+exp(3))+(-1-x)*exp(x)+3-2*x,x, algorithm="giac")

[Out]

-x^2 - x*e^x + x*e^(e^3 + 2) + 3*x

Mupad [B] (verification not implemented)

Time = 0.06 (sec) , antiderivative size = 15, normalized size of antiderivative = 0.71 \[ \int \left (3+e^{2+e^3}+e^x (-1-x)-2 x\right ) \, dx=-x\,\left (x-{\mathrm {e}}^{{\mathrm {e}}^3+2}+{\mathrm {e}}^x-3\right ) \]

[In]

int(exp(exp(3) + 2) - 2*x - exp(x)*(x + 1) + 3,x)

[Out]

-x*(x - exp(exp(3) + 2) + exp(x) - 3)