\(\int (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} (5+e^{e^3})) \, dx\) [1795]

Optimal result

Integrand size = 30, antiderivative size = 22 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=-2-2 e^x+e^{\left (4+e^{e^3}\right ) (-5+x)+x} \]

[Out]

-2-2*exp(x)+exp((4+exp(exp(3)))*(-5+x)+x)

Rubi [A] (verified)

Time = 0.03 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.23, number of steps used = 4, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.067, Rules used = {2225, 2259} \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=e^{\left (5+e^{e^3}\right ) x-5 \left (4+e^{e^3}\right )}-2 e^x \]

[In]

Int[-2*E^x + E^(-20 + E^E^3*(-5 + x) + 5*x)*(5 + E^E^3),x]

[Out]

-2*E^x + E^(-5*(4 + E^E^3) + (5 + E^E^3)*x)

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]

Rule 2259

Int[(u_.)*(F_)^((a_.) + (b_.)*(v_)), x_Symbol] :> Int[u*F^(a + b*NormalizePowerOfLinear[v, x]), x] /; FreeQ[{F
, a, b}, x] && PolynomialQ[u, x] && PowerOfLinearQ[v, x] &&  !PowerOfLinearMatchQ[v, x]

Rubi steps \begin{align*} \text {integral}& = -\left (2 \int e^x \, dx\right )+\left (5+e^{e^3}\right ) \int e^{-20+e^{e^3} (-5+x)+5 x} \, dx \\ & = -2 e^x+\left (5+e^{e^3}\right ) \int e^{-5 \left (4+e^{e^3}\right )+\left (5+e^{e^3}\right ) x} \, dx \\ & = -2 e^x+e^{-5 \left (4+e^{e^3}\right )+\left (5+e^{e^3}\right ) x} \\ \end{align*}

Mathematica [A] (verified)

Time = 0.13 (sec) , antiderivative size = 23, normalized size of antiderivative = 1.05 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=e^{e^{e^3} (-5+x)+5 (-4+x)}-2 e^x \]

[In]

Integrate[-2*E^x + E^(-20 + E^E^3*(-5 + x) + 5*x)*(5 + E^E^3),x]

[Out]

E^(E^E^3*(-5 + x) + 5*(-4 + x)) - 2*E^x

Maple [A] (verified)

Time = 0.05 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86

method	result	size
default	\({\mathrm e}^{\left (-5+x \right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
norman	\({\mathrm e}^{\left (-5+x \right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
parallelrisch	\({\mathrm e}^{\left (-5+x \right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
parts	\({\mathrm e}^{\left (-5+x \right ) {\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(19\)
risch	\({\mathrm e}^{x \,{\mathrm e}^{{\mathrm e}^{3}}-5 \,{\mathrm e}^{{\mathrm e}^{3}}+5 x -20}-2 \,{\mathrm e}^{x}\)	\(22\)
meijerg	\(\frac {\left ({\mathrm e}^{{\mathrm e}^{3}-5 \,{\mathrm e}^{{\mathrm e}^{3}}-20}+5 \,{\mathrm e}^{-5 \,{\mathrm e}^{{\mathrm e}^{3}}-20}\right ) \left (1-{\mathrm e}^{-x \left (-{\mathrm e}^{{\mathrm e}^{3}}-5\right )}\right )}{-{\mathrm e}^{{\mathrm e}^{3}}-5}+2-2 \,{\mathrm e}^{x}\)	\(53\)

[In]

int((exp(exp(3))+5)*exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x),x,method=_RETURNVERBOSE)

[Out]

exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x)

Fricas [A] (verification not implemented)

none

Time = 0.24 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \]

[In]

integrate((exp(exp(3))+5)*exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="fricas")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

Sympy [A] (verification not implemented)

Time = 0.07 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.86 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=- 2 e^{x} + e^{5 x + \left (x - 5\right ) e^{e^{3}} - 20} \]

[In]

integrate((exp(exp(3))+5)*exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x),x)

[Out]

-2*exp(x) + exp(5*x + (x - 5)*exp(exp(3)) - 20)

Maxima [A] (verification not implemented)

none

Time = 0.19 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \]

[In]

integrate((exp(exp(3))+5)*exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="maxima")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

Giac [A] (verification not implemented)

none

Time = 0.26 (sec) , antiderivative size = 18, normalized size of antiderivative = 0.82 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx=e^{\left ({\left (x - 5\right )} e^{\left (e^{3}\right )} + 5 \, x - 20\right )} - 2 \, e^{x} \]

[In]

integrate((exp(exp(3))+5)*exp((-5+x)*exp(exp(3))+5*x-20)-2*exp(x),x, algorithm="giac")

[Out]

e^((x - 5)*e^(e^3) + 5*x - 20) - 2*e^x

Mupad [B] (verification not implemented)

Time = 0.12 (sec) , antiderivative size = 24, normalized size of antiderivative = 1.09 \[ \int \left (-2 e^x+e^{-20+e^{e^3} (-5+x)+5 x} \left (5+e^{e^3}\right )\right ) \, dx={\mathrm {e}}^{x\,{\mathrm {e}}^{{\mathrm {e}}^3}}\,{\mathrm {e}}^{5\,x}\,{\mathrm {e}}^{-20}\,{\mathrm {e}}^{-5\,{\mathrm {e}}^{{\mathrm {e}}^3}}-2\,{\mathrm {e}}^x \]

[In]

int(exp(5*x + exp(exp(3))*(x - 5) - 20)*(exp(exp(3)) + 5) - 2*exp(x),x)

[Out]

exp(x*exp(exp(3)))*exp(5*x)*exp(-20)*exp(-5*exp(exp(3))) - 2*exp(x)