\(\int (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5))) \, dx\) [8854]

Optimal result

Integrand size = 116, antiderivative size = 28 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3-e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x}+3 x \]

[Out]

3*x+3-exp(x+exp(exp((exp(exp(1))+x)^2*x^4)))*exp(x)

Rubi [F]

\[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx \]

[In]

Int[3 + E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + x)*(-2*E^x + E^(E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(2*E)*x
^4 + 2*E^E*x^5 + x^6)*(-4*E^(2*E + x)*x^3 - 10*E^(E + x)*x^4 - 6*E^x*x^5)),x]

[Out]

3*x - 2*Defer[Int][E^(E^E^(x^4*(E^E + x)^2) + 2*x), x] - 4*Defer[Int][E^(2*E + E^E^(E^(2*E)*x^4 + 2*E^E*x^5 +
x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^3, x] - 10*Defer[Int][E^(E + E^E^(E^(2*E)*
x^4 + 2*E^E*x^5 + x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^4, x] - 6*Defer[Int][E^(
E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(x^4*(E^E + x)^2) + 2*x + E^(2*E)*x^4 + 2*E^E*x^5 + x^6)*x^5, x]

Rubi steps \begin{align*} \text {integral}& = 3 x+\int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+\exp \left (e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6\right ) \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right ) \, dx \\ & = 3 x+\int \left (-2 e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}-2 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right )\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x} \, dx-2 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \left (2 e^{2 e}+5 e^e x+3 x^2\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-2 \int \left (2 \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3+5 \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4+3 \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5\right ) \, dx \\ & = 3 x-2 \int e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x} \, dx-4 \int \exp \left (2 e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^3 \, dx-6 \int \exp \left (e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^5 \, dx-10 \int \exp \left (e+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+e^{x^4 \left (e^e+x\right )^2}+2 x+e^{2 e} x^4+2 e^e x^5+x^6\right ) x^4 \, dx \\ \end{align*}

Mathematica [A] (verified)

Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=-e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}+3 x \]

[In]

Integrate[3 + E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + x)*(-2*E^x + E^(E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + E^(
2*E)*x^4 + 2*E^E*x^5 + x^6)*(-4*E^(2*E + x)*x^3 - 10*E^(E + x)*x^4 - 6*E^x*x^5)),x]

[Out]

-E^(E^E^(E^(2*E)*x^4 + 2*E^E*x^5 + x^6) + 2*x) + 3*x

Maple [A] (verified)

Time = 295.79 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.18

method	result	size
risch	\(-{\mathrm e}^{2 x +{\mathrm e}^{{\mathrm e}^{x^{4} \left (2 x \,{\mathrm e}^{{\mathrm e}}+x^{2}+{\mathrm e}^{2 \,{\mathrm e}}\right )}}}+3 x\)	\(33\)
parallelrisch	\(-{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{4} {\mathrm e}^{2 \,{\mathrm e}}+2 x^{5} {\mathrm e}^{{\mathrm e}}+x^{6}}}+x}+3 x\)	\(35\)

[In]

int(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(
1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(e
xp(1))+x^6))+x)+3,x,method=_RETURNVERBOSE)

[Out]

-exp(2*x+exp(exp(x^4*(2*x*exp(exp(1))+x^2+exp(2*exp(1))))))+3*x

Fricas [F(-1)]

Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="fricas")

[Out]

Timed out

Sympy [F(-1)]

Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]

[In]

integrate(((-4*x**3*exp(x)*exp(exp(1))**2-10*x**4*exp(x)*exp(exp(1))-6*x**5*exp(x))*exp(x**4*exp(exp(1))**2+2*
x**5*exp(exp(1))+x**6)*exp(exp(x**4*exp(exp(1))**2+2*x**5*exp(exp(1))+x**6))-2*exp(x))*exp(exp(exp(x**4*exp(ex
p(1))**2+2*x**5*exp(exp(1))+x**6))+x)+3,x)

[Out]

Timed out

Maxima [A] (verification not implemented)

none

Time = 0.38 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3 \, x - e^{\left (2 \, x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} \]

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="maxima")

[Out]

3*x - e^(2*x + e^(e^(x^6 + 2*x^5*e^e + x^4*e^(2*e))))

Giac [F]

\[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\int { -2 \, {\left ({\left (3 \, x^{5} e^{x} + 5 \, x^{4} e^{\left (x + e\right )} + 2 \, x^{3} e^{\left (x + 2 \, e\right )}\right )} e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )} + e^{x}\right )} e^{\left (x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} + 3 \,d x } \]

[In]

integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*exp(x))*exp(x^4*exp(exp(1))^2+2*x^5*ex
p(exp(1))+x^6)*exp(exp(x^4*exp(exp(1))^2+2*x^5*exp(exp(1))+x^6))-2*exp(x))*exp(exp(exp(x^4*exp(exp(1))^2+2*x^5
*exp(exp(1))+x^6))+x)+3,x, algorithm="giac")

[Out]

integrate(-2*((3*x^5*e^x + 5*x^4*e^(x + e) + 2*x^3*e^(x + 2*e))*e^(x^6 + 2*x^5*e^e + x^4*e^(2*e) + e^(x^6 + 2*
x^5*e^e + x^4*e^(2*e))) + e^x)*e^(x + e^(e^(x^6 + 2*x^5*e^e + x^4*e^(2*e)))) + 3, x)

Mupad [B] (verification not implemented)

Time = 12.76 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3\,x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x^6}\,{\mathrm {e}}^{2\,x^5\,{\mathrm {e}}^{\mathrm {e}}}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{2\,\mathrm {e}}}}} \]

[In]

int(3 - exp(x + exp(exp(2*x^5*exp(exp(1)) + x^4*exp(2*exp(1)) + x^6)))*(2*exp(x) + exp(exp(2*x^5*exp(exp(1)) +
x^4*exp(2*exp(1)) + x^6))*exp(2*x^5*exp(exp(1)) + x^4*exp(2*exp(1)) + x^6)*(6*x^5*exp(x) + 4*x^3*exp(2*exp(1)
)*exp(x) + 10*x^4*exp(exp(1))*exp(x))),x)

[Out]

3*x - exp(2*x)*exp(exp(exp(x^6)*exp(2*x^5*exp(exp(1)))*exp(x^4*exp(2*exp(1)))))