Integrand size = 116, antiderivative size = 28 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3-e^{e^{e^{x^4 \left (e^e+x\right )^2}}+2 x}+3 x \]
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.32 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=-e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+2 x}+3 x \]
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]
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
\(\displaystyle \int \left (e^{e^{e^{x^6+2 e^e x^5+e^{2 e} x^4}}+x} \left (\left (-6 e^x x^5-10 e^{x+e} x^4-4 e^{x+2 e} x^3\right ) \exp \left (x^6+2 e^e x^5+e^{2 e} x^4+e^{x^6+2 e^e x^5+e^{2 e} x^4}\right )-2 e^x\right )+3\right ) \, dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -10 \int \exp \left (x^6+2 e^e x^5+e^{2 e} x^4+2 x+e^{e^{x^6+2 e^e x^5+e^{2 e} x^4}}+e^{x^4 \left (x+e^e\right )^2}+e\right ) x^4dx-6 \int \exp \left (x^6+2 e^e x^5+e^{2 e} x^4+2 x+e^{e^{x^6+2 e^e x^5+e^{2 e} x^4}}+e^{x^4 \left (x+e^e\right )^2}\right ) x^5dx-4 \int \exp \left (x^6+2 e^e x^5+e^{2 e} x^4+2 x+e^{e^{x^6+2 e^e x^5+e^{2 e} x^4}}+e^{x^4 \left (x+e^e\right )^2}+2 e\right ) x^3dx-2 \int e^{2 x+e^{e^{x^6+2 e^e x^5+e^{2 e} x^4}}}dx+3 x\) |
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]
3.29.54.3.1 Defintions of rubi rules used
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 | \(-{\mathrm e}^{x} {\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x^{4} {\mathrm e}^{2 \,{\mathrm e}}+2 x^{5} {\mathrm e}^{{\mathrm e}}+x^{6}}}+x}+3 x\) | \(35\) |
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(exp (1))+x^6))+x)+3,x,method=_RETURNVERBOSE)
Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]
integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*ex p(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*e xp(exp(1))+x^6))+x)+3,x, algorithm=\
Timed out. \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\text {Timed out} \]
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*ex p(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)
Time = 0.38 (sec) , antiderivative size = 34, normalized size of antiderivative = 1.21 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3 \, x - e^{\left (2 \, x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} \]
integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*ex p(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*e xp(exp(1))+x^6))+x)+3,x, algorithm=\
\[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=\int { -2 \, {\left ({\left (3 \, x^{5} e^{x} + 5 \, x^{4} e^{\left (x + e\right )} + 2 \, x^{3} e^{\left (x + 2 \, e\right )}\right )} e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )} + e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )} + e^{x}\right )} e^{\left (x + e^{\left (e^{\left (x^{6} + 2 \, x^{5} e^{e} + x^{4} e^{\left (2 \, e\right )}\right )}\right )}\right )} + 3 \,d x } \]
integrate(((-4*x^3*exp(x)*exp(exp(1))^2-10*x^4*exp(x)*exp(exp(1))-6*x^5*ex p(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*e xp(exp(1))+x^6))+x)+3,x, algorithm=\
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)
Time = 12.76 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.29 \[ \int \left (3+e^{e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}}+x} \left (-2 e^x+e^{e^{e^{2 e} x^4+2 e^e x^5+x^6}+e^{2 e} x^4+2 e^e x^5+x^6} \left (-4 e^{2 e+x} x^3-10 e^{e+x} x^4-6 e^x x^5\right )\right )\right ) \, dx=3\,x-{\mathrm {e}}^{2\,x}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^{x^6}\,{\mathrm {e}}^{2\,x^5\,{\mathrm {e}}^{\mathrm {e}}}\,{\mathrm {e}}^{x^4\,{\mathrm {e}}^{2\,\mathrm {e}}}}} \]