Integrand size = 52, antiderivative size = 25 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=\left (e^5+e^{e^{-x} x}\right ) \left (1+e^{2-e} x\right ) \] Output:
(1+exp(1)^2/exp(exp(1))*x)*(exp(x/exp(x))+exp(5))
Time = 2.17 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=e^{7-e} x+e^{e^{-x} x} \left (1+e^{2-e} x\right ) \] Input:
Integrate[E^(-E - x)*(E^(7 + x) + E^(x/E^x)*(E^(2 + x) + E^E*(1 - x) + E^2 *(x - x^2))),x]
Output:
E^(7 - E)*x + E^(x/E^x)*(1 + E^(2 - E)*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.
\(\displaystyle \int e^{-x-e} \left (e^{e^{-x} x} \left (e^2 \left (x-x^2\right )+e^e (1-x)+e^{x+2}\right )+e^{x+7}\right ) \, dx\) |
\(\Big \downarrow \) 7293 |
\(\displaystyle \int \left (e^{e^{-x} x-x-e} \left (-e^2 x^2+e^2 \left (1-e^{e-2}\right ) x+e^{x+2}+e^e\right )+e^{7-e}\right )dx\) |
\(\Big \downarrow \) 2009 |
\(\displaystyle -\int e^{e^{-x} x-x+2 \left (1-\frac {e}{2}\right )} x^2dx+\int e^{-e^{-x} \left (-1+e^x\right ) x}dx+\int e^{e^{-x} x+2 \left (1-\frac {e}{2}\right )}dx+\left (e^2-e^e\right ) \int e^{e^{-x} x-x-e} xdx+e^{7-e} x\) |
Input:
Int[E^(-E - x)*(E^(7 + x) + E^(x/E^x)*(E^(2 + x) + E^E*(1 - x) + E^2*(x - x^2))),x]
Output:
$Aborted
Time = 0.36 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.32
method | result | size |
risch | \(x \,{\mathrm e}^{2-{\mathrm e}+x \,{\mathrm e}^{-x}}+{\mathrm e}^{x \,{\mathrm e}^{-x}}+x \,{\mathrm e}^{7-{\mathrm e}}\) | \(33\) |
parallelrisch | \({\mathrm e}^{-{\mathrm e}} \left ({\mathrm e}^{2} {\mathrm e}^{5} x +{\mathrm e}^{2} {\mathrm e}^{x \,{\mathrm e}^{-x}} x +{\mathrm e}^{x \,{\mathrm e}^{-x}} {\mathrm e}^{{\mathrm e}}\right )\) | \(40\) |
norman | \(\left ({\mathrm e}^{x} {\mathrm e}^{x \,{\mathrm e}^{-x}}+{\mathrm e}^{2} {\mathrm e}^{-{\mathrm e}} x \,{\mathrm e}^{x} {\mathrm e}^{x \,{\mathrm e}^{-x}}+{\mathrm e}^{-{\mathrm e}} {\mathrm e}^{2} {\mathrm e}^{5} x \,{\mathrm e}^{x}\right ) {\mathrm e}^{-x}\) | \(52\) |
Input:
int((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp(x))+e xp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x,method=_RETURNVERBOSE)
Output:
x*exp(2-exp(1)+x*exp(-x))+exp(x*exp(-x))+x*exp(7-exp(1))
Time = 0.07 (sec) , antiderivative size = 27, normalized size of antiderivative = 1.08 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx={\left (x e^{7} + {\left (x e^{2} + e^{e}\right )} e^{\left (x e^{\left (-x\right )}\right )}\right )} e^{\left (-e\right )} \] Input:
integrate((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp (x))+exp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x, algorithm="fricas")
Output:
(x*e^7 + (x*e^2 + e^e)*e^(x*e^(-x)))*e^(-e)
Time = 0.15 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=\frac {x e^{7}}{e^{e}} + \frac {\left (x e^{2} + e^{e}\right ) e^{x e^{- x}}}{e^{e}} \] Input:
integrate((((1-x)*exp(exp(1))+exp(1)**2*exp(x)+(-x**2+x)*exp(1)**2)*exp(x/ exp(x))+exp(1)**2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x)
Output:
x*exp(7)*exp(-E) + (x*exp(2) + exp(E))*exp(-E)*exp(x*exp(-x))
\[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=\int { -{\left ({\left ({\left (x^{2} - x\right )} e^{2} + {\left (x - 1\right )} e^{e} - e^{\left (x + 2\right )}\right )} e^{\left (x e^{\left (-x\right )}\right )} - e^{\left (x + 7\right )}\right )} e^{\left (-x - e\right )} \,d x } \] Input:
integrate((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp (x))+exp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x, algorithm="maxima")
Output:
x*e^(-e + 7) + integrate(-(x^2*e^2 - x*(e^2 - e^e) - e^(x + 2) - e^e)*e^(x *e^(-x) - x - e), x)
\[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=\int { -{\left ({\left ({\left (x^{2} - x\right )} e^{2} + {\left (x - 1\right )} e^{e} - e^{\left (x + 2\right )}\right )} e^{\left (x e^{\left (-x\right )}\right )} - e^{\left (x + 7\right )}\right )} e^{\left (-x - e\right )} \,d x } \] Input:
integrate((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp (x))+exp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x, algorithm="giac")
Output:
integrate(-(((x^2 - x)*e^2 + (x - 1)*e^e - e^(x + 2))*e^(x*e^(-x)) - e^(x + 7))*e^(-x - e), x)
Time = 2.00 (sec) , antiderivative size = 31, normalized size of antiderivative = 1.24 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=x\,{\mathrm {e}}^{7-\mathrm {e}}+{\mathrm {e}}^{x\,{\mathrm {e}}^{-x}-\mathrm {e}}\,\left ({\mathrm {e}}^{\mathrm {e}}+x\,{\mathrm {e}}^2\right ) \] Input:
int(exp(-exp(1))*exp(-x)*(exp(7)*exp(x) + exp(x*exp(-x))*(exp(2)*exp(x) - exp(exp(1))*(x - 1) + exp(2)*(x - x^2))),x)
Output:
x*exp(7 - exp(1)) + exp(x*exp(-x) - exp(1))*(exp(exp(1)) + x*exp(2))
Time = 0.20 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.64 \[ \int e^{-e-x} \left (e^{7+x}+e^{e^{-x} x} \left (e^{2+x}+e^e (1-x)+e^2 \left (x-x^2\right )\right )\right ) \, dx=\frac {e^{\frac {e^{x} e +x}{e^{x}}}+e^{\frac {x}{e^{x}}} e^{2} x +e^{7} x}{e^{e}} \] Input:
int((((1-x)*exp(exp(1))+exp(1)^2*exp(x)+(-x^2+x)*exp(1)^2)*exp(x/exp(x))+e xp(1)^2*exp(5)*exp(x))/exp(x)/exp(exp(1)),x)
Output:
(e**((e**x*e + x)/e**x) + e**(x/e**x)*e**2*x + e**7*x)/e**e