Integrand size = 213, antiderivative size = 31 \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\frac {x}{5+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}}-x+x^2} \] Output:
x/(x^2-x+exp(exp(exp(ln(x)*ln(x+exp(2))))^2)^2+5)
\[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx \] Input:
Integrate[(5*x - x^3 + E^2*(5 - x^2) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x]))) *(E^2 + x + E^(2*E^(Log[x]*Log[E^2 + x]) + Log[x]*Log[E^2 + x])*(-4*x*Log[ x] + (-4*E^2 - 4*x)*Log[E^2 + x])))/(25*x - 10*x^2 + 11*x^3 - 2*x^4 + x^5 + E^(4*E^(2*E^(Log[x]*Log[E^2 + x])))*(E^2 + x) + E^2*(25 - 10*x + 11*x^2 - 2*x^3 + x^4) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x])))*(10*x - 2*x^2 + 2*x^3 + E^2*(10 - 2*x + 2*x^2))),x]
Output:
Integrate[(5*x - x^3 + E^2*(5 - x^2) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x]))) *(E^2 + x + E^(2*E^(Log[x]*Log[E^2 + x]) + Log[x]*Log[E^2 + x])*(-4*x*Log[ x] + (-4*E^2 - 4*x)*Log[E^2 + x])))/(25*x - 10*x^2 + 11*x^3 - 2*x^4 + x^5 + E^(4*E^(2*E^(Log[x]*Log[E^2 + x])))*(E^2 + x) + E^2*(25 - 10*x + 11*x^2 - 2*x^3 + x^4) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x])))*(10*x - 2*x^2 + 2*x^3 + E^2*(10 - 2*x + 2*x^2))), 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.
| \(\displaystyle \int \frac {e^{2 e^{2 e^{\log (x) \log \left (x+e^2\right )}}} \left (\left (\left (-4 x-4 e^2\right ) \log \left (x+e^2\right )-4 x \log (x)\right ) \exp \left (\log (x) \log \left (x+e^2\right )+2 e^{\log (x) \log \left (x+e^2\right )}\right )+x+e^2\right )-x^3+e^2 \left (5-x^2\right )+5 x}{x^5-2 x^4+11 x^3-10 x^2+\left (2 x^3-2 x^2+e^2 \left (2 x^2-2 x+10\right )+10 x\right ) e^{2 e^{2 e^{\log (x) \log \left (x+e^2\right )}}}+e^2 \left (x^4-2 x^3+11 x^2-10 x+25\right )+25 x+\left (x+e^2\right ) e^{4 e^{2 e^{\log (x) \log \left (x+e^2\right )}}}} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^{2 e^{2 e^{\log (x) \log \left (x+e^2\right )}}} \left (\left (\left (-4 x-4 e^2\right ) \log \left (x+e^2\right )-4 x \log (x)\right ) \exp \left (\log (x) \log \left (x+e^2\right )+2 e^{\log (x) \log \left (x+e^2\right )}\right )+x+e^2\right )-x^3+e^2 \left (5-x^2\right )+5 x}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {4 \left (x \log (x)+x \log \left (x+e^2\right )+e^2 \log \left (x+e^2\right )\right ) \exp \left (2 x^{\log \left (x+e^2\right )}+2 e^{2 x^{\log \left (x+e^2\right )}}+\log (x) \log \left (x+e^2\right )\right )}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}+\frac {x e^{2 e^{2 x^{\log \left (x+e^2\right )}}}}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}+\frac {5 x}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}-\frac {e^2 \left (x^2-5\right )}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}+\frac {e^{2 \left (e^{2 x^{\log \left (x+e^2\right )}}+1\right )}}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}-\frac {x^3}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-4 x \log (x) \exp \left (2 \left (x^{\log \left (x+e^2\right )}+e^{2 x^{\log \left (x+e^2\right )}}\right )+\log (x) \log \left (x+e^2\right )\right )-\left (x+e^2\right ) \left (4 \log \left (x+e^2\right ) \exp \left (2 \left (x^{\log \left (x+e^2\right )}+e^{2 x^{\log \left (x+e^2\right )}}\right )+\log (x) \log \left (x+e^2\right )\right )-e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-5\right )}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {4 \left (x \log (x)+x \log \left (x+e^2\right )+e^2 \log \left (x+e^2\right )\right ) \exp \left (2 x^{\log \left (x+e^2\right )}+2 e^{2 x^{\log \left (x+e^2\right )}}+\log (x) \log \left (x+e^2\right )\right )}{\left (x+e^2\right ) \left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}-\frac {x^2}{\left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}+\frac {e^{2 e^{2 x^{\log \left (x+e^2\right )}}}}{\left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}+\frac {5}{\left (e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+x^2-x+5\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -4 \int \frac {\exp \left (2 x^{\log \left (x+e^2\right )}+2 e^{2 x^{\log \left (x+e^2\right )}}+\log (x) \log \left (x+e^2\right )\right ) \log (x)}{\left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx+4 \int \frac {\exp \left (2 x^{\log \left (x+e^2\right )}+2 e^{2 x^{\log \left (x+e^2\right )}}+\log (x) \log \left (x+e^2\right )+2\right ) \log (x)}{\left (x+e^2\right ) \left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx-4 \int \frac {\exp \left (2 x^{\log \left (x+e^2\right )}+2 e^{2 x^{\log \left (x+e^2\right )}}+\log (x) \log \left (x+e^2\right )\right ) \log \left (x+e^2\right )}{\left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx+5 \int \frac {1}{\left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx+\int \frac {e^{2 e^{2 x^{\log \left (x+e^2\right )}}}}{\left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx-\int \frac {x^2}{\left (x^2-x+e^{2 e^{2 x^{\log \left (x+e^2\right )}}}+5\right )^2}dx\) |
Input:
Int[(5*x - x^3 + E^2*(5 - x^2) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x])))*(E^2 + x + E^(2*E^(Log[x]*Log[E^2 + x]) + Log[x]*Log[E^2 + x])*(-4*x*Log[x] + ( -4*E^2 - 4*x)*Log[E^2 + x])))/(25*x - 10*x^2 + 11*x^3 - 2*x^4 + x^5 + E^(4 *E^(2*E^(Log[x]*Log[E^2 + x])))*(E^2 + x) + E^2*(25 - 10*x + 11*x^2 - 2*x^ 3 + x^4) + E^(2*E^(2*E^(Log[x]*Log[E^2 + x])))*(10*x - 2*x^2 + 2*x^3 + E^2 *(10 - 2*x + 2*x^2))),x]
Output:
$Aborted
Time = 0.11 (sec) , antiderivative size = 26, normalized size of antiderivative = 0.84
\[\frac {x}{x^{2}-x +{\mathrm e}^{2 \,{\mathrm e}^{2 \left (x +{\mathrm e}^{2}\right )^{\ln \left (x \right )}}}+5}\]
Input:
int(((((-4*exp(2)-4*x)*ln(x+exp(2))-4*x*ln(x))*exp(ln(x)*ln(x+exp(2)))*exp (exp(ln(x)*ln(x+exp(2))))^2+x+exp(2))*exp(exp(exp(ln(x)*ln(x+exp(2))))^2)^ 2+(-x^2+5)*exp(2)-x^3+5*x)/((x+exp(2))*exp(exp(exp(ln(x)*ln(x+exp(2))))^2) ^4+((2*x^2-2*x+10)*exp(2)+2*x^3-2*x^2+10*x)*exp(exp(exp(ln(x)*ln(x+exp(2)) ))^2)^2+(x^4-2*x^3+11*x^2-10*x+25)*exp(2)+x^5-2*x^4+11*x^3-10*x^2+25*x),x)
Output:
x/(x^2-x+exp(2*exp(2*(x+exp(2))^ln(x)))+5)
Time = 0.10 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\frac {x}{x^{2} - x + e^{\left (2 \, e^{\left (2 \, e^{\left (\log \left (x + e^{2}\right ) \log \left (x\right )\right )}\right )}\right )} + 5} \] Input:
integrate(((((-4*exp(2)-4*x)*log(x+exp(2))-4*x*log(x))*exp(log(x)*log(x+ex p(2)))*exp(exp(log(x)*log(x+exp(2))))^2+x+exp(2))*exp(exp(exp(log(x)*log(x +exp(2))))^2)^2+(-x^2+5)*exp(2)-x^3+5*x)/((x+exp(2))*exp(exp(exp(log(x)*lo g(x+exp(2))))^2)^4+((2*x^2-2*x+10)*exp(2)+2*x^3-2*x^2+10*x)*exp(exp(exp(lo g(x)*log(x+exp(2))))^2)^2+(x^4-2*x^3+11*x^2-10*x+25)*exp(2)+x^5-2*x^4+11*x ^3-10*x^2+25*x),x, algorithm="fricas")
Output:
x/(x^2 - x + e^(2*e^(2*e^(log(x + e^2)*log(x)))) + 5)
Timed out. \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((((-4*exp(2)-4*x)*ln(x+exp(2))-4*x*ln(x))*exp(ln(x)*ln(x+exp(2) ))*exp(exp(ln(x)*ln(x+exp(2))))**2+x+exp(2))*exp(exp(exp(ln(x)*ln(x+exp(2) )))**2)**2+(-x**2+5)*exp(2)-x**3+5*x)/((x+exp(2))*exp(exp(exp(ln(x)*ln(x+e xp(2))))**2)**4+((2*x**2-2*x+10)*exp(2)+2*x**3-2*x**2+10*x)*exp(exp(exp(ln (x)*ln(x+exp(2))))**2)**2+(x**4-2*x**3+11*x**2-10*x+25)*exp(2)+x**5-2*x**4 +11*x**3-10*x**2+25*x),x)
Output:
Timed out
Time = 0.35 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\frac {x}{x^{2} - x + e^{\left (2 \, e^{\left (2 \, e^{\left (\log \left (x + e^{2}\right ) \log \left (x\right )\right )}\right )}\right )} + 5} \] Input:
integrate(((((-4*exp(2)-4*x)*log(x+exp(2))-4*x*log(x))*exp(log(x)*log(x+ex p(2)))*exp(exp(log(x)*log(x+exp(2))))^2+x+exp(2))*exp(exp(exp(log(x)*log(x +exp(2))))^2)^2+(-x^2+5)*exp(2)-x^3+5*x)/((x+exp(2))*exp(exp(exp(log(x)*lo g(x+exp(2))))^2)^4+((2*x^2-2*x+10)*exp(2)+2*x^3-2*x^2+10*x)*exp(exp(exp(lo g(x)*log(x+exp(2))))^2)^2+(x^4-2*x^3+11*x^2-10*x+25)*exp(2)+x^5-2*x^4+11*x ^3-10*x^2+25*x),x, algorithm="maxima")
Output:
x/(x^2 - x + e^(2*e^(2*e^(log(x + e^2)*log(x)))) + 5)
Timed out. \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\text {Timed out} \] Input:
integrate(((((-4*exp(2)-4*x)*log(x+exp(2))-4*x*log(x))*exp(log(x)*log(x+ex p(2)))*exp(exp(log(x)*log(x+exp(2))))^2+x+exp(2))*exp(exp(exp(log(x)*log(x +exp(2))))^2)^2+(-x^2+5)*exp(2)-x^3+5*x)/((x+exp(2))*exp(exp(exp(log(x)*lo g(x+exp(2))))^2)^4+((2*x^2-2*x+10)*exp(2)+2*x^3-2*x^2+10*x)*exp(exp(exp(lo g(x)*log(x+exp(2))))^2)^2+(x^4-2*x^3+11*x^2-10*x+25)*exp(2)+x^5-2*x^4+11*x ^3-10*x^2+25*x),x, algorithm="giac")
Output:
Timed out
Time = 3.26 (sec) , antiderivative size = 732, normalized size of antiderivative = 23.61 \[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\text {Too large to display} \] Input:
int((5*x + exp(2*exp(2*exp(log(x + exp(2))*log(x))))*(x + exp(2) - exp(2*e xp(log(x + exp(2))*log(x)))*exp(log(x + exp(2))*log(x))*(log(x + exp(2))*( 4*x + 4*exp(2)) + 4*x*log(x))) - x^3 - exp(2)*(x^2 - 5))/(25*x + exp(2*exp (2*exp(log(x + exp(2))*log(x))))*(10*x + exp(2)*(2*x^2 - 2*x + 10) - 2*x^2 + 2*x^3) + exp(2)*(11*x^2 - 10*x - 2*x^3 + x^4 + 25) + exp(4*exp(2*exp(lo g(x + exp(2))*log(x))))*(x + exp(2)) - 10*x^2 + 11*x^3 - 2*x^4 + x^5),x)
Output:
((x*exp(2) + x^2)^2*(x*exp(2) - 2*x^2*exp(2) + x^2 - 2*x^3 + 20*x^log(x + exp(2))*exp(2*x^log(x + exp(2)) + 2)*log(x + exp(2)) + 4*x^log(x + exp(2)) *x^2*exp(2*x^log(x + exp(2)) + 2)*log(x + exp(2)) + 20*x*x^log(x + exp(2)) *exp(2*x^log(x + exp(2)))*log(x + exp(2)) + 20*x*x^log(x + exp(2))*exp(2*x ^log(x + exp(2)))*log(x) - 4*x*x^log(x + exp(2))*exp(2*x^log(x + exp(2)) + 2)*log(x + exp(2)) - 4*x^log(x + exp(2))*x^2*exp(2*x^log(x + exp(2)))*log (x + exp(2)) + 4*x^log(x + exp(2))*x^3*exp(2*x^log(x + exp(2)))*log(x + ex p(2)) - 4*x^log(x + exp(2))*x^2*exp(2*x^log(x + exp(2)))*log(x) + 4*x^log( x + exp(2))*x^3*exp(2*x^log(x + exp(2)))*log(x)))/((x + exp(2))*(exp(2*exp (2*x^log(x + exp(2)))) - x + x^2 + 5)*(2*x^3*exp(2) + x^2*exp(4) - 4*x^4*e xp(2) - 2*x^3*exp(4) + x^4 - 2*x^5 + 40*x^log(x + exp(2))*x^2*exp(2*x^log( x + exp(2)) + 2)*log(x + exp(2)) - 8*x^log(x + exp(2))*x^3*exp(2*x^log(x + exp(2)) + 2)*log(x + exp(2)) - 4*x^log(x + exp(2))*x^2*exp(2*x^log(x + ex p(2)) + 4)*log(x + exp(2)) + 8*x^log(x + exp(2))*x^4*exp(2*x^log(x + exp(2 )) + 2)*log(x + exp(2)) + 4*x^log(x + exp(2))*x^3*exp(2*x^log(x + exp(2)) + 4)*log(x + exp(2)) + 20*x^log(x + exp(2))*x^2*exp(2*x^log(x + exp(2)) + 2)*log(x) - 4*x^log(x + exp(2))*x^3*exp(2*x^log(x + exp(2)) + 2)*log(x) + 4*x^log(x + exp(2))*x^4*exp(2*x^log(x + exp(2)) + 2)*log(x) + 20*x*x^log(x + exp(2))*exp(2*x^log(x + exp(2)) + 4)*log(x + exp(2)) + 20*x^log(x + exp (2))*x^3*exp(2*x^log(x + exp(2)))*log(x + exp(2)) - 4*x^log(x + exp(2))...
\[ \int \frac {5 x-x^3+e^2 \left (5-x^2\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x+e^{2 e^{\log (x) \log \left (e^2+x\right )}+\log (x) \log \left (e^2+x\right )} \left (-4 x \log (x)+\left (-4 e^2-4 x\right ) \log \left (e^2+x\right )\right )\right )}{25 x-10 x^2+11 x^3-2 x^4+x^5+e^{4 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (e^2+x\right )+e^2 \left (25-10 x+11 x^2-2 x^3+x^4\right )+e^{2 e^{2 e^{\log (x) \log \left (e^2+x\right )}}} \left (10 x-2 x^2+2 x^3+e^2 \left (10-2 x+2 x^2\right )\right )} \, dx=\text {too large to display} \] Input:
int(((((-4*exp(2)-4*x)*log(x+exp(2))-4*x*log(x))*exp(log(x)*log(x+exp(2))) *exp(exp(log(x)*log(x+exp(2))))^2+x+exp(2))*exp(exp(exp(log(x)*log(x+exp(2 ))))^2)^2+(-x^2+5)*exp(2)-x^3+5*x)/((x+exp(2))*exp(exp(exp(log(x)*log(x+ex p(2))))^2)^4+((2*x^2-2*x+10)*exp(2)+2*x^3-2*x^2+10*x)*exp(exp(exp(log(x)*l og(x+exp(2))))^2)^2+(x^4-2*x^3+11*x^2-10*x+25)*exp(2)+x^5-2*x^4+11*x^3-10* x^2+25*x),x)
Output:
int(e**(2*e**(2*(e**2 + x)**log(x)))/(e**(4*e**(2*(e**2 + x)**log(x)))*e** 2 + e**(4*e**(2*(e**2 + x)**log(x)))*x + 2*e**(2*e**(2*(e**2 + x)**log(x)) )*e**2*x**2 - 2*e**(2*e**(2*(e**2 + x)**log(x)))*e**2*x + 10*e**(2*e**(2*( e**2 + x)**log(x)))*e**2 + 2*e**(2*e**(2*(e**2 + x)**log(x)))*x**3 - 2*e** (2*e**(2*(e**2 + x)**log(x)))*x**2 + 10*e**(2*e**(2*(e**2 + x)**log(x)))*x + e**2*x**4 - 2*e**2*x**3 + 11*e**2*x**2 - 10*e**2*x + 25*e**2 + x**5 - 2 *x**4 + 11*x**3 - 10*x**2 + 25*x),x)*e**2 - int(x**3/(e**(4*e**(2*(e**2 + x)**log(x)))*e**2 + e**(4*e**(2*(e**2 + x)**log(x)))*x + 2*e**(2*e**(2*(e* *2 + x)**log(x)))*e**2*x**2 - 2*e**(2*e**(2*(e**2 + x)**log(x)))*e**2*x + 10*e**(2*e**(2*(e**2 + x)**log(x)))*e**2 + 2*e**(2*e**(2*(e**2 + x)**log(x )))*x**3 - 2*e**(2*e**(2*(e**2 + x)**log(x)))*x**2 + 10*e**(2*e**(2*(e**2 + x)**log(x)))*x + e**2*x**4 - 2*e**2*x**3 + 11*e**2*x**2 - 10*e**2*x + 25 *e**2 + x**5 - 2*x**4 + 11*x**3 - 10*x**2 + 25*x),x) - int(x**2/(e**(4*e** (2*(e**2 + x)**log(x)))*e**2 + e**(4*e**(2*(e**2 + x)**log(x)))*x + 2*e**( 2*e**(2*(e**2 + x)**log(x)))*e**2*x**2 - 2*e**(2*e**(2*(e**2 + x)**log(x)) )*e**2*x + 10*e**(2*e**(2*(e**2 + x)**log(x)))*e**2 + 2*e**(2*e**(2*(e**2 + x)**log(x)))*x**3 - 2*e**(2*e**(2*(e**2 + x)**log(x)))*x**2 + 10*e**(2*e **(2*(e**2 + x)**log(x)))*x + e**2*x**4 - 2*e**2*x**3 + 11*e**2*x**2 - 10* e**2*x + 25*e**2 + x**5 - 2*x**4 + 11*x**3 - 10*x**2 + 25*x),x)*e**2 - 4*i nt((e**(2*(e**2 + x)**log(x) + 2*e**(2*(e**2 + x)**log(x)))*(e**2 + x)*...