Integrand size = 288, antiderivative size = 31 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=\frac {e^{x+x^2} x}{-\frac {3}{x}+x \left (x-\log \left (-1+e^4+\log (x)\right )\right )} \]
Time = 0.17 (sec) , antiderivative size = 33, normalized size of antiderivative = 1.06 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=-\frac {e^{x+x^2} x^2}{3-x^3+x^2 \log \left (-1+e^4+\log (x)\right )} \]
Integrate[(E^(x + x^2)*(6*x + 3*x^2 + 7*x^3 + x^4 - x^5 - 2*x^6 + E^4*(-6* x - 3*x^2 - 6*x^3 - x^4 + x^5 + 2*x^6)) + E^(x + x^2)*(-6*x - 3*x^2 - 6*x^ 3 - x^4 + x^5 + 2*x^6)*Log[x] + (E^(x + x^2)*(x^4 + 2*x^5 + E^4*(-x^4 - 2* x^5)) + E^(x + x^2)*(-x^4 - 2*x^5)*Log[x])*Log[-1 + E^4 + Log[x]])/(-9 + 6 *x^3 - x^6 + E^4*(9 - 6*x^3 + x^6) + (9 - 6*x^3 + x^6)*Log[x] + (-6*x^2 + 2*x^5 + E^4*(6*x^2 - 2*x^5) + (6*x^2 - 2*x^5)*Log[x])*Log[-1 + E^4 + Log[x ]] + (-x^4 + E^4*x^4 + x^4*Log[x])*Log[-1 + E^4 + Log[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.
| \(\displaystyle \int \frac {\left (e^{x^2+x} \left (2 x^5+x^4+e^4 \left (-2 x^5-x^4\right )\right )+e^{x^2+x} \left (-2 x^5-x^4\right ) \log (x)\right ) \log \left (\log (x)+e^4-1\right )+e^{x^2+x} \left (-2 x^6-x^5+x^4+7 x^3+3 x^2+e^4 \left (2 x^6+x^5-x^4-6 x^3-3 x^2-6 x\right )+6 x\right )+e^{x^2+x} \left (2 x^6+x^5-x^4-6 x^3-3 x^2-6 x\right ) \log (x)}{-x^6+\left (e^4 x^4-x^4+x^4 \log (x)\right ) \log ^2\left (\log (x)+e^4-1\right )+6 x^3+e^4 \left (x^6-6 x^3+9\right )+\left (x^6-6 x^3+9\right ) \log (x)+\left (2 x^5-6 x^2+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (\log (x)+e^4-1\right )-9} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-\left (e^{x^2+x} \left (2 x^5+x^4+e^4 \left (-2 x^5-x^4\right )\right )+e^{x^2+x} \left (-2 x^5-x^4\right ) \log (x)\right ) \log \left (\log (x)+e^4-1\right )-e^{x^2+x} \left (-2 x^6-x^5+x^4+7 x^3+3 x^2+e^4 \left (2 x^6+x^5-x^4-6 x^3-3 x^2-6 x\right )+6 x\right )-e^{x^2+x} \left (2 x^6+x^5-x^4-6 x^3-3 x^2-6 x\right ) \log (x)}{\left (-\log (x)-e^4+1\right ) \left (-x^3+x^2 \log \left (\log (x)+e^4-1\right )+3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (-\frac {6 e^{x^2+x} x^3 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {7 \left (1-\frac {6 e^4}{7}\right ) e^{x^2+x} x^3}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {3 e^{x^2+x} x^2 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {3 \left (1-e^4\right ) e^{x^2+x} x^2}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {6 e^{x^2+x} x \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {6 \left (1-e^4\right ) e^{x^2+x} x}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {2 e^{x^2+x} x^6 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {2 \left (1-e^4\right ) e^{x^2+x} x^6}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {2 e^{x^2+x} x^5 \log (x) \log \left (\log (x)+e^4-1\right )}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {2 \left (1-e^4\right ) e^{x^2+x} x^5 \log \left (\log (x)+e^4-1\right )}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {e^{x^2+x} x^5 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {\left (1-e^4\right ) e^{x^2+x} x^5}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {e^{x^2+x} x^4 \log (x) \log \left (\log (x)+e^4-1\right )}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {\left (1-e^4\right ) e^{x^2+x} x^4 \log \left (\log (x)+e^4-1\right )}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}-\frac {e^{x^2+x} x^4 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}+\frac {\left (1-e^4\right ) e^{x^2+x} x^4}{\left (\log (x)+e^4-1\right ) \left (x^3-x^2 \log \left (\log (x)+e^4-1\right )-3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {e^{x^2+x} x \left (2 \left (1-e^4\right ) x^5+\left (1-e^4\right ) x^4-\left (1-e^4\right ) x^3+\left (e^4-1\right ) (2 x+1) x^3 \log \left (\log (x)+e^4-1\right )-7 \left (1-\frac {6 e^4}{7}\right ) x^2-\log (x) \left (2 x^5+x^4-x^3-(2 x+1) x^3 \log \left (\log (x)+e^4-1\right )-6 x^2-3 x-6\right )-3 \left (1-e^4\right ) x-6 \left (1-e^4\right )\right )}{\left (-\log (x)-e^4+1\right ) \left (-x^3+x^2 \log \left (\log (x)+e^4-1\right )+3\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {e^{x^2+x} (2 x+1) x^2}{x^3-x^2 \log \left (\log (x)+e^4-1\right )-3}+\frac {e^{x^2+x} x \left (-\left (1-e^4\right ) x^3+x^3 \log (x)-x^2+6 \log (x)-6 \left (1-e^4\right )\right )}{\left (-\log (x)-e^4+1\right ) \left (-x^3+x^2 \log \left (\log (x)+e^4-1\right )+3\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 6 \left (1-e^4\right ) \int \frac {e^{x^2+x} x}{\left (\log (x)+e^4-1\right ) \left (x^3-\log \left (\log (x)+e^4-1\right ) x^2-3\right )^2}dx+\int \frac {e^{x^2+x} x^3}{\left (\log (x)+e^4-1\right ) \left (x^3-\log \left (\log (x)+e^4-1\right ) x^2-3\right )^2}dx-6 \int \frac {e^{x^2+x} x \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-\log \left (\log (x)+e^4-1\right ) x^2-3\right )^2}dx+\int \frac {e^{x^2+x} x^2}{x^3-\log \left (\log (x)+e^4-1\right ) x^2-3}dx+2 \int \frac {e^{x^2+x} x^3}{x^3-\log \left (\log (x)+e^4-1\right ) x^2-3}dx+\left (1-e^4\right ) \int \frac {e^{x^2+x} x^4}{\left (\log (x)+e^4-1\right ) \left (x^3-\log \left (\log (x)+e^4-1\right ) x^2-3\right )^2}dx-\int \frac {e^{x^2+x} x^4 \log (x)}{\left (\log (x)+e^4-1\right ) \left (x^3-\log \left (\log (x)+e^4-1\right ) x^2-3\right )^2}dx\) |
Int[(E^(x + x^2)*(6*x + 3*x^2 + 7*x^3 + x^4 - x^5 - 2*x^6 + E^4*(-6*x - 3* x^2 - 6*x^3 - x^4 + x^5 + 2*x^6)) + E^(x + x^2)*(-6*x - 3*x^2 - 6*x^3 - x^ 4 + x^5 + 2*x^6)*Log[x] + (E^(x + x^2)*(x^4 + 2*x^5 + E^4*(-x^4 - 2*x^5)) + E^(x + x^2)*(-x^4 - 2*x^5)*Log[x])*Log[-1 + E^4 + Log[x]])/(-9 + 6*x^3 - x^6 + E^4*(9 - 6*x^3 + x^6) + (9 - 6*x^3 + x^6)*Log[x] + (-6*x^2 + 2*x^5 + E^4*(6*x^2 - 2*x^5) + (6*x^2 - 2*x^5)*Log[x])*Log[-1 + E^4 + Log[x]] + ( -x^4 + E^4*x^4 + x^4*Log[x])*Log[-1 + E^4 + Log[x]]^2),x]
3.14.15.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 109.76 (sec) , antiderivative size = 30, normalized size of antiderivative = 0.97
| method | result | size |
| risch | \(\frac {x^{2} {\mathrm e}^{\left (1+x \right ) x}}{x^{3}-x^{2} \ln \left (\ln \left (x \right )+{\mathrm e}^{4}-1\right )-3}\) | \(30\) |
| parallelrisch | \(\frac {x^{2} {\mathrm e}^{x^{2}+x}}{x^{3}-x^{2} \ln \left (\ln \left (x \right )+{\mathrm e}^{4}-1\right )-3}\) | \(30\) |
int((((-2*x^5-x^4)*exp(x^2+x)*ln(x)+((-2*x^5-x^4)*exp(4)+2*x^5+x^4)*exp(x^ 2+x))*ln(ln(x)+exp(4)-1)+(2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(x^2+x)*ln(x)+ ((2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(4)-2*x^6-x^5+x^4+7*x^3+3*x^2+6*x)*exp (x^2+x))/((x^4*ln(x)+x^4*exp(4)-x^4)*ln(ln(x)+exp(4)-1)^2+((-2*x^5+6*x^2)* ln(x)+(-2*x^5+6*x^2)*exp(4)+2*x^5-6*x^2)*ln(ln(x)+exp(4)-1)+(x^6-6*x^3+9)* ln(x)+(x^6-6*x^3+9)*exp(4)-x^6+6*x^3-9),x,method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=\frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \left (x\right ) - 1\right ) - 3} \]
integrate((((-2*x^5-x^4)*exp(x^2+x)*log(x)+((-2*x^5-x^4)*exp(4)+2*x^5+x^4) *exp(x^2+x))*log(log(x)+exp(4)-1)+(2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(x^2+ x)*log(x)+((2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(4)-2*x^6-x^5+x^4+7*x^3+3*x^ 2+6*x)*exp(x^2+x))/((x^4*log(x)+x^4*exp(4)-x^4)*log(log(x)+exp(4)-1)^2+((- 2*x^5+6*x^2)*log(x)+(-2*x^5+6*x^2)*exp(4)+2*x^5-6*x^2)*log(log(x)+exp(4)-1 )+(x^6-6*x^3+9)*log(x)+(x^6-6*x^3+9)*exp(4)-x^6+6*x^3-9),x, algorithm=\
Time = 0.30 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.87 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=\frac {x^{2} e^{x^{2} + x}}{x^{3} - x^{2} \log {\left (\log {\left (x \right )} - 1 + e^{4} \right )} - 3} \]
integrate((((-2*x**5-x**4)*exp(x**2+x)*ln(x)+((-2*x**5-x**4)*exp(4)+2*x**5 +x**4)*exp(x**2+x))*ln(ln(x)+exp(4)-1)+(2*x**6+x**5-x**4-6*x**3-3*x**2-6*x )*exp(x**2+x)*ln(x)+((2*x**6+x**5-x**4-6*x**3-3*x**2-6*x)*exp(4)-2*x**6-x* *5+x**4+7*x**3+3*x**2+6*x)*exp(x**2+x))/((x**4*ln(x)+x**4*exp(4)-x**4)*ln( ln(x)+exp(4)-1)**2+((-2*x**5+6*x**2)*ln(x)+(-2*x**5+6*x**2)*exp(4)+2*x**5- 6*x**2)*ln(ln(x)+exp(4)-1)+(x**6-6*x**3+9)*ln(x)+(x**6-6*x**3+9)*exp(4)-x* *6+6*x**3-9),x)
Time = 0.29 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=\frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \left (x\right ) - 1\right ) - 3} \]
integrate((((-2*x^5-x^4)*exp(x^2+x)*log(x)+((-2*x^5-x^4)*exp(4)+2*x^5+x^4) *exp(x^2+x))*log(log(x)+exp(4)-1)+(2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(x^2+ x)*log(x)+((2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(4)-2*x^6-x^5+x^4+7*x^3+3*x^ 2+6*x)*exp(x^2+x))/((x^4*log(x)+x^4*exp(4)-x^4)*log(log(x)+exp(4)-1)^2+((- 2*x^5+6*x^2)*log(x)+(-2*x^5+6*x^2)*exp(4)+2*x^5-6*x^2)*log(log(x)+exp(4)-1 )+(x^6-6*x^3+9)*log(x)+(x^6-6*x^3+9)*exp(4)-x^6+6*x^3-9),x, algorithm=\
Time = 0.46 (sec) , antiderivative size = 29, normalized size of antiderivative = 0.94 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=\frac {x^{2} e^{\left (x^{2} + x\right )}}{x^{3} - x^{2} \log \left (e^{4} + \log \left (x\right ) - 1\right ) - 3} \]
integrate((((-2*x^5-x^4)*exp(x^2+x)*log(x)+((-2*x^5-x^4)*exp(4)+2*x^5+x^4) *exp(x^2+x))*log(log(x)+exp(4)-1)+(2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(x^2+ x)*log(x)+((2*x^6+x^5-x^4-6*x^3-3*x^2-6*x)*exp(4)-2*x^6-x^5+x^4+7*x^3+3*x^ 2+6*x)*exp(x^2+x))/((x^4*log(x)+x^4*exp(4)-x^4)*log(log(x)+exp(4)-1)^2+((- 2*x^5+6*x^2)*log(x)+(-2*x^5+6*x^2)*exp(4)+2*x^5-6*x^2)*log(log(x)+exp(4)-1 )+(x^6-6*x^3+9)*log(x)+(x^6-6*x^3+9)*exp(4)-x^6+6*x^3-9),x, algorithm=\
Time = 13.42 (sec) , antiderivative size = 268, normalized size of antiderivative = 8.65 \[ \int \frac {e^{x+x^2} \left (6 x+3 x^2+7 x^3+x^4-x^5-2 x^6+e^4 \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right )\right )+e^{x+x^2} \left (-6 x-3 x^2-6 x^3-x^4+x^5+2 x^6\right ) \log (x)+\left (e^{x+x^2} \left (x^4+2 x^5+e^4 \left (-x^4-2 x^5\right )\right )+e^{x+x^2} \left (-x^4-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )}{-9+6 x^3-x^6+e^4 \left (9-6 x^3+x^6\right )+\left (9-6 x^3+x^6\right ) \log (x)+\left (-6 x^2+2 x^5+e^4 \left (6 x^2-2 x^5\right )+\left (6 x^2-2 x^5\right ) \log (x)\right ) \log \left (-1+e^4+\log (x)\right )+\left (-x^4+e^4 x^4+x^4 \log (x)\right ) \log ^2\left (-1+e^4+\log (x)\right )} \, dx=-\frac {x^3\,\left (6\,{\mathrm {e}}^{x^2+x}-12\,{\mathrm {e}}^{x^2+x+4}+6\,{\mathrm {e}}^{x^2+x+8}-12\,{\mathrm {e}}^{x^2+x}\,\ln \left (x\right )+12\,{\mathrm {e}}^{x^2+x+4}\,\ln \left (x\right )+6\,{\mathrm {e}}^{x^2+x}\,{\ln \left (x\right )}^2\right )-x^5\,\left ({\mathrm {e}}^{x^2+x+4}-{\mathrm {e}}^{x^2+x}+{\mathrm {e}}^{x^2+x}\,\ln \left (x\right )\right )+x^6\,\left ({\mathrm {e}}^{x^2+x}-2\,{\mathrm {e}}^{x^2+x+4}+{\mathrm {e}}^{x^2+x+8}-2\,{\mathrm {e}}^{x^2+x}\,\ln \left (x\right )+2\,{\mathrm {e}}^{x^2+x+4}\,\ln \left (x\right )+{\mathrm {e}}^{x^2+x}\,{\ln \left (x\right )}^2\right )}{\left (x^2\,\ln \left ({\mathrm {e}}^4+\ln \left (x\right )-1\right )-x^3+3\right )\,\left (6\,x+6\,x\,{\ln \left (x\right )}^2-x^3\,\ln \left (x\right )-2\,x^4\,\ln \left (x\right )-12\,x\,{\mathrm {e}}^4+6\,x\,{\mathrm {e}}^8+x^4\,{\ln \left (x\right )}^2-x^3\,{\mathrm {e}}^4-2\,x^4\,{\mathrm {e}}^4+x^4\,{\mathrm {e}}^8-12\,x\,\ln \left (x\right )+x^3+x^4+12\,x\,{\mathrm {e}}^4\,\ln \left (x\right )+2\,x^4\,{\mathrm {e}}^4\,\ln \left (x\right )\right )} \]
int((exp(x + x^2)*(6*x - exp(4)*(6*x + 3*x^2 + 6*x^3 + x^4 - x^5 - 2*x^6) + 3*x^2 + 7*x^3 + x^4 - x^5 - 2*x^6) + log(exp(4) + log(x) - 1)*(exp(x + x ^2)*(x^4 - exp(4)*(x^4 + 2*x^5) + 2*x^5) - exp(x + x^2)*log(x)*(x^4 + 2*x^ 5)) - exp(x + x^2)*log(x)*(6*x + 3*x^2 + 6*x^3 + x^4 - x^5 - 2*x^6))/(log( exp(4) + log(x) - 1)^2*(x^4*log(x) + x^4*exp(4) - x^4) + exp(4)*(x^6 - 6*x ^3 + 9) + log(x)*(x^6 - 6*x^3 + 9) + 6*x^3 - x^6 + log(exp(4) + log(x) - 1 )*(log(x)*(6*x^2 - 2*x^5) + exp(4)*(6*x^2 - 2*x^5) - 6*x^2 + 2*x^5) - 9),x )
-(x^3*(6*exp(x + x^2) - 12*exp(x + x^2 + 4) + 6*exp(x + x^2 + 8) - 12*exp( x + x^2)*log(x) + 12*exp(x + x^2 + 4)*log(x) + 6*exp(x + x^2)*log(x)^2) - x^5*(exp(x + x^2 + 4) - exp(x + x^2) + exp(x + x^2)*log(x)) + x^6*(exp(x + x^2) - 2*exp(x + x^2 + 4) + exp(x + x^2 + 8) - 2*exp(x + x^2)*log(x) + 2* exp(x + x^2 + 4)*log(x) + exp(x + x^2)*log(x)^2))/((x^2*log(exp(4) + log(x ) - 1) - x^3 + 3)*(6*x + 6*x*log(x)^2 - x^3*log(x) - 2*x^4*log(x) - 12*x*e xp(4) + 6*x*exp(8) + x^4*log(x)^2 - x^3*exp(4) - 2*x^4*exp(4) + x^4*exp(8) - 12*x*log(x) + x^3 + x^4 + 12*x*exp(4)*log(x) + 2*x^4*exp(4)*log(x)))