Integrand size = 153, antiderivative size = 32 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2}{\left (e^{2 e^{4+x+(x+\log (x))^2}}+e^{-2+3 e^x}\right ) x} \]
Time = 0.42 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2 e^2}{\left (e^{3 e^x}+e^{2+2 e^{4+x+x^2+\log ^2(x)} x^{2 x}}\right ) x} \]
Integrate[(E^(-2 + 3*E^x)*(-2 - 6*E^x*x) + E^(2*E^(4 + x + x^2 + 2*x*Log[x ] + Log[x]^2))*(-2 + E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2)*(-12*x - 8*x^ 2 + (-8 - 8*x)*Log[x])))/(E^(4*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*x^ 2 + E^(-4 + 6*E^x)*x^2 + 2*E^(-2 + 3*E^x + 2*E^(4 + x + x^2 + 2*x*Log[x] + Log[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.
| \(\displaystyle \int \frac {e^{2 e^{x^2+x+\log ^2(x)+2 x \log (x)+4}} \left (e^{x^2+x+\log ^2(x)+2 x \log (x)+4} \left (-8 x^2-12 x+(-8 x-8) \log (x)\right )-2\right )+e^{3 e^x-2} \left (-6 e^x x-2\right )}{2 x^2 \exp \left (2 e^{x^2+x+\log ^2(x)+2 x \log (x)+4}+3 e^x-2\right )+e^{6 e^x-4} x^2+x^2 e^{4 e^{x^2+x+\log ^2(x)+2 x \log (x)+4}}} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {e^4 \left (e^{2 e^{x^2+x+\log ^2(x)+2 x \log (x)+4}} \left (e^{x^2+x+\log ^2(x)+2 x \log (x)+4} \left (-8 x^2-12 x+(-8 x-8) \log (x)\right )-2\right )+e^{3 e^x-2} \left (-6 e^x x-2\right )\right )}{x^2 \left (e^{2 x^{2 x} e^{x^2+x+\log ^2(x)+4}+2}+e^{3 e^x}\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle e^4 \int -\frac {2 \left (e^{-2+3 e^x} \left (3 e^x x+1\right )+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}} \left (2 e^{x^2+x+\log ^2(x)+4} \left (2 x^2+3 x+2 (x+1) \log (x)\right ) x^{2 x}+1\right )\right )}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2 x^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -2 e^4 \int \frac {e^{-2+3 e^x} \left (3 e^x x+1\right )+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}} \left (2 e^{x^2+x+\log ^2(x)+4} \left (2 x^2+3 x+2 (x+1) \log (x)\right ) x^{2 x}+1\right )}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2 x^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -2 e^4 \int \left (\frac {2 \exp \left (2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+x^2+x+\log ^2(x)+4\right ) \left (2 x^2+2 \log (x) x+3 x+2 \log (x)\right ) x^{2 x-2}}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2}+\frac {3 e^{x+3 e^x} x+e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}}{e^2 \left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2 x^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -2 e^4 \left (4 \int \frac {\exp \left (2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+x^2+x+\log ^2(x)+4\right ) x^{2 x}}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2}dx+6 \int \frac {\exp \left (2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+x^2+x+\log ^2(x)+4\right ) x^{2 x-1}}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2}dx+4 \int \frac {\exp \left (2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+x^2+x+\log ^2(x)+4\right ) x^{2 x-2} \log (x)}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2}dx+4 \int \frac {\exp \left (2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+x^2+x+\log ^2(x)+4\right ) x^{2 x-1} \log (x)}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2}dx+\frac {\int \frac {1}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right ) x^2}dx}{e^2}+\frac {3 \int \frac {e^{x+3 e^x}}{\left (e^{3 e^x}+e^{2 e^{x^2+x+\log ^2(x)+4} x^{2 x}+2}\right )^2 x}dx}{e^2}\right )\) |
Int[(E^(-2 + 3*E^x)*(-2 - 6*E^x*x) + E^(2*E^(4 + x + x^2 + 2*x*Log[x] + Lo g[x]^2))*(-2 + E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2)*(-12*x - 8*x^2 + (- 8 - 8*x)*Log[x])))/(E^(4*E^(4 + x + x^2 + 2*x*Log[x] + Log[x]^2))*x^2 + E^ (-4 + 6*E^x)*x^2 + 2*E^(-2 + 3*E^x + 2*E^(4 + x + x^2 + 2*x*Log[x] + Log[x ]^2))*x^2),x]
3.26.45.3.1 Defintions of rubi rules used
Int[(a_)*(Fx_), x_Symbol] :> Simp[a Int[Fx, x], x] /; FreeQ[a, x] && !Ma tchQ[Fx, (b_)*(Gx_) /; FreeQ[b, x]]
Time = 47.31 (sec) , antiderivative size = 35, normalized size of antiderivative = 1.09
| method | result | size |
| risch | \(\frac {2}{x \left ({\mathrm e}^{2 x^{2 x} {\mathrm e}^{\ln \left (x \right )^{2}+4+x^{2}+x}}+{\mathrm e}^{3 \,{\mathrm e}^{x}-2}\right )}\) | \(35\) |
| parallelrisch | \(\frac {2}{x \left ({\mathrm e}^{2 \,{\mathrm e}^{\ln \left (x \right )^{2}+2 x \ln \left (x \right )+x^{2}+x +4}}+{\mathrm e}^{3 \,{\mathrm e}^{x}-2}\right )}\) | \(35\) |
int(((((-8*x-8)*ln(x)-8*x^2-12*x)*exp(ln(x)^2+2*x*ln(x)+x^2+x+4)-2)*exp(ex p(ln(x)^2+2*x*ln(x)+x^2+x+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2))/(x^2*exp( exp(ln(x)^2+2*x*ln(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp(exp(ln(x)^2+2* x*ln(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x,method=_RETURNVERBOSE)
Time = 0.27 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.50 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2 \, e^{\left (3 \, e^{x} - 2\right )}}{x e^{\left (2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 3 \, e^{x} - 2\right )} + x e^{\left (6 \, e^{x} - 4\right )}} \]
integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)- 2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2) )/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp(e xp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm=\
2*e^(3*e^x - 2)/(x*e^(2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 3*e^x - 2) + x*e^(6*e^x - 4))
Time = 12.55 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.12 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2}{x e^{3 e^{x} - 2} + x e^{2 e^{x^{2} + 2 x \log {\left (x \right )} + x + \log {\left (x \right )}^{2} + 4}}} \]
integrate(((((-8*x-8)*ln(x)-8*x**2-12*x)*exp(ln(x)**2+2*x*ln(x)+x**2+x+4)- 2)*exp(exp(ln(x)**2+2*x*ln(x)+x**2+x+4))**2+(-6*exp(x)*x-2)*exp(3*exp(x)-2 ))/(x**2*exp(exp(ln(x)**2+2*x*ln(x)+x**2+x+4))**4+2*x**2*exp(3*exp(x)-2)*e xp(exp(ln(x)**2+2*x*ln(x)+x**2+x+4))**2+x**2*exp(3*exp(x)-2)**2),x)
Time = 0.31 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2 \, e^{2}}{x e^{\left (3 \, e^{x}\right )} + x e^{\left (2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 2\right )}} \]
integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)- 2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2) )/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp(e xp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 394 vs. \(2 (28) = 56\).
Time = 0.42 (sec) , antiderivative size = 394, normalized size of antiderivative = 12.31 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {2 \, {\left (4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 10\right )} + 4 \, x e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 10\right )} \log \left (x\right ) + 6 \, x e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 10\right )} - 3 \, x e^{\left (x + 6\right )} + 4 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 10\right )} \log \left (x\right )\right )}}{4 \, x^{3} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 10\right )} + 4 \, x^{3} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 3 \, e^{x} + 8\right )} + 4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 10\right )} \log \left (x\right ) + 4 \, x^{2} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 3 \, e^{x} + 8\right )} \log \left (x\right ) + 6 \, x^{2} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 10\right )} + 6 \, x^{2} e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 3 \, e^{x} + 8\right )} - 3 \, x^{2} e^{\left (x + 2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 6\right )} - 3 \, x^{2} e^{\left (x + 3 \, e^{x} + 4\right )} + 4 \, x e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 2 \, e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 4\right )} + 10\right )} \log \left (x\right ) + 4 \, x e^{\left (x^{2} + 2 \, x \log \left (x\right ) + \log \left (x\right )^{2} + x + 3 \, e^{x} + 8\right )} \log \left (x\right )} \]
integrate(((((-8*x-8)*log(x)-8*x^2-12*x)*exp(log(x)^2+2*x*log(x)+x^2+x+4)- 2)*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^2+(-6*exp(x)*x-2)*exp(3*exp(x)-2) )/(x^2*exp(exp(log(x)^2+2*x*log(x)+x^2+x+4))^4+2*x^2*exp(3*exp(x)-2)*exp(e xp(log(x)^2+2*x*log(x)+x^2+x+4))^2+x^2*exp(3*exp(x)-2)^2),x, algorithm=\
2*(4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10) + 4*x*e^(x^2 + 2*x*log(x ) + log(x)^2 + x + 10)*log(x) + 6*x*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 1 0) - 3*x*e^(x + 6) + 4*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 10)*log(x))/(4 *x^3*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 10) + 4*x^3*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 3*e^x + 8) + 4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*log(x) + log(x)^ 2 + x + 4) + 10)*log(x) + 4*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 3*e^x + 8)*log(x) + 6*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e^(x^2 + 2*x*l og(x) + log(x)^2 + x + 4) + 10) + 6*x^2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 3*e^x + 8) - 3*x^2*e^(x + 2*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 6 ) - 3*x^2*e^(x + 3*e^x + 4) + 4*x*e^(x^2 + 2*x*log(x) + log(x)^2 + x + 2*e ^(x^2 + 2*x*log(x) + log(x)^2 + x + 4) + 10)*log(x) + 4*x*e^(x^2 + 2*x*log (x) + log(x)^2 + x + 3*e^x + 8)*log(x))
Time = 8.72 (sec) , antiderivative size = 259, normalized size of antiderivative = 8.09 \[ \int \frac {e^{-2+3 e^x} \left (-2-6 e^x x\right )+e^{2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} \left (-2+e^{4+x+x^2+2 x \log (x)+\log ^2(x)} \left (-12 x-8 x^2+(-8-8 x) \log (x)\right )\right )}{e^{4 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2+e^{-4+6 e^x} x^2+2 e^{-2+3 e^x+2 e^{4+x+x^2+2 x \log (x)+\log ^2(x)}} x^2} \, dx=\frac {x\,\left (12\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}-6\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x-2}+8\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}\,\ln \left (x\right )\right )+8\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}+8\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}\,\ln \left (x\right )}{\left ({\mathrm {e}}^{3\,{\mathrm {e}}^x-2}+{\mathrm {e}}^{2\,x^{2\,x}\,{\mathrm {e}}^{x^2}\,{\mathrm {e}}^4\,{\mathrm {e}}^{{\ln \left (x\right )}^2}\,{\mathrm {e}}^x}\right )\,\left (6\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}-3\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x-2}+4\,x^{2\,x}\,x^3\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}+4\,x^{2\,x}\,x^2\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}\,\ln \left (x\right )+4\,x\,x^{2\,x}\,{\mathrm {e}}^{x+3\,{\mathrm {e}}^x+{\ln \left (x\right )}^2+x^2+2}\,\ln \left (x\right )\right )} \]
int(-(exp(3*exp(x) - 2)*(6*x*exp(x) + 2) + exp(2*exp(x + log(x)^2 + 2*x*lo g(x) + x^2 + 4))*(exp(x + log(x)^2 + 2*x*log(x) + x^2 + 4)*(12*x + log(x)* (8*x + 8) + 8*x^2) + 2))/(x^2*exp(4*exp(x + log(x)^2 + 2*x*log(x) + x^2 + 4)) + x^2*exp(6*exp(x) - 4) + 2*x^2*exp(3*exp(x) - 2)*exp(2*exp(x + log(x) ^2 + 2*x*log(x) + x^2 + 4))),x)
(x*(12*x^(2*x)*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) - 6*exp(x + 3*exp(x) - 2) + 8*x^(2*x)*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2)*log(x)) + 8*x^(2* x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) + 8*x^(2*x)*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2)*log(x))/((exp(3*exp(x) - 2) + exp(2*x^(2*x)*exp(x^2 )*exp(4)*exp(log(x)^2)*exp(x)))*(6*x^(2*x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) - 3*x^2*exp(x + 3*exp(x) - 2) + 4*x^(2*x)*x^3*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2) + 4*x^(2*x)*x^2*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2)*log(x) + 4*x*x^(2*x)*exp(x + 3*exp(x) + log(x)^2 + x^2 + 2)*log(x)))