Integrand size = 237, antiderivative size = 20 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {4+x}{-2+e+e^x+x-\log (3+\log (x))} \]
Time = 0.73 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {4+x}{-2+e+e^x+x-\log (3+\log (x))} \]
Integrate[(4 - 17*x + 3*E*x + E^x*(-9*x - 3*x^2) + (-6*x + E*x + E^x*(-3*x - x^2))*Log[x] + (-3*x - x*Log[x])*Log[3 + Log[x]])/(12*x + 3*E^2*x + 3*E ^(2*x)*x - 12*x^2 + 3*x^3 + E*(-12*x + 6*x^2) + E^x*(-12*x + 6*E*x + 6*x^2 ) + (4*x + E^2*x + E^(2*x)*x - 4*x^2 + x^3 + E*(-4*x + 2*x^2) + E^x*(-4*x + 2*E*x + 2*x^2))*Log[x] + (12*x - 6*E*x - 6*E^x*x - 6*x^2 + (4*x - 2*E*x - 2*E^x*x - 2*x^2)*Log[x])*Log[3 + Log[x]] + (3*x + x*Log[x])*Log[3 + 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.
| \(\displaystyle \int \frac {e^x \left (-3 x^2-9 x\right )+\left (e^x \left (-x^2-3 x\right )+e x-6 x\right ) \log (x)+3 e x-17 x+(x (-\log (x))-3 x) \log (\log (x)+3)+4}{3 x^3-12 x^2+e \left (6 x^2-12 x\right )+e^x \left (6 x^2+6 e x-12 x\right )+\left (-6 x^2+\left (-2 x^2-2 e^x x-2 e x+4 x\right ) \log (x)-6 e^x x-6 e x+12 x\right ) \log (\log (x)+3)+\left (x^3-4 x^2+e \left (2 x^2-4 x\right )+e^x \left (2 x^2+2 e x-4 x\right )+e^{2 x} x+e^2 x+4 x\right ) \log (x)+3 e^{2 x} x+3 e^2 x+12 x+(3 x+x \log (x)) \log ^2(\log (x)+3)} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {e^x \left (-3 x^2-9 x\right )+\left (e^x \left (-x^2-3 x\right )+e x-6 x\right ) \log (x)+(3 e-17) x+(x (-\log (x))-3 x) \log (\log (x)+3)+4}{3 x^3-12 x^2+e \left (6 x^2-12 x\right )+e^x \left (6 x^2+6 e x-12 x\right )+\left (-6 x^2+\left (-2 x^2-2 e^x x-2 e x+4 x\right ) \log (x)-6 e^x x-6 e x+12 x\right ) \log (\log (x)+3)+\left (x^3-4 x^2+e \left (2 x^2-4 x\right )+e^x \left (2 x^2+2 e x-4 x\right )+e^{2 x} x+e^2 x+4 x\right ) \log (x)+3 e^{2 x} x+3 e^2 x+12 x+(3 x+x \log (x)) \log ^2(\log (x)+3)}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {e^x \left (-3 x^2-9 x\right )+\left (e^x \left (-x^2-3 x\right )+e x-6 x\right ) \log (x)+(3 e-17) x+(x (-\log (x))-3 x) \log (\log (x)+3)+4}{3 x^3-12 x^2+e \left (6 x^2-12 x\right )+e^x \left (6 x^2+6 e x-12 x\right )+\left (-6 x^2+\left (-2 x^2-2 e^x x-2 e x+4 x\right ) \log (x)-6 e^x x-6 e x+12 x\right ) \log (\log (x)+3)+\left (x^3-4 x^2+e \left (2 x^2-4 x\right )+e^x \left (2 x^2+2 e x-4 x\right )+e^{2 x} x+e^2 x+4 x\right ) \log (x)+3 e^{2 x} x+\left (12+3 e^2\right ) x+(3 x+x \log (x)) \log ^2(\log (x)+3)}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-3 e^x x^2-9 e^x x-17 \left (1-\frac {3 e}{17}\right ) x-3 x \log (\log (x)+3)-x \log (x) \left (e^x (x+3)+\log (\log (x)+3)-e+6\right )+4}{x (\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {(x+4) \left (3 x^2+x^2 \log (x)-9 \left (1-\frac {e}{3}\right ) x-3 \left (1-\frac {e}{3}\right ) x \log (x)-x \log (x) \log (\log (x)+3)-3 x \log (\log (x)+3)+1\right )}{x (\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}+\frac {x+3}{-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 3 \int \frac {x^2}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+\int \frac {x^2 \log (x)}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx-12 (3-e) \int \frac {1}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+\int \frac {1}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+4 \int \frac {1}{x (\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx-3 (3-e) \int \frac {x}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+12 \int \frac {x}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx-4 (3-e) \int \frac {\log (x)}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx-(3-e) \int \frac {x \log (x)}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+4 \int \frac {x \log (x)}{(\log (x)+3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+12 \int \frac {\log (\log (x)+3)}{(-\log (x)-3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+3 \int \frac {x \log (\log (x)+3)}{(-\log (x)-3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+4 \int \frac {\log (x) \log (\log (x)+3)}{(-\log (x)-3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+\int \frac {x \log (x) \log (\log (x)+3)}{(-\log (x)-3) \left (-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )\right )^2}dx+3 \int \frac {1}{-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )}dx+\int \frac {x}{-x-e^x+\log (\log (x)+3)+2 \left (1-\frac {e}{2}\right )}dx\) |
Int[(4 - 17*x + 3*E*x + E^x*(-9*x - 3*x^2) + (-6*x + E*x + E^x*(-3*x - x^2 ))*Log[x] + (-3*x - x*Log[x])*Log[3 + Log[x]])/(12*x + 3*E^2*x + 3*E^(2*x) *x - 12*x^2 + 3*x^3 + E*(-12*x + 6*x^2) + E^x*(-12*x + 6*E*x + 6*x^2) + (4 *x + E^2*x + E^(2*x)*x - 4*x^2 + x^3 + E*(-4*x + 2*x^2) + E^x*(-4*x + 2*E* x + 2*x^2))*Log[x] + (12*x - 6*E*x - 6*E^x*x - 6*x^2 + (4*x - 2*E*x - 2*E^ x*x - 2*x^2)*Log[x])*Log[3 + Log[x]] + (3*x + x*Log[x])*Log[3 + Log[x]]^2) ,x]
3.9.41.3.1 Defintions of rubi rules used
Int[(u_.)*((v_.) + (a_.)*(Fx_) + (b_.)*(Fx_))^(p_.), x_Symbol] :> Int[u*(v + (a + b)*Fx)^p, x] /; FreeQ[{a, b}, x] && !FreeQ[Fx, x]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 4.71 (sec) , antiderivative size = 21, normalized size of antiderivative = 1.05
| method | result | size |
| risch | \(\frac {4+x}{x -2+{\mathrm e}^{x}+{\mathrm e}-\ln \left (3+\ln \left (x \right )\right )}\) | \(21\) |
| parallelrisch | \(-\frac {-4-x}{x -2+{\mathrm e}^{x}+{\mathrm e}-\ln \left (3+\ln \left (x \right )\right )}\) | \(24\) |
int(((-x*ln(x)-3*x)*ln(3+ln(x))+((-x^2-3*x)*exp(x)+x*exp(1)-6*x)*ln(x)+(-3 *x^2-9*x)*exp(x)+3*x*exp(1)-17*x+4)/((x*ln(x)+3*x)*ln(3+ln(x))^2+((-2*exp( x)*x-2*x*exp(1)-2*x^2+4*x)*ln(x)-6*exp(x)*x-6*x*exp(1)-6*x^2+12*x)*ln(3+ln (x))+(x*exp(x)^2+(2*x*exp(1)+2*x^2-4*x)*exp(x)+x*exp(1)^2+(2*x^2-4*x)*exp( 1)+x^3-4*x^2+4*x)*ln(x)+3*x*exp(x)^2+(6*x*exp(1)+6*x^2-12*x)*exp(x)+3*x*ex p(1)^2+(6*x^2-12*x)*exp(1)+3*x^3-12*x^2+12*x),x,method=_RETURNVERBOSE)
Time = 0.28 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {x + 4}{x + e + e^{x} - \log \left (\log \left (x\right ) + 3\right ) - 2} \]
integrate(((-x*log(x)-3*x)*log(3+log(x))+((-x^2-3*x)*exp(x)+x*exp(1)-6*x)* log(x)+(-3*x^2-9*x)*exp(x)+3*x*exp(1)-17*x+4)/((x*log(x)+3*x)*log(3+log(x) )^2+((-2*exp(x)*x-2*x*exp(1)-2*x^2+4*x)*log(x)-6*exp(x)*x-6*x*exp(1)-6*x^2 +12*x)*log(3+log(x))+(x*exp(x)^2+(2*x*exp(1)+2*x^2-4*x)*exp(x)+x*exp(1)^2+ (2*x^2-4*x)*exp(1)+x^3-4*x^2+4*x)*log(x)+3*x*exp(x)^2+(6*x*exp(1)+6*x^2-12 *x)*exp(x)+3*x*exp(1)^2+(6*x^2-12*x)*exp(1)+3*x^3-12*x^2+12*x),x, algorith m=\
Time = 0.17 (sec) , antiderivative size = 19, normalized size of antiderivative = 0.95 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {x + 4}{x + e^{x} - \log {\left (\log {\left (x \right )} + 3 \right )} - 2 + e} \]
integrate(((-x*ln(x)-3*x)*ln(3+ln(x))+((-x**2-3*x)*exp(x)+x*exp(1)-6*x)*ln (x)+(-3*x**2-9*x)*exp(x)+3*x*exp(1)-17*x+4)/((x*ln(x)+3*x)*ln(3+ln(x))**2+ ((-2*exp(x)*x-2*x*exp(1)-2*x**2+4*x)*ln(x)-6*exp(x)*x-6*x*exp(1)-6*x**2+12 *x)*ln(3+ln(x))+(x*exp(x)**2+(2*x*exp(1)+2*x**2-4*x)*exp(x)+x*exp(1)**2+(2 *x**2-4*x)*exp(1)+x**3-4*x**2+4*x)*ln(x)+3*x*exp(x)**2+(6*x*exp(1)+6*x**2- 12*x)*exp(x)+3*x*exp(1)**2+(6*x**2-12*x)*exp(1)+3*x**3-12*x**2+12*x),x)
Time = 0.36 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {x + 4}{x + e + e^{x} - \log \left (\log \left (x\right ) + 3\right ) - 2} \]
integrate(((-x*log(x)-3*x)*log(3+log(x))+((-x^2-3*x)*exp(x)+x*exp(1)-6*x)* log(x)+(-3*x^2-9*x)*exp(x)+3*x*exp(1)-17*x+4)/((x*log(x)+3*x)*log(3+log(x) )^2+((-2*exp(x)*x-2*x*exp(1)-2*x^2+4*x)*log(x)-6*exp(x)*x-6*x*exp(1)-6*x^2 +12*x)*log(3+log(x))+(x*exp(x)^2+(2*x*exp(1)+2*x^2-4*x)*exp(x)+x*exp(1)^2+ (2*x^2-4*x)*exp(1)+x^3-4*x^2+4*x)*log(x)+3*x*exp(x)^2+(6*x*exp(1)+6*x^2-12 *x)*exp(x)+3*x*exp(1)^2+(6*x^2-12*x)*exp(1)+3*x^3-12*x^2+12*x),x, algorith m=\
Time = 0.35 (sec) , antiderivative size = 20, normalized size of antiderivative = 1.00 \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\frac {x + 4}{x + e + e^{x} - \log \left (\log \left (x\right ) + 3\right ) - 2} \]
integrate(((-x*log(x)-3*x)*log(3+log(x))+((-x^2-3*x)*exp(x)+x*exp(1)-6*x)* log(x)+(-3*x^2-9*x)*exp(x)+3*x*exp(1)-17*x+4)/((x*log(x)+3*x)*log(3+log(x) )^2+((-2*exp(x)*x-2*x*exp(1)-2*x^2+4*x)*log(x)-6*exp(x)*x-6*x*exp(1)-6*x^2 +12*x)*log(3+log(x))+(x*exp(x)^2+(2*x*exp(1)+2*x^2-4*x)*exp(x)+x*exp(1)^2+ (2*x^2-4*x)*exp(1)+x^3-4*x^2+4*x)*log(x)+3*x*exp(x)^2+(6*x*exp(1)+6*x^2-12 *x)*exp(x)+3*x*exp(1)^2+(6*x^2-12*x)*exp(1)+3*x^3-12*x^2+12*x),x, algorith m=\
Timed out. \[ \int \frac {4-17 x+3 e x+e^x \left (-9 x-3 x^2\right )+\left (-6 x+e x+e^x \left (-3 x-x^2\right )\right ) \log (x)+(-3 x-x \log (x)) \log (3+\log (x))}{12 x+3 e^2 x+3 e^{2 x} x-12 x^2+3 x^3+e \left (-12 x+6 x^2\right )+e^x \left (-12 x+6 e x+6 x^2\right )+\left (4 x+e^2 x+e^{2 x} x-4 x^2+x^3+e \left (-4 x+2 x^2\right )+e^x \left (-4 x+2 e x+2 x^2\right )\right ) \log (x)+\left (12 x-6 e x-6 e^x x-6 x^2+\left (4 x-2 e x-2 e^x x-2 x^2\right ) \log (x)\right ) \log (3+\log (x))+(3 x+x \log (x)) \log ^2(3+\log (x))} \, dx=\int -\frac {17\,x+\ln \left (\ln \left (x\right )+3\right )\,\left (3\,x+x\,\ln \left (x\right )\right )+\ln \left (x\right )\,\left (6\,x-x\,\mathrm {e}+{\mathrm {e}}^x\,\left (x^2+3\,x\right )\right )-3\,x\,\mathrm {e}+{\mathrm {e}}^x\,\left (3\,x^2+9\,x\right )-4}{12\,x-\ln \left (\ln \left (x\right )+3\right )\,\left (6\,x\,\mathrm {e}-12\,x+\ln \left (x\right )\,\left (2\,x\,\mathrm {e}-4\,x+2\,x\,{\mathrm {e}}^x+2\,x^2\right )+6\,x\,{\mathrm {e}}^x+6\,x^2\right )+3\,x\,{\mathrm {e}}^{2\,x}-\mathrm {e}\,\left (12\,x-6\,x^2\right )+3\,x\,{\mathrm {e}}^2+{\ln \left (\ln \left (x\right )+3\right )}^2\,\left (3\,x+x\,\ln \left (x\right )\right )-12\,x^2+3\,x^3+{\mathrm {e}}^x\,\left (6\,x\,\mathrm {e}-12\,x+6\,x^2\right )+\ln \left (x\right )\,\left (4\,x+x\,{\mathrm {e}}^{2\,x}-\mathrm {e}\,\left (4\,x-2\,x^2\right )+x\,{\mathrm {e}}^2-4\,x^2+x^3+{\mathrm {e}}^x\,\left (2\,x\,\mathrm {e}-4\,x+2\,x^2\right )\right )} \,d x \]
int(-(17*x + log(log(x) + 3)*(3*x + x*log(x)) + log(x)*(6*x - x*exp(1) + e xp(x)*(3*x + x^2)) - 3*x*exp(1) + exp(x)*(9*x + 3*x^2) - 4)/(12*x - log(lo g(x) + 3)*(6*x*exp(1) - 12*x + log(x)*(2*x*exp(1) - 4*x + 2*x*exp(x) + 2*x ^2) + 6*x*exp(x) + 6*x^2) + 3*x*exp(2*x) - exp(1)*(12*x - 6*x^2) + 3*x*exp (2) + log(log(x) + 3)^2*(3*x + x*log(x)) - 12*x^2 + 3*x^3 + exp(x)*(6*x*ex p(1) - 12*x + 6*x^2) + log(x)*(4*x + x*exp(2*x) - exp(1)*(4*x - 2*x^2) + x *exp(2) - 4*x^2 + x^3 + exp(x)*(2*x*exp(1) - 4*x + 2*x^2))),x)
int(-(17*x + log(log(x) + 3)*(3*x + x*log(x)) + log(x)*(6*x - x*exp(1) + e xp(x)*(3*x + x^2)) - 3*x*exp(1) + exp(x)*(9*x + 3*x^2) - 4)/(12*x - log(lo g(x) + 3)*(6*x*exp(1) - 12*x + log(x)*(2*x*exp(1) - 4*x + 2*x*exp(x) + 2*x ^2) + 6*x*exp(x) + 6*x^2) + 3*x*exp(2*x) - exp(1)*(12*x - 6*x^2) + 3*x*exp (2) + log(log(x) + 3)^2*(3*x + x*log(x)) - 12*x^2 + 3*x^3 + exp(x)*(6*x*ex p(1) - 12*x + 6*x^2) + log(x)*(4*x + x*exp(2*x) - exp(1)*(4*x - 2*x^2) + x *exp(2) - 4*x^2 + x^3 + exp(x)*(2*x*exp(1) - 4*x + 2*x^2))), x)