Integrand size = 259, antiderivative size = 31 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {x}{1+2 x-x \left (-e^{3 x}+\frac {\log (5)}{1+e-x}\right )} \]
Time = 0.09 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {(1+e-x) x}{1+e+x+2 e x+e^{1+3 x} x-e^{3 x} (-1+x) x-2 x^2-x \log (5)} \]
Integrate[(1 + E^2 + E*(2 - 2*x) - 2*x + x^2 + E^(3*x)*(-3*x^2 - 3*E^2*x^2 + 6*x^3 - 3*x^4 + E*(-6*x^2 + 6*x^3)) + x^2*Log[5])/(1 + 2*x - 3*x^2 - 4* x^3 + 4*x^4 + E^2*(1 + 4*x + 4*x^2) + E*(2 + 6*x - 8*x^3) + E^(6*x)*(x^2 + E^2*x^2 - 2*x^3 + x^4 + E*(2*x^2 - 2*x^3)) + (-2*x - 2*x^2 + 4*x^3 + E*(- 2*x - 4*x^2))*Log[5] + x^2*Log[5]^2 + E^(3*x)*(2*x - 6*x^3 + 4*x^4 + E^2*( 2*x + 4*x^2) + E*(4*x + 4*x^2 - 8*x^3) + (-2*x^2 - 2*E*x^2 + 2*x^3)*Log[5] )),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.
| \(\displaystyle \int \frac {x^2+x^2 \log (5)+e^{3 x} \left (-3 x^4+6 x^3-3 e^2 x^2-3 x^2+e \left (6 x^3-6 x^2\right )\right )-2 x+e (2-2 x)+e^2+1}{4 x^4-4 x^3+e \left (-8 x^3+6 x+2\right )-3 x^2+e^2 \left (4 x^2+4 x+1\right )+x^2 \log ^2(5)+\left (4 x^3-2 x^2+e \left (-4 x^2-2 x\right )-2 x\right ) \log (5)+e^{6 x} \left (x^4-2 x^3+e^2 x^2+x^2+e \left (2 x^2-2 x^3\right )\right )+e^{3 x} \left (4 x^4-6 x^3+e^2 \left (4 x^2+2 x\right )+e \left (-8 x^3+4 x^2+4 x\right )+\left (2 x^3-2 e x^2-2 x^2\right ) \log (5)+2 x\right )+2 x+1} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x^2 (1+\log (5))+e^{3 x} \left (-3 x^4+6 x^3-3 e^2 x^2-3 x^2+e \left (6 x^3-6 x^2\right )\right )-2 x+e (2-2 x)+e^2+1}{4 x^4-4 x^3+e \left (-8 x^3+6 x+2\right )-3 x^2+e^2 \left (4 x^2+4 x+1\right )+x^2 \log ^2(5)+\left (4 x^3-2 x^2+e \left (-4 x^2-2 x\right )-2 x\right ) \log (5)+e^{6 x} \left (x^4-2 x^3+e^2 x^2+x^2+e \left (2 x^2-2 x^3\right )\right )+e^{3 x} \left (4 x^4-6 x^3+e^2 \left (4 x^2+2 x\right )+e \left (-8 x^3+4 x^2+4 x\right )+\left (2 x^3-2 e x^2-2 x^2\right ) \log (5)+2 x\right )+2 x+1}dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {x^2 (1+\log (5))+e^{3 x} \left (-3 x^4+6 x^3-3 e^2 x^2-3 x^2+e \left (6 x^3-6 x^2\right )\right )-2 x+e (2-2 x)+e^2+1}{4 x^4-4 x^3+e \left (-8 x^3+6 x+2\right )+e^2 \left (4 x^2+4 x+1\right )+x^2 \left (\log ^2(5)-3\right )+\left (4 x^3-2 x^2+e \left (-4 x^2-2 x\right )-2 x\right ) \log (5)+e^{6 x} \left (x^4-2 x^3+e^2 x^2+x^2+e \left (2 x^2-2 x^3\right )\right )+e^{3 x} \left (4 x^4-6 x^3+e^2 \left (4 x^2+2 x\right )+e \left (-8 x^3+4 x^2+4 x\right )+\left (2 x^3-2 e x^2-2 x^2\right ) \log (5)+2 x\right )+2 x+1}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {-3 e^{3 x+2} x^2-3 e^{3 x} (x-1)^2 x^2+6 e^{3 x+1} (x-1) x^2+x^2 (1+\log (5))-2 x-2 e (x-1)+e^2+1}{\left (-2 x^2+e^{3 x+1} x-e^{3 x} (x-1) x+x (1+2 e-\log (5))+e+1\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {3 x (x-e-1)}{-e^{3 x} x^2-2 x^2+(1+e) e^{3 x} x+x (1+2 e-\log (5))+e+1}+\frac {6 x^4-3 x^3 (3+4 e-\log (5))+x^2 \left (1+6 e^2+3 e (2-\log (5))-2 \log (5)\right )+(1+e) (1+3 e) x+(1+e)^2}{\left (-e^{3 x} x^2-2 x^2+(1+e) e^{3 x} x+x (1+2 e-\log (5))+e+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle (1+e)^2 \int \frac {1}{\left (-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1\right )^2}dx+(1+e) (1+3 e) \int \frac {x}{\left (-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1\right )^2}dx+\left (1+6 e^2+3 e (2-\log (5))-2 \log (5)\right ) \int \frac {x^2}{\left (-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1\right )^2}dx-3 (1+e) \int \frac {x}{-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1}dx+3 \int \frac {x^2}{-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1}dx+6 \int \frac {x^4}{\left (-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1\right )^2}dx-3 (3+4 e-\log (5)) \int \frac {x^3}{\left (-e^{3 x} x^2-2 x^2+(1+2 e-\log (5)) x+e^{3 x} (1+e) x+e+1\right )^2}dx\) |
Int[(1 + E^2 + E*(2 - 2*x) - 2*x + x^2 + E^(3*x)*(-3*x^2 - 3*E^2*x^2 + 6*x ^3 - 3*x^4 + E*(-6*x^2 + 6*x^3)) + x^2*Log[5])/(1 + 2*x - 3*x^2 - 4*x^3 + 4*x^4 + E^2*(1 + 4*x + 4*x^2) + E*(2 + 6*x - 8*x^3) + E^(6*x)*(x^2 + E^2*x ^2 - 2*x^3 + x^4 + E*(2*x^2 - 2*x^3)) + (-2*x - 2*x^2 + 4*x^3 + E*(-2*x - 4*x^2))*Log[5] + x^2*Log[5]^2 + E^(3*x)*(2*x - 6*x^3 + 4*x^4 + E^2*(2*x + 4*x^2) + E*(4*x + 4*x^2 - 8*x^3) + (-2*x^2 - 2*E*x^2 + 2*x^3)*Log[5])),x]
3.29.36.3.1 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 = 0.92 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.77
| method | result | size |
| risch | \(\frac {\left ({\mathrm e}-x +1\right ) x}{x \,{\mathrm e}^{1+3 x}-x^{2} {\mathrm e}^{3 x}+2 x \,{\mathrm e}-x \ln \left (5\right )+x \,{\mathrm e}^{3 x}-2 x^{2}+{\mathrm e}+x +1}\) | \(55\) |
| norman | \(\frac {-x^{2}+\left (1+{\mathrm e}\right ) x}{{\mathrm e} \,{\mathrm e}^{3 x} x -x^{2} {\mathrm e}^{3 x}+2 x \,{\mathrm e}-x \ln \left (5\right )+x \,{\mathrm e}^{3 x}-2 x^{2}+{\mathrm e}+x +1}\) | \(59\) |
| parallelrisch | \(-\frac {-x \,{\mathrm e}+x^{2}-x}{{\mathrm e} \,{\mathrm e}^{3 x} x -x^{2} {\mathrm e}^{3 x}+2 x \,{\mathrm e}-x \ln \left (5\right )+x \,{\mathrm e}^{3 x}-2 x^{2}+{\mathrm e}+x +1}\) | \(60\) |
int(((-3*x^2*exp(1)^2+(6*x^3-6*x^2)*exp(1)-3*x^4+6*x^3-3*x^2)*exp(3*x)+x^2 *ln(5)+exp(1)^2+(2-2*x)*exp(1)+x^2-2*x+1)/((x^2*exp(1)^2+(-2*x^3+2*x^2)*ex p(1)+x^4-2*x^3+x^2)*exp(3*x)^2+((-2*x^2*exp(1)+2*x^3-2*x^2)*ln(5)+(4*x^2+2 *x)*exp(1)^2+(-8*x^3+4*x^2+4*x)*exp(1)+4*x^4-6*x^3+2*x)*exp(3*x)+x^2*ln(5) ^2+((-4*x^2-2*x)*exp(1)+4*x^3-2*x^2-2*x)*ln(5)+(4*x^2+4*x+1)*exp(1)^2+(-8* x^3+6*x+2)*exp(1)+4*x^4-4*x^3-3*x^2+2*x+1),x,method=_RETURNVERBOSE)
Time = 0.24 (sec) , antiderivative size = 55, normalized size of antiderivative = 1.77 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {x^{2} - x e - x}{2 \, x^{2} - {\left (2 \, x + 1\right )} e + {\left (x^{2} - x e - x\right )} e^{\left (3 \, x\right )} + x \log \left (5\right ) - x - 1} \]
integrate(((-3*x^2*exp(1)^2+(6*x^3-6*x^2)*exp(1)-3*x^4+6*x^3-3*x^2)*exp(3* x)+x^2*log(5)+exp(1)^2+(2-2*x)*exp(1)+x^2-2*x+1)/((x^2*exp(1)^2+(-2*x^3+2* x^2)*exp(1)+x^4-2*x^3+x^2)*exp(3*x)^2+((-2*x^2*exp(1)+2*x^3-2*x^2)*log(5)+ (4*x^2+2*x)*exp(1)^2+(-8*x^3+4*x^2+4*x)*exp(1)+4*x^4-6*x^3+2*x)*exp(3*x)+x ^2*log(5)^2+((-4*x^2-2*x)*exp(1)+4*x^3-2*x^2-2*x)*log(5)+(4*x^2+4*x+1)*exp (1)^2+(-8*x^3+6*x+2)*exp(1)+4*x^4-4*x^3-3*x^2+2*x+1),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 48 vs. \(2 (22) = 44\).
Time = 0.37 (sec) , antiderivative size = 48, normalized size of antiderivative = 1.55 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {x^{2} - e x - x}{2 x^{2} - 2 e x - x + x \log {\left (5 \right )} + \left (x^{2} - e x - x\right ) e^{3 x} - e - 1} \]
integrate(((-3*x**2*exp(1)**2+(6*x**3-6*x**2)*exp(1)-3*x**4+6*x**3-3*x**2) *exp(3*x)+x**2*ln(5)+exp(1)**2+(2-2*x)*exp(1)+x**2-2*x+1)/((x**2*exp(1)**2 +(-2*x**3+2*x**2)*exp(1)+x**4-2*x**3+x**2)*exp(3*x)**2+((-2*x**2*exp(1)+2* x**3-2*x**2)*ln(5)+(4*x**2+2*x)*exp(1)**2+(-8*x**3+4*x**2+4*x)*exp(1)+4*x* *4-6*x**3+2*x)*exp(3*x)+x**2*ln(5)**2+((-4*x**2-2*x)*exp(1)+4*x**3-2*x**2- 2*x)*ln(5)+(4*x**2+4*x+1)*exp(1)**2+(-8*x**3+6*x+2)*exp(1)+4*x**4-4*x**3-3 *x**2+2*x+1),x)
Time = 0.53 (sec) , antiderivative size = 54, normalized size of antiderivative = 1.74 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {x^{2} - x {\left (e + 1\right )}}{2 \, x^{2} - x {\left (2 \, e - \log \left (5\right ) + 1\right )} + {\left (x^{2} - x {\left (e + 1\right )}\right )} e^{\left (3 \, x\right )} - e - 1} \]
integrate(((-3*x^2*exp(1)^2+(6*x^3-6*x^2)*exp(1)-3*x^4+6*x^3-3*x^2)*exp(3* x)+x^2*log(5)+exp(1)^2+(2-2*x)*exp(1)+x^2-2*x+1)/((x^2*exp(1)^2+(-2*x^3+2* x^2)*exp(1)+x^4-2*x^3+x^2)*exp(3*x)^2+((-2*x^2*exp(1)+2*x^3-2*x^2)*log(5)+ (4*x^2+2*x)*exp(1)^2+(-8*x^3+4*x^2+4*x)*exp(1)+4*x^4-6*x^3+2*x)*exp(3*x)+x ^2*log(5)^2+((-4*x^2-2*x)*exp(1)+4*x^3-2*x^2-2*x)*log(5)+(4*x^2+4*x+1)*exp (1)^2+(-8*x^3+6*x+2)*exp(1)+4*x^4-4*x^3-3*x^2+2*x+1),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 62 vs. \(2 (28) = 56\).
Time = 0.43 (sec) , antiderivative size = 62, normalized size of antiderivative = 2.00 \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\frac {x^{2} - x e - x}{x^{2} e^{\left (3 \, x\right )} + 2 \, x^{2} - 2 \, x e - x e^{\left (3 \, x\right )} - x e^{\left (3 \, x + 1\right )} + x \log \left (5\right ) - x - e - 1} \]
integrate(((-3*x^2*exp(1)^2+(6*x^3-6*x^2)*exp(1)-3*x^4+6*x^3-3*x^2)*exp(3* x)+x^2*log(5)+exp(1)^2+(2-2*x)*exp(1)+x^2-2*x+1)/((x^2*exp(1)^2+(-2*x^3+2* x^2)*exp(1)+x^4-2*x^3+x^2)*exp(3*x)^2+((-2*x^2*exp(1)+2*x^3-2*x^2)*log(5)+ (4*x^2+2*x)*exp(1)^2+(-8*x^3+4*x^2+4*x)*exp(1)+4*x^4-6*x^3+2*x)*exp(3*x)+x ^2*log(5)^2+((-4*x^2-2*x)*exp(1)+4*x^3-2*x^2-2*x)*log(5)+(4*x^2+4*x+1)*exp (1)^2+(-8*x^3+6*x+2)*exp(1)+4*x^4-4*x^3-3*x^2+2*x+1),x, algorithm=\
(x^2 - x*e - x)/(x^2*e^(3*x) + 2*x^2 - 2*x*e - x*e^(3*x) - x*e^(3*x + 1) + x*log(5) - x - e - 1)
Timed out. \[ \int \frac {1+e^2+e (2-2 x)-2 x+x^2+e^{3 x} \left (-3 x^2-3 e^2 x^2+6 x^3-3 x^4+e \left (-6 x^2+6 x^3\right )\right )+x^2 \log (5)}{1+2 x-3 x^2-4 x^3+4 x^4+e^2 \left (1+4 x+4 x^2\right )+e \left (2+6 x-8 x^3\right )+e^{6 x} \left (x^2+e^2 x^2-2 x^3+x^4+e \left (2 x^2-2 x^3\right )\right )+\left (-2 x-2 x^2+4 x^3+e \left (-2 x-4 x^2\right )\right ) \log (5)+x^2 \log ^2(5)+e^{3 x} \left (2 x-6 x^3+4 x^4+e^2 \left (2 x+4 x^2\right )+e \left (4 x+4 x^2-8 x^3\right )+\left (-2 x^2-2 e x^2+2 x^3\right ) \log (5)\right )} \, dx=\int \frac {{\mathrm {e}}^2-2\,x+x^2\,\ln \left (5\right )-{\mathrm {e}}^{3\,x}\,\left (\mathrm {e}\,\left (6\,x^2-6\,x^3\right )+3\,x^2\,{\mathrm {e}}^2+3\,x^2-6\,x^3+3\,x^4\right )+x^2-\mathrm {e}\,\left (2\,x-2\right )+1}{2\,x+x^2\,{\ln \left (5\right )}^2+{\mathrm {e}}^{6\,x}\,\left (\mathrm {e}\,\left (2\,x^2-2\,x^3\right )+x^2\,{\mathrm {e}}^2+x^2-2\,x^3+x^4\right )+{\mathrm {e}}^{3\,x}\,\left (2\,x+{\mathrm {e}}^2\,\left (4\,x^2+2\,x\right )-\ln \left (5\right )\,\left (2\,x^2\,\mathrm {e}+2\,x^2-2\,x^3\right )+\mathrm {e}\,\left (-8\,x^3+4\,x^2+4\,x\right )-6\,x^3+4\,x^4\right )+{\mathrm {e}}^2\,\left (4\,x^2+4\,x+1\right )+\mathrm {e}\,\left (-8\,x^3+6\,x+2\right )-\ln \left (5\right )\,\left (2\,x+\mathrm {e}\,\left (4\,x^2+2\,x\right )+2\,x^2-4\,x^3\right )-3\,x^2-4\,x^3+4\,x^4+1} \,d x \]
int((exp(2) - 2*x + x^2*log(5) - exp(3*x)*(exp(1)*(6*x^2 - 6*x^3) + 3*x^2* exp(2) + 3*x^2 - 6*x^3 + 3*x^4) + x^2 - exp(1)*(2*x - 2) + 1)/(2*x + x^2*l og(5)^2 + exp(6*x)*(exp(1)*(2*x^2 - 2*x^3) + x^2*exp(2) + x^2 - 2*x^3 + x^ 4) + exp(3*x)*(2*x + exp(2)*(2*x + 4*x^2) - log(5)*(2*x^2*exp(1) + 2*x^2 - 2*x^3) + exp(1)*(4*x + 4*x^2 - 8*x^3) - 6*x^3 + 4*x^4) + exp(2)*(4*x + 4* x^2 + 1) + exp(1)*(6*x - 8*x^3 + 2) - log(5)*(2*x + exp(1)*(2*x + 4*x^2) + 2*x^2 - 4*x^3) - 3*x^2 - 4*x^3 + 4*x^4 + 1),x)
int((exp(2) - 2*x + x^2*log(5) - exp(3*x)*(exp(1)*(6*x^2 - 6*x^3) + 3*x^2* exp(2) + 3*x^2 - 6*x^3 + 3*x^4) + x^2 - exp(1)*(2*x - 2) + 1)/(2*x + x^2*l og(5)^2 + exp(6*x)*(exp(1)*(2*x^2 - 2*x^3) + x^2*exp(2) + x^2 - 2*x^3 + x^ 4) + exp(3*x)*(2*x + exp(2)*(2*x + 4*x^2) - log(5)*(2*x^2*exp(1) + 2*x^2 - 2*x^3) + exp(1)*(4*x + 4*x^2 - 8*x^3) - 6*x^3 + 4*x^4) + exp(2)*(4*x + 4* x^2 + 1) + exp(1)*(6*x - 8*x^3 + 2) - log(5)*(2*x + exp(1)*(2*x + 4*x^2) + 2*x^2 - 4*x^3) - 3*x^2 - 4*x^3 + 4*x^4 + 1), x)