Integrand size = 260, antiderivative size = 29 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=5+\frac {2-x+\log (x)}{5 \left (x+(1+x) \left (1+e^x+x\right )^2\right )} \]
Time = 0.17 (sec) , antiderivative size = 45, normalized size of antiderivative = 1.55 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=\frac {2-x+\log (x)}{5 \left (1+4 x+3 x^2+x^3+e^{2 x} (1+x)+2 e^x (1+x)^2\right )} \]
Integrate[(1 - 5*x - 9*x^2 - 2*x^3 + 2*x^4 + E^(2*x)*(1 - 6*x - 2*x^2 + 2* x^3) + E^x*(2 - 10*x - 12*x^2 + 2*x^3 + 2*x^4) + (-4*x - 6*x^2 - 3*x^3 + E ^(2*x)*(-3*x - 2*x^2) + E^x*(-6*x - 8*x^2 - 2*x^3))*Log[x])/(5*x + 40*x^2 + 110*x^3 + 130*x^4 + 85*x^5 + 30*x^6 + 5*x^7 + E^(4*x)*(5*x + 10*x^2 + 5* x^3) + E^(3*x)*(20*x + 60*x^2 + 60*x^3 + 20*x^4) + E^(2*x)*(30*x + 130*x^2 + 190*x^3 + 120*x^4 + 30*x^5) + E^x*(20*x + 120*x^2 + 240*x^3 + 220*x^4 + 100*x^5 + 20*x^6)),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.
| \(\displaystyle \int \frac {2 x^4-2 x^3-9 x^2+e^{2 x} \left (2 x^3-2 x^2-6 x+1\right )+\left (-3 x^3-6 x^2+e^{2 x} \left (-2 x^2-3 x\right )+e^x \left (-2 x^3-8 x^2-6 x\right )-4 x\right ) \log (x)+e^x \left (2 x^4+2 x^3-12 x^2-10 x+2\right )-5 x+1}{5 x^7+30 x^6+85 x^5+130 x^4+110 x^3+40 x^2+e^{4 x} \left (5 x^3+10 x^2+5 x\right )+e^{3 x} \left (20 x^4+60 x^3+60 x^2+20 x\right )+e^{2 x} \left (30 x^5+120 x^4+190 x^3+130 x^2+30 x\right )+e^x \left (20 x^6+100 x^5+220 x^4+240 x^3+120 x^2+20 x\right )+5 x} \, dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {2 x^4-2 x^3-9 x^2-\left (3 x^2+2 e^x \left (x^2+4 x+3\right )+6 x+e^{2 x} (2 x+3)+4\right ) x \log (x)+e^{2 x} \left (2 x^3-2 x^2-6 x+1\right )+2 e^x \left (x^4+x^3-6 x^2-5 x+1\right )-5 x+1}{5 x \left (x^3+3 x^2+4 x+2 e^x (x+1)^2+e^{2 x} (x+1)+1\right )^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \frac {1}{5} \int \frac {2 x^4-2 x^3-9 x^2-\left (3 x^2+6 x+e^{2 x} (2 x+3)+2 e^x \left (x^2+4 x+3\right )+4\right ) \log (x) x-5 x+e^{2 x} \left (2 x^3-2 x^2-6 x+1\right )+2 e^x \left (x^4+x^3-6 x^2-5 x+1\right )+1}{x \left (x^3+3 x^2+4 x+2 e^x (x+1)^2+e^{2 x} (x+1)+1\right )^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \frac {1}{5} \int \left (\frac {2 x^3-2 \log (x) x^2-2 x^2-3 \log (x) x-6 x+1}{x (x+1) \left (x^3+2 e^x x^2+3 x^2+4 e^x x+e^{2 x} x+4 x+2 e^x+e^{2 x}+1\right )}-\frac {\left (2 x^4+2 e^x x^3+6 x^3+4 e^x x^2+8 x^2+2 e^x x+4 x-1\right ) (x-\log (x)-2)}{(x+1) \left (x^3+2 e^x x^2+3 x^2+4 e^x x+e^{2 x} x+4 x+2 e^x+e^{2 x}+1\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \frac {1}{5} \int \left (\frac {2 x^3-2 \log (x) x^2-2 x^2-3 \log (x) x-6 x+1}{x (x+1) \left (x^3+2 e^x x^2+3 x^2+4 e^x x+e^{2 x} x+4 x+2 e^x+e^{2 x}+1\right )}-\frac {\left (2 x^4+2 e^x x^3+6 x^3+4 e^x x^2+8 x^2+2 e^x x+4 x-1\right ) (x-\log (x)-2)}{(x+1) \left (x^3+2 e^x x^2+3 x^2+4 e^x x+e^{2 x} x+4 x+2 e^x+e^{2 x}+1\right )^2}\right )dx\) |
Int[(1 - 5*x - 9*x^2 - 2*x^3 + 2*x^4 + E^(2*x)*(1 - 6*x - 2*x^2 + 2*x^3) + E^x*(2 - 10*x - 12*x^2 + 2*x^3 + 2*x^4) + (-4*x - 6*x^2 - 3*x^3 + E^(2*x) *(-3*x - 2*x^2) + E^x*(-6*x - 8*x^2 - 2*x^3))*Log[x])/(5*x + 40*x^2 + 110* x^3 + 130*x^4 + 85*x^5 + 30*x^6 + 5*x^7 + E^(4*x)*(5*x + 10*x^2 + 5*x^3) + E^(3*x)*(20*x + 60*x^2 + 60*x^3 + 20*x^4) + E^(2*x)*(30*x + 130*x^2 + 190 *x^3 + 120*x^4 + 30*x^5) + E^x*(20*x + 120*x^2 + 240*x^3 + 220*x^4 + 100*x ^5 + 20*x^6)),x]
3.23.9.3.1 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]]
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Time = 0.91 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.76
| method | result | size |
| parallelrisch | \(\frac {2+\ln \left (x \right )-x}{5 x \,{\mathrm e}^{2 x}+10 \,{\mathrm e}^{x} x^{2}+5 x^{3}+5 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} x +15 x^{2}+10 \,{\mathrm e}^{x}+20 x +5}\) | \(51\) |
| risch | \(\frac {\ln \left (x \right )}{5 x \,{\mathrm e}^{2 x}+10 \,{\mathrm e}^{x} x^{2}+5 x^{3}+5 \,{\mathrm e}^{2 x}+20 \,{\mathrm e}^{x} x +15 x^{2}+10 \,{\mathrm e}^{x}+20 x +5}-\frac {-2+x}{5 \left (x \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x} x^{2}+x^{3}+{\mathrm e}^{2 x}+4 \,{\mathrm e}^{x} x +3 x^{2}+2 \,{\mathrm e}^{x}+4 x +1\right )}\) | \(93\) |
int((((-2*x^2-3*x)*exp(x)^2+(-2*x^3-8*x^2-6*x)*exp(x)-3*x^3-6*x^2-4*x)*ln( x)+(2*x^3-2*x^2-6*x+1)*exp(x)^2+(2*x^4+2*x^3-12*x^2-10*x+2)*exp(x)+2*x^4-2 *x^3-9*x^2-5*x+1)/((5*x^3+10*x^2+5*x)*exp(x)^4+(20*x^4+60*x^3+60*x^2+20*x) *exp(x)^3+(30*x^5+120*x^4+190*x^3+130*x^2+30*x)*exp(x)^2+(20*x^6+100*x^5+2 20*x^4+240*x^3+120*x^2+20*x)*exp(x)+5*x^7+30*x^6+85*x^5+130*x^4+110*x^3+40 *x^2+5*x),x,method=_RETURNVERBOSE)
Time = 0.26 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=-\frac {x - \log \left (x\right ) - 2}{5 \, {\left (x^{3} + 3 \, x^{2} + {\left (x + 1\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} + 2 \, x + 1\right )} e^{x} + 4 \, x + 1\right )}} \]
integrate((((-2*x^2-3*x)*exp(x)^2+(-2*x^3-8*x^2-6*x)*exp(x)-3*x^3-6*x^2-4* x)*log(x)+(2*x^3-2*x^2-6*x+1)*exp(x)^2+(2*x^4+2*x^3-12*x^2-10*x+2)*exp(x)+ 2*x^4-2*x^3-9*x^2-5*x+1)/((5*x^3+10*x^2+5*x)*exp(x)^4+(20*x^4+60*x^3+60*x^ 2+20*x)*exp(x)^3+(30*x^5+120*x^4+190*x^3+130*x^2+30*x)*exp(x)^2+(20*x^6+10 0*x^5+220*x^4+240*x^3+120*x^2+20*x)*exp(x)+5*x^7+30*x^6+85*x^5+130*x^4+110 *x^3+40*x^2+5*x),x, algorithm=\
Time = 0.25 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=\frac {- x + \log {\left (x \right )} + 2}{5 x^{3} + 15 x^{2} + 20 x + \left (5 x + 5\right ) e^{2 x} + \left (10 x^{2} + 20 x + 10\right ) e^{x} + 5} \]
integrate((((-2*x**2-3*x)*exp(x)**2+(-2*x**3-8*x**2-6*x)*exp(x)-3*x**3-6*x **2-4*x)*ln(x)+(2*x**3-2*x**2-6*x+1)*exp(x)**2+(2*x**4+2*x**3-12*x**2-10*x +2)*exp(x)+2*x**4-2*x**3-9*x**2-5*x+1)/((5*x**3+10*x**2+5*x)*exp(x)**4+(20 *x**4+60*x**3+60*x**2+20*x)*exp(x)**3+(30*x**5+120*x**4+190*x**3+130*x**2+ 30*x)*exp(x)**2+(20*x**6+100*x**5+220*x**4+240*x**3+120*x**2+20*x)*exp(x)+ 5*x**7+30*x**6+85*x**5+130*x**4+110*x**3+40*x**2+5*x),x)
(-x + log(x) + 2)/(5*x**3 + 15*x**2 + 20*x + (5*x + 5)*exp(2*x) + (10*x**2 + 20*x + 10)*exp(x) + 5)
Time = 0.37 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.52 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=-\frac {x - \log \left (x\right ) - 2}{5 \, {\left (x^{3} + 3 \, x^{2} + {\left (x + 1\right )} e^{\left (2 \, x\right )} + 2 \, {\left (x^{2} + 2 \, x + 1\right )} e^{x} + 4 \, x + 1\right )}} \]
integrate((((-2*x^2-3*x)*exp(x)^2+(-2*x^3-8*x^2-6*x)*exp(x)-3*x^3-6*x^2-4* x)*log(x)+(2*x^3-2*x^2-6*x+1)*exp(x)^2+(2*x^4+2*x^3-12*x^2-10*x+2)*exp(x)+ 2*x^4-2*x^3-9*x^2-5*x+1)/((5*x^3+10*x^2+5*x)*exp(x)^4+(20*x^4+60*x^3+60*x^ 2+20*x)*exp(x)^3+(30*x^5+120*x^4+190*x^3+130*x^2+30*x)*exp(x)^2+(20*x^6+10 0*x^5+220*x^4+240*x^3+120*x^2+20*x)*exp(x)+5*x^7+30*x^6+85*x^5+130*x^4+110 *x^3+40*x^2+5*x),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 381 vs. \(2 (26) = 52\).
Time = 0.38 (sec) , antiderivative size = 381, normalized size of antiderivative = 13.14 \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=-\frac {4 \, x^{9} + 4 \, x^{8} e^{x} - 6 \, x^{8} \log \left (x\right ) - 6 \, x^{7} e^{x} \log \left (x\right ) + 16 \, x^{8} + 8 \, x^{7} e^{x} - 40 \, x^{7} \log \left (x\right ) - 30 \, x^{6} e^{x} \log \left (x\right ) - 10 \, x^{7} - 18 \, x^{6} e^{x} - 98 \, x^{6} \log \left (x\right ) - 62 \, x^{5} e^{x} \log \left (x\right ) - 102 \, x^{6} - 72 \, x^{5} e^{x} - 120 \, x^{5} \log \left (x\right ) - 66 \, x^{4} e^{x} \log \left (x\right ) - 154 \, x^{5} - 86 \, x^{4} e^{x} - 79 \, x^{4} \log \left (x\right ) - 36 \, x^{3} e^{x} \log \left (x\right ) - 102 \, x^{4} - 42 \, x^{3} e^{x} - 25 \, x^{3} \log \left (x\right ) - 8 \, x^{2} e^{x} \log \left (x\right ) - 25 \, x^{3} - 4 \, x^{2} e^{x} - 6 \, x^{2} \log \left (x\right ) - x^{2} + 2 \, x e^{x} - 5 \, x \log \left (x\right ) - 6 \, x + 1}{5 \, {\left (4 \, x^{10} + 8 \, x^{9} e^{x} + 24 \, x^{9} + 4 \, x^{8} e^{\left (2 \, x\right )} + 40 \, x^{8} e^{x} + 68 \, x^{8} + 16 \, x^{7} e^{\left (2 \, x\right )} + 88 \, x^{7} e^{x} + 112 \, x^{7} + 28 \, x^{6} e^{\left (2 \, x\right )} + 112 \, x^{6} e^{x} + 112 \, x^{6} + 28 \, x^{5} e^{\left (2 \, x\right )} + 80 \, x^{5} e^{x} + 60 \, x^{5} + 12 \, x^{4} e^{\left (2 \, x\right )} + 16 \, x^{4} e^{x} + x^{4} - 4 \, x^{3} e^{\left (2 \, x\right )} - 14 \, x^{3} e^{x} - 13 \, x^{3} - 3 \, x^{2} e^{\left (2 \, x\right )} - 4 \, x^{2} e^{x} + x e^{\left (2 \, x\right )} + 2 \, x e^{x} + x\right )}} \]
integrate((((-2*x^2-3*x)*exp(x)^2+(-2*x^3-8*x^2-6*x)*exp(x)-3*x^3-6*x^2-4* x)*log(x)+(2*x^3-2*x^2-6*x+1)*exp(x)^2+(2*x^4+2*x^3-12*x^2-10*x+2)*exp(x)+ 2*x^4-2*x^3-9*x^2-5*x+1)/((5*x^3+10*x^2+5*x)*exp(x)^4+(20*x^4+60*x^3+60*x^ 2+20*x)*exp(x)^3+(30*x^5+120*x^4+190*x^3+130*x^2+30*x)*exp(x)^2+(20*x^6+10 0*x^5+220*x^4+240*x^3+120*x^2+20*x)*exp(x)+5*x^7+30*x^6+85*x^5+130*x^4+110 *x^3+40*x^2+5*x),x, algorithm=\
-1/5*(4*x^9 + 4*x^8*e^x - 6*x^8*log(x) - 6*x^7*e^x*log(x) + 16*x^8 + 8*x^7 *e^x - 40*x^7*log(x) - 30*x^6*e^x*log(x) - 10*x^7 - 18*x^6*e^x - 98*x^6*lo g(x) - 62*x^5*e^x*log(x) - 102*x^6 - 72*x^5*e^x - 120*x^5*log(x) - 66*x^4* e^x*log(x) - 154*x^5 - 86*x^4*e^x - 79*x^4*log(x) - 36*x^3*e^x*log(x) - 10 2*x^4 - 42*x^3*e^x - 25*x^3*log(x) - 8*x^2*e^x*log(x) - 25*x^3 - 4*x^2*e^x - 6*x^2*log(x) - x^2 + 2*x*e^x - 5*x*log(x) - 6*x + 1)/(4*x^10 + 8*x^9*e^ x + 24*x^9 + 4*x^8*e^(2*x) + 40*x^8*e^x + 68*x^8 + 16*x^7*e^(2*x) + 88*x^7 *e^x + 112*x^7 + 28*x^6*e^(2*x) + 112*x^6*e^x + 112*x^6 + 28*x^5*e^(2*x) + 80*x^5*e^x + 60*x^5 + 12*x^4*e^(2*x) + 16*x^4*e^x + x^4 - 4*x^3*e^(2*x) - 14*x^3*e^x - 13*x^3 - 3*x^2*e^(2*x) - 4*x^2*e^x + x*e^(2*x) + 2*x*e^x + x )
Timed out. \[ \int \frac {1-5 x-9 x^2-2 x^3+2 x^4+e^{2 x} \left (1-6 x-2 x^2+2 x^3\right )+e^x \left (2-10 x-12 x^2+2 x^3+2 x^4\right )+\left (-4 x-6 x^2-3 x^3+e^{2 x} \left (-3 x-2 x^2\right )+e^x \left (-6 x-8 x^2-2 x^3\right )\right ) \log (x)}{5 x+40 x^2+110 x^3+130 x^4+85 x^5+30 x^6+5 x^7+e^{4 x} \left (5 x+10 x^2+5 x^3\right )+e^{3 x} \left (20 x+60 x^2+60 x^3+20 x^4\right )+e^{2 x} \left (30 x+130 x^2+190 x^3+120 x^4+30 x^5\right )+e^x \left (20 x+120 x^2+240 x^3+220 x^4+100 x^5+20 x^6\right )} \, dx=\int -\frac {5\,x-{\mathrm {e}}^x\,\left (2\,x^4+2\,x^3-12\,x^2-10\,x+2\right )+{\mathrm {e}}^{2\,x}\,\left (-2\,x^3+2\,x^2+6\,x-1\right )+\ln \left (x\right )\,\left (4\,x+{\mathrm {e}}^{2\,x}\,\left (2\,x^2+3\,x\right )+6\,x^2+3\,x^3+{\mathrm {e}}^x\,\left (2\,x^3+8\,x^2+6\,x\right )\right )+9\,x^2+2\,x^3-2\,x^4-1}{5\,x+{\mathrm {e}}^{4\,x}\,\left (5\,x^3+10\,x^2+5\,x\right )+{\mathrm {e}}^{3\,x}\,\left (20\,x^4+60\,x^3+60\,x^2+20\,x\right )+{\mathrm {e}}^x\,\left (20\,x^6+100\,x^5+220\,x^4+240\,x^3+120\,x^2+20\,x\right )+{\mathrm {e}}^{2\,x}\,\left (30\,x^5+120\,x^4+190\,x^3+130\,x^2+30\,x\right )+40\,x^2+110\,x^3+130\,x^4+85\,x^5+30\,x^6+5\,x^7} \,d x \]
int(-(5*x - exp(x)*(2*x^3 - 12*x^2 - 10*x + 2*x^4 + 2) + exp(2*x)*(6*x + 2 *x^2 - 2*x^3 - 1) + log(x)*(4*x + exp(2*x)*(3*x + 2*x^2) + 6*x^2 + 3*x^3 + exp(x)*(6*x + 8*x^2 + 2*x^3)) + 9*x^2 + 2*x^3 - 2*x^4 - 1)/(5*x + exp(4*x )*(5*x + 10*x^2 + 5*x^3) + exp(3*x)*(20*x + 60*x^2 + 60*x^3 + 20*x^4) + ex p(x)*(20*x + 120*x^2 + 240*x^3 + 220*x^4 + 100*x^5 + 20*x^6) + exp(2*x)*(3 0*x + 130*x^2 + 190*x^3 + 120*x^4 + 30*x^5) + 40*x^2 + 110*x^3 + 130*x^4 + 85*x^5 + 30*x^6 + 5*x^7),x)
int(-(5*x - exp(x)*(2*x^3 - 12*x^2 - 10*x + 2*x^4 + 2) + exp(2*x)*(6*x + 2 *x^2 - 2*x^3 - 1) + log(x)*(4*x + exp(2*x)*(3*x + 2*x^2) + 6*x^2 + 3*x^3 + exp(x)*(6*x + 8*x^2 + 2*x^3)) + 9*x^2 + 2*x^3 - 2*x^4 - 1)/(5*x + exp(4*x )*(5*x + 10*x^2 + 5*x^3) + exp(3*x)*(20*x + 60*x^2 + 60*x^3 + 20*x^4) + ex p(x)*(20*x + 120*x^2 + 240*x^3 + 220*x^4 + 100*x^5 + 20*x^6) + exp(2*x)*(3 0*x + 130*x^2 + 190*x^3 + 120*x^4 + 30*x^5) + 40*x^2 + 110*x^3 + 130*x^4 + 85*x^5 + 30*x^6 + 5*x^7), x)