Integrand size = 130, antiderivative size = 32 \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=e^{4+\frac {5 x^2 \left (1+e^x+2 x\right ) \log \left (e^{-x} x\right )}{3-x}} \]
Leaf count is larger than twice the leaf count of optimal. \(98\) vs. \(2(32)=64\).
Time = 0.41 (sec) , antiderivative size = 98, normalized size of antiderivative = 3.06 \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=e^{4+\frac {5 x \left (21 (-3+x)+\left (-21+x+e^x x+2 x^2\right ) \log (x)-\left (-21+x+e^x x+2 x^2\right ) \log \left (e^{-x} x\right )\right )}{-3+x}} x^{-\frac {5 \left (-63+\left (1+e^x\right ) x^2+2 x^3\right )}{-3+x}} \left (e^{-x} x\right )^{-\frac {315}{-3+x}} \]
Integrate[(E^((-12 + 4*x + (-5*x^2 - 5*E^x*x^2 - 10*x^3)*Log[x/E^x])/(-3 + x))*(15*x + 10*x^2 - 35*x^3 + 10*x^4 + E^x*(15*x - 20*x^2 + 5*x^3) + (30* x + 85*x^2 - 20*x^3 + E^x*(30*x + 10*x^2 - 5*x^3))*Log[x/E^x]))/(9 - 6*x + x^2),x]
E^(4 + (5*x*(21*(-3 + x) + (-21 + x + E^x*x + 2*x^2)*Log[x] - (-21 + x + E ^x*x + 2*x^2)*Log[x/E^x]))/(-3 + x))/(x^((5*(-63 + (1 + E^x)*x^2 + 2*x^3)) /(-3 + x))*(x/E^x)^(315/(-3 + 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.
| \(\displaystyle \int \frac {\left (10 x^4-35 x^3+10 x^2+e^x \left (5 x^3-20 x^2+15 x\right )+\left (-20 x^3+85 x^2+e^x \left (-5 x^3+10 x^2+30 x\right )+30 x\right ) \log \left (e^{-x} x\right )+15 x\right ) \exp \left (\frac {\left (-10 x^3-5 e^x x^2-5 x^2\right ) \log \left (e^{-x} x\right )+4 x-12}{x-3}\right )}{x^2-6 x+9} \, dx\) |
| \(\Big \downarrow \) 7277 |
| \(\displaystyle 4 \int \frac {5 e^4 \left (e^{-x} x\right )^{\frac {10 x^3+5 e^x x^2+5 x^2}{3-x}} \left (2 x^4-7 x^3+2 x^2+3 x+e^x \left (x^3-4 x^2+3 x\right )+\left (-4 x^3+17 x^2+6 x+e^x \left (-x^3+2 x^2+6 x\right )\right ) \log \left (e^{-x} x\right )\right )}{4 (3-x)^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 5 e^4 \int \frac {\left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}} \left (2 x^4-7 x^3+2 x^2+3 x+e^x \left (x^3-4 x^2+3 x\right )+\left (-4 x^3+17 x^2+6 x+e^x \left (-x^3+2 x^2+6 x\right )\right ) \log \left (e^{-x} x\right )\right )}{(3-x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 5 e^4 \int \left (\frac {2 x^4 \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}-\frac {7 x^3 \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}+\frac {2 x^2 \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}+\frac {3 x \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}-\frac {4 x^3 \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}+\frac {17 x^2 \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}+\frac {6 x \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}-\frac {e^x x \left (\log \left (e^{-x} x\right ) x^2-x^2-2 \log \left (e^{-x} x\right ) x+4 x-6 \log \left (e^{-x} x\right )-3\right ) \left (e^{-x} x\right )^{\frac {5 \left (2 x^3+e^x x^2+x^2\right )}{3-x}}}{(x-3)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle 5 e^4 \int \frac {x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}} \left (\left (2 x+e^x+1\right ) \left (x^2-4 x+3\right )+\left (-4 x^2+17 x+e^x \left (-x^2+2 x+6\right )+6\right ) \log \left (e^{-x} x\right )\right )}{(3-x)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle 5 e^4 \int \left (\frac {x^3 \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}+\frac {2 (x-1) x^2 \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}-\frac {4 x^2 \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}+\frac {3 x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}-\frac {4 x^3 \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}+\frac {17 x^2 \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}+\frac {6 x \log \left (e^{-x} x\right ) \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}-\frac {e^x x \left (\log \left (e^{-x} x\right ) x^2-x^2-2 \log \left (e^{-x} x\right ) x+4 x-6 \log \left (e^{-x} x\right )-3\right ) \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 5 e^4 \left (-7 \log \left (e^{-x} x\right ) \int \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+14 \int \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx-4 \log \left (e^{-x} x\right ) \int e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+2 \int e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+63 \log \left (e^{-x} x\right ) \int \frac {\left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dx+9 \log \left (e^{-x} x\right ) \int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dx+42 \int \frac {\left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}dx-9 \log \left (e^{-x} x\right ) \int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}dx+6 \int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}dx-4 \log \left (e^{-x} x\right ) \int x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+5 \int x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx-\log \left (e^{-x} x\right ) \int e^x x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+\int e^x x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx+2 \int x^2 \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx-7 \int \int \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dxdx+7 \int \frac {\int \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx}{x}dx-4 \int \int e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dxdx+4 \int \frac {\int e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx}{x}dx+63 \int \int \frac {\left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dxdx-63 \int \frac {\int \frac {\left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dx}{x}dx+9 \int \int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dxdx-9 \int \frac {\int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{(x-3)^2}dx}{x}dx-9 \int \int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}dxdx+9 \int \frac {\int \frac {e^x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}}{x-3}dx}{x}dx-4 \int \int x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dxdx+4 \int \frac {\int x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx}{x}dx-\int \int e^x x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dxdx+\int \frac {\int e^x x \left (e^{-x} x\right )^{-\frac {5 x^2 \left (2 x+e^x+1\right )}{x-3}}dx}{x}dx\right )\) |
Int[(E^((-12 + 4*x + (-5*x^2 - 5*E^x*x^2 - 10*x^3)*Log[x/E^x])/(-3 + x))*( 15*x + 10*x^2 - 35*x^3 + 10*x^4 + E^x*(15*x - 20*x^2 + 5*x^3) + (30*x + 85 *x^2 - 20*x^3 + E^x*(30*x + 10*x^2 - 5*x^3))*Log[x/E^x]))/(9 - 6*x + x^2), x]
3.3.48.3.1 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]]
Int[(u_)*((a_.) + (b_.)*(x_)^(n_.) + (c_.)*(x_)^(n2_.))^(p_.), x_Symbol] :> Simp[1/(4^p*c^p) Int[u*(b + 2*c*x^n)^(2*p), x], x] /; FreeQ[{a, b, c, n} , x] && EqQ[n2, 2*n] && EqQ[b^2 - 4*a*c, 0] && IntegerQ[p] && !AlgebraicFu nctionQ[u, x]
Time = 7.12 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.22
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {\left (-5 \,{\mathrm e}^{x} x^{2}-10 x^{3}-5 x^{2}\right ) \ln \left (x \,{\mathrm e}^{-x}\right )+4 x -12}{-3+x}}\) | \(39\) |
| risch | \(x^{-\frac {5 \,{\mathrm e}^{x} x^{2}}{-3+x}} x^{-\frac {10 x^{3}}{-3+x}} \left ({\mathrm e}^{x}\right )^{\frac {5 \,{\mathrm e}^{x} x^{2}}{-3+x}} \left ({\mathrm e}^{x}\right )^{\frac {10 x^{3}}{-3+x}} x^{-\frac {5 x^{2}}{-3+x}} \left ({\mathrm e}^{x}\right )^{\frac {5 x^{2}}{-3+x}} {\mathrm e}^{\frac {5 i \pi \,{\mathrm e}^{x} \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} x^{2}-5 i \pi \,{\mathrm e}^{x} \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i x \right ) x^{2}-5 i \pi \,{\mathrm e}^{x} \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{2}+5 i \pi \,{\mathrm e}^{x} \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{2}+10 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} x^{3}-10 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i x \right ) x^{3}-10 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}+10 i \pi \,\operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{3}+5 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{3} x^{2}-5 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i x \right ) x^{2}-5 i \pi \operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right )^{2} \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{2}+5 i \pi \,\operatorname {csgn}\left (i x \,{\mathrm e}^{-x}\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i {\mathrm e}^{-x}\right ) x^{2}+8 x -24}{2 x -6}}\) | \(390\) |
int((((-5*x^3+10*x^2+30*x)*exp(x)-20*x^3+85*x^2+30*x)*ln(x/exp(x))+(5*x^3- 20*x^2+15*x)*exp(x)+10*x^4-35*x^3+10*x^2+15*x)*exp(((-5*exp(x)*x^2-10*x^3- 5*x^2)*ln(x/exp(x))+4*x-12)/(-3+x))/(x^2-6*x+9),x,method=_RETURNVERBOSE)
Time = 0.25 (sec) , antiderivative size = 37, normalized size of antiderivative = 1.16 \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=e^{\left (-\frac {5 \, {\left (2 \, x^{3} + x^{2} e^{x} + x^{2}\right )} \log \left (x e^{\left (-x\right )}\right ) - 4 \, x + 12}{x - 3}\right )} \]
integrate((((-5*x^3+10*x^2+30*x)*exp(x)-20*x^3+85*x^2+30*x)*log(x/exp(x))+ (5*x^3-20*x^2+15*x)*exp(x)+10*x^4-35*x^3+10*x^2+15*x)*exp(((-5*exp(x)*x^2- 10*x^3-5*x^2)*log(x/exp(x))+4*x-12)/(-3+x))/(x^2-6*x+9),x, algorithm=\
Timed out. \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=\text {Timed out} \]
integrate((((-5*x**3+10*x**2+30*x)*exp(x)-20*x**3+85*x**2+30*x)*ln(x/exp(x ))+(5*x**3-20*x**2+15*x)*exp(x)+10*x**4-35*x**3+10*x**2+15*x)*exp(((-5*exp (x)*x**2-10*x**3-5*x**2)*ln(x/exp(x))+4*x-12)/(-3+x))/(x**2-6*x+9),x)
Timed out. \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=\text {Timed out} \]
integrate((((-5*x^3+10*x^2+30*x)*exp(x)-20*x^3+85*x^2+30*x)*log(x/exp(x))+ (5*x^3-20*x^2+15*x)*exp(x)+10*x^4-35*x^3+10*x^2+15*x)*exp(((-5*exp(x)*x^2- 10*x^3-5*x^2)*log(x/exp(x))+4*x-12)/(-3+x))/(x^2-6*x+9),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 70 vs. \(2 (27) = 54\).
Time = 0.93 (sec) , antiderivative size = 70, normalized size of antiderivative = 2.19 \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=e^{\left (-\frac {10 \, x^{3} \log \left (x e^{\left (-x\right )}\right )}{x - 3} - \frac {5 \, x^{2} e^{x} \log \left (x e^{\left (-x\right )}\right )}{x - 3} - \frac {5 \, x^{2} \log \left (x e^{\left (-x\right )}\right )}{x - 3} + \frac {4 \, x}{x - 3} - \frac {12}{x - 3}\right )} \]
integrate((((-5*x^3+10*x^2+30*x)*exp(x)-20*x^3+85*x^2+30*x)*log(x/exp(x))+ (5*x^3-20*x^2+15*x)*exp(x)+10*x^4-35*x^3+10*x^2+15*x)*exp(((-5*exp(x)*x^2- 10*x^3-5*x^2)*log(x/exp(x))+4*x-12)/(-3+x))/(x^2-6*x+9),x, algorithm=\
e^(-10*x^3*log(x*e^(-x))/(x - 3) - 5*x^2*e^x*log(x*e^(-x))/(x - 3) - 5*x^2 *log(x*e^(-x))/(x - 3) + 4*x/(x - 3) - 12/(x - 3))
Time = 9.14 (sec) , antiderivative size = 79, normalized size of antiderivative = 2.47 \[ \int \frac {e^{\frac {-12+4 x+\left (-5 x^2-5 e^x x^2-10 x^3\right ) \log \left (e^{-x} x\right )}{-3+x}} \left (15 x+10 x^2-35 x^3+10 x^4+e^x \left (15 x-20 x^2+5 x^3\right )+\left (30 x+85 x^2-20 x^3+e^x \left (30 x+10 x^2-5 x^3\right )\right ) \log \left (e^{-x} x\right )\right )}{9-6 x+x^2} \, dx=\frac {{\mathrm {e}}^{\frac {4\,x}{x-3}}\,{\mathrm {e}}^{\frac {5\,x^3\,{\mathrm {e}}^x}{x-3}}\,{\mathrm {e}}^{\frac {5\,x^3}{x-3}}\,{\mathrm {e}}^{\frac {10\,x^4}{x-3}}\,{\mathrm {e}}^{-\frac {12}{x-3}}}{x^{\frac {5\,\left (x^2\,{\mathrm {e}}^x+x^2+2\,x^3\right )}{x-3}}} \]
int((exp(-(log(x*exp(-x))*(5*x^2*exp(x) + 5*x^2 + 10*x^3) - 4*x + 12)/(x - 3))*(15*x + log(x*exp(-x))*(30*x + 85*x^2 - 20*x^3 + exp(x)*(30*x + 10*x^ 2 - 5*x^3)) + 10*x^2 - 35*x^3 + 10*x^4 + exp(x)*(15*x - 20*x^2 + 5*x^3)))/ (x^2 - 6*x + 9),x)