Integrand size = 145, antiderivative size = 27 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{29+e^x-x+x^2-\frac {x \log (x)}{3+x-\log (3)}} \]
\[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx \]
Integrate[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x + Log[3]))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 + ( -6 - 2*x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x)*Log[3] + Log[3]^2),x]
Integrate[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x + Log[3]))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 + ( -6 - 2*x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x)*Log[3] + Log[3]^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.
| \(\displaystyle \int \frac {\left (2 x^3+11 x^2+e^x \left (x^2+6 x+(-2 x-6) \log (3)+9+\log ^2(3)\right )+\left (-4 x^2-10 x+7\right ) \log (3)+11 x+(2 x-1) \log ^2(3)+(\log (3)-3) \log (x)-12\right ) \exp \left (\frac {-x^3-2 x^2+\left (x^2-x+29\right ) \log (3)-26 x+x \log (x)+e^x (-x-3+\log (3))-87}{-x-3+\log (3)}\right )}{x^2+6 x+(-2 x-6) \log (3)+9+\log ^2(3)} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {\left (2 x^3+11 x^2+e^x \left (x^2+6 x+(-2 x-6) \log (3)+9+\log ^2(3)\right )+\left (-4 x^2-10 x+7\right ) \log (3)+11 x+(2 x-1) \log ^2(3)+(\log (3)-3) \log (x)-12\right ) \exp \left (\frac {-x^3-2 x^2+\left (x^2-x+29\right ) \log (3)-26 x+x \log (x)+e^x (-x-3+\log (3))-87}{-x-3+\log (3)}\right )}{x^2+2 x (3-\log (3))+(\log (3)-3)^2}dx\) |
| \(\Big \downarrow \) 7277 |
| \(\displaystyle 4 \int -\frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}} \left (-2 x^3-11 x^2-11 x-e^x \left (x^2+6 x+\log ^2(3)-2 (x+3) \log (3)+9\right )+(3-\log (3)) \log (x)+(1-2 x) \log ^2(3)-\left (-4 x^2-10 x+7\right ) \log (3)+12\right )}{(2 x-\log (9)+6)^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle -4 \int \frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}} \left (-2 x^3-11 x^2-11 x-e^x \left (x^2+6 x+\log ^2(3)-2 (x+3) \log (3)+9\right )+(3-\log (3)) \log (x)+(1-2 x) \log ^2(3)-\left (-4 x^2-10 x+7\right ) \log (3)+12\right )}{(2 x-\log (9)+6)^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle -4 \int \left (-\frac {11\ 3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{1-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}-\frac {11\ 3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{2-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}-\frac {2\ 3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{3-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}-\frac {1}{4} 3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (x+\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}}-\frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) (-3+\log (3)) \log (x) x^{-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}+\frac {4\ 3^{1-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}-\frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) (2 x-1) \log ^2(3) x^{-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}+\frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) \left (4 x^2+10 x-7\right ) \log (3) x^{-\frac {x}{x-\log (3)+3}}}{(2 x-\log (9)+6)^2}\right )dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle -4 \int \frac {3^{\frac {-x^2+x-29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}} \left (-e^x (-2 x+\log (9)-6)^2-4 \left (2 x^3+(11-4 \log (3)) x^2+\left (11-10 \log (3)+2 \log ^2(3)\right ) x-\log ^2(3)+7 \log (3)-12\right )-4 (-3+\log (3)) \log (x)\right )}{4 (2 x-\log (9)+6)^2}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle -\int -\frac {3^{-\frac {x^2-x+29}{x-\log (3)+3}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x-\log (3)+3)+87}{x-\log (3)+3}\right ) x^{-\frac {x}{x-\log (3)+3}} \left (e^x (2 x-\log (9)+6)^2+4 \left (2 x^3+(11-4 \log (3)) x^2+\left (11-10 \log (3)+2 \log ^2(3)\right ) x-(3-\log (3)) (4-\log (3))\right )-4 (3-\log (3)) \log (x)\right )}{(2 x-\log (9)+6)^2}dx\) |
| \(\Big \downarrow \) 25 |
| \(\displaystyle \int \frac {3^{-\frac {x^2-x+29}{x+3-\log (3)}} x^{-\frac {x}{x+3-\log (3)}} \left (4 \left (2 x^3+x^2 (11-4 \log (3))+x \left (11+2 \log ^2(3)-10 \log (3)\right )-(3-\log (3)) (4-\log (3))\right )+e^x (2 x+6-\log (9))^2-4 (3-\log (3)) \log (x)\right ) \exp \left (\frac {x^3+2 x^2+26 x+e^x (x+3-\log (3))+87}{x+3-\log (3)}\right )}{(2 x+6-\log (9))^2}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (3^{-\frac {x^2-x+29}{x+3-\log (3)}} x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x+3-\log (3))+87}{x+3-\log (3)}+x\right )+\frac {4\ 3^{-\frac {x^2-x+29}{x+3-\log (3)}} \left (2 x^3+11 x^2 \left (1-\frac {4 \log (3)}{11}\right )+11 x \left (1+\frac {2}{11} (\log (3)-5) \log (3)\right )-3 \left (1-\frac {\log (3)}{3}\right ) \log (x)-12 \left (1+\frac {1}{12} (\log (3)-7) \log (3)\right )\right ) x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+2 x^2+26 x+e^x (x+3-\log (3))+87}{x+3-\log (3)}\right )}{(2 x+6-\log (9))^2}\right )dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (3^{\frac {-x^2+x-29}{x+3-\log (3)}} x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+3 x^2+e^x x+29 x \left (1-\frac {\log (3)}{29}\right )+3 e^x \left (1-\frac {\log (3)}{3}\right )+87}{x+3-\log (3)}\right )+\frac {4\ 3^{\frac {-x^2+x-29}{x+3-\log (3)}} \left (2 x^3+11 x^2 \left (1-\frac {4 \log (3)}{11}\right )+11 x \left (1+\frac {2}{11} (\log (3)-5) \log (3)\right )-3 \left (1-\frac {\log (3)}{3}\right ) \log (x)-12 \left (1+\frac {1}{12} (\log (3)-7) \log (3)\right )\right ) x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+2 x^2+e^x x+26 x+3 e^x \left (1-\frac {\log (3)}{3}\right )+87}{x+3-\log (3)}\right )}{(2 x+6-\log (9))^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (3^{\frac {-x^2+x-29}{x+3-\log (3)}} x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+3 x^2+e^x x+29 x \left (1-\frac {\log (3)}{29}\right )+3 e^x \left (1-\frac {\log (3)}{3}\right )+87}{x+3-\log (3)}\right )+\frac {4\ 3^{\frac {-x^2+x-29}{x+3-\log (3)}} \left (2 x^3+11 x^2 \left (1-\frac {4 \log (3)}{11}\right )+11 x \left (1+\frac {2}{11} (\log (3)-5) \log (3)\right )-3 \left (1-\frac {\log (3)}{3}\right ) \log (x)-12 \left (1+\frac {1}{12} (\log (3)-7) \log (3)\right )\right ) x^{-\frac {x}{x+3-\log (3)}} \exp \left (\frac {x^3+2 x^2+e^x x+26 x+3 e^x \left (1-\frac {\log (3)}{3}\right )+87}{x+3-\log (3)}\right )}{(2 x+6-\log (9))^2}\right )dx\) |
Int[(E^((-87 - 26*x - 2*x^2 - x^3 + (29 - x + x^2)*Log[3] + E^x*(-3 - x + Log[3]) + x*Log[x])/(-3 - x + Log[3]))*(-12 + 11*x + 11*x^2 + 2*x^3 + (7 - 10*x - 4*x^2)*Log[3] + (-1 + 2*x)*Log[3]^2 + E^x*(9 + 6*x + x^2 + (-6 - 2 *x)*Log[3] + Log[3]^2) + (-3 + Log[3])*Log[x]))/(9 + 6*x + x^2 + (-6 - 2*x )*Log[3] + Log[3]^2),x]
3.20.84.3.1 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]
Leaf count of result is larger than twice the leaf count of optimal. \(51\) vs. \(2(25)=50\).
Time = 9.50 (sec) , antiderivative size = 52, normalized size of antiderivative = 1.93
| method | result | size |
| parallelrisch | \({\mathrm e}^{\frac {x \ln \left (x \right )+\left (\ln \left (3\right )-3-x \right ) {\mathrm e}^{x}+\left (x^{2}-x +29\right ) \ln \left (3\right )-x^{3}-2 x^{2}-26 x -87}{\ln \left (3\right )-3-x}}\) | \(52\) |
| risch | \({\mathrm e}^{\frac {x^{2} \ln \left (3\right )-x^{3}+x \ln \left (x \right )+\ln \left (3\right ) {\mathrm e}^{x}-{\mathrm e}^{x} x -x \ln \left (3\right )-2 x^{2}-3 \,{\mathrm e}^{x}+29 \ln \left (3\right )-26 x -87}{\ln \left (3\right )-3-x}}\) | \(60\) |
int(((ln(3)-3)*ln(x)+(ln(3)^2+(-2*x-6)*ln(3)+x^2+6*x+9)*exp(x)+(-1+2*x)*ln (3)^2+(-4*x^2-10*x+7)*ln(3)+2*x^3+11*x^2+11*x-12)*exp((x*ln(x)+(ln(3)-3-x) *exp(x)+(x^2-x+29)*ln(3)-x^3-2*x^2-26*x-87)/(ln(3)-3-x))/(ln(3)^2+(-2*x-6) *ln(3)+x^2+6*x+9),x,method=_RETURNVERBOSE)
Leaf count of result is larger than twice the leaf count of optimal. 51 vs. \(2 (25) = 50\).
Time = 0.28 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.89 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\left (\frac {x^{3} + 2 \, x^{2} + {\left (x - \log \left (3\right ) + 3\right )} e^{x} - {\left (x^{2} - x + 29\right )} \log \left (3\right ) - x \log \left (x\right ) + 26 \, x + 87}{x - \log \left (3\right ) + 3}\right )} \]
integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+( -1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x )+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))/( log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm=\
e^((x^3 + 2*x^2 + (x - log(3) + 3)*e^x - (x^2 - x + 29)*log(3) - x*log(x) + 26*x + 87)/(x - log(3) + 3))
Leaf count of result is larger than twice the leaf count of optimal. 46 vs. \(2 (22) = 44\).
Time = 0.75 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.70 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\frac {- x^{3} - 2 x^{2} + x \log {\left (x \right )} - 26 x + \left (- x - 3 + \log {\left (3 \right )}\right ) e^{x} + \left (x^{2} - x + 29\right ) \log {\left (3 \right )} - 87}{- x - 3 + \log {\left (3 \right )}}} \]
integrate(((ln(3)-3)*ln(x)+(ln(3)**2+(-2*x-6)*ln(3)+x**2+6*x+9)*exp(x)+(-1 +2*x)*ln(3)**2+(-4*x**2-10*x+7)*ln(3)+2*x**3+11*x**2+11*x-12)*exp((x*ln(x) +(ln(3)-3-x)*exp(x)+(x**2-x+29)*ln(3)-x**3-2*x**2-26*x-87)/(ln(3)-3-x))/(l n(3)**2+(-2*x-6)*ln(3)+x**2+6*x+9),x)
exp((-x**3 - 2*x**2 + x*log(x) - 26*x + (-x - 3 + log(3))*exp(x) + (x**2 - x + 29)*log(3) - 87)/(-x - 3 + log(3)))
Time = 0.55 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.59 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\frac {e^{\left (x^{2} - x - \frac {\log \left (3\right ) \log \left (x\right )}{x - \log \left (3\right ) + 3} + \frac {3 \, \log \left (x\right )}{x - \log \left (3\right ) + 3} + e^{x} + 29\right )}}{x} \]
integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+( -1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x )+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))/( log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm=\
Leaf count of result is larger than twice the leaf count of optimal. 149 vs. \(2 (25) = 50\).
Time = 0.53 (sec) , antiderivative size = 149, normalized size of antiderivative = 5.52 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=e^{\left (\frac {x^{3}}{x - \log \left (3\right ) + 3} - \frac {x^{2} \log \left (3\right )}{x - \log \left (3\right ) + 3} + \frac {2 \, x^{2}}{x - \log \left (3\right ) + 3} + \frac {x e^{x}}{x - \log \left (3\right ) + 3} + \frac {x \log \left (3\right )}{x - \log \left (3\right ) + 3} - \frac {e^{x} \log \left (3\right )}{x - \log \left (3\right ) + 3} - \frac {x \log \left (x\right )}{x - \log \left (3\right ) + 3} + \frac {26 \, x}{x - \log \left (3\right ) + 3} + \frac {3 \, e^{x}}{x - \log \left (3\right ) + 3} - \frac {29 \, \log \left (3\right )}{x - \log \left (3\right ) + 3} + \frac {87}{x - \log \left (3\right ) + 3}\right )} \]
integrate(((log(3)-3)*log(x)+(log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9)*exp(x)+( -1+2*x)*log(3)^2+(-4*x^2-10*x+7)*log(3)+2*x^3+11*x^2+11*x-12)*exp((x*log(x )+(log(3)-3-x)*exp(x)+(x^2-x+29)*log(3)-x^3-2*x^2-26*x-87)/(log(3)-3-x))/( log(3)^2+(-2*x-6)*log(3)+x^2+6*x+9),x, algorithm=\
e^(x^3/(x - log(3) + 3) - x^2*log(3)/(x - log(3) + 3) + 2*x^2/(x - log(3) + 3) + x*e^x/(x - log(3) + 3) + x*log(3)/(x - log(3) + 3) - e^x*log(3)/(x - log(3) + 3) - x*log(x)/(x - log(3) + 3) + 26*x/(x - log(3) + 3) + 3*e^x/ (x - log(3) + 3) - 29*log(3)/(x - log(3) + 3) + 87/(x - log(3) + 3))
Time = 12.98 (sec) , antiderivative size = 120, normalized size of antiderivative = 4.44 \[ \int \frac {e^{\frac {-87-26 x-2 x^2-x^3+\left (29-x+x^2\right ) \log (3)+e^x (-3-x+\log (3))+x \log (x)}{-3-x+\log (3)}} \left (-12+11 x+11 x^2+2 x^3+\left (7-10 x-4 x^2\right ) \log (3)+(-1+2 x) \log ^2(3)+e^x \left (9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)\right )+(-3+\log (3)) \log (x)\right )}{9+6 x+x^2+(-6-2 x) \log (3)+\log ^2(3)} \, dx=\frac {{\left (\frac {1}{3}\right )}^{\frac {{\mathrm {e}}^x-x+x^2+29}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {x\,{\mathrm {e}}^x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {26\,x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {x^3}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {2\,x^2}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {3\,{\mathrm {e}}^x}{x-\ln \left (3\right )+3}}\,{\mathrm {e}}^{\frac {87}{x-\ln \left (3\right )+3}}}{x^{\frac {x}{x-\ln \left (3\right )+3}}} \]
int((exp((26*x - x*log(x) + 2*x^2 + x^3 - log(3)*(x^2 - x + 29) + exp(x)*( x - log(3) + 3) + 87)/(x - log(3) + 3))*(11*x + log(x)*(log(3) - 3) + exp( x)*(6*x - log(3)*(2*x + 6) + log(3)^2 + x^2 + 9) - log(3)*(10*x + 4*x^2 - 7) + log(3)^2*(2*x - 1) + 11*x^2 + 2*x^3 - 12))/(6*x - log(3)*(2*x + 6) + log(3)^2 + x^2 + 9),x)