Integrand size = 409, antiderivative size = 32 \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\frac {x}{\log \left (\log \left (\frac {x}{-e^{1+x}+x+\frac {\log (x)}{3+e^{25}-x}}\right )\right )} \]
Time = 0.40 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.28 \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\frac {x}{\log \left (\log \left (\frac {x \left (-3-e^{25}+x\right )}{\left (3+e^{25}-x\right ) \left (e^{1+x}-x\right )-\log (x)}\right )\right )} \]
Integrate[(3 + E^25 - x + E^(1 + x)*(9 + E^50*(1 - x) - 15*x + 7*x^2 - x^3 + E^25*(6 - 8*x + 2*x^2)) + (-3 - E^25 + 2*x)*Log[x] + (9*x + E^50*x - 6* x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*( -6 + 2*x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x + E^25*x - x^2) /(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]])/((9*x + E^50 *x - 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*(-6 + 2*x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + 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.
| \(\displaystyle \int \frac {e^{x+1} \left (-x^3+7 x^2+e^{25} \left (2 x^2-8 x+6\right )-15 x+e^{50} (1-x)+9\right )+\left (x^3-6 x^2+e^{25} \left (6 x-2 x^2\right )+e^{x+1} \left (-x^2+6 x+e^{25} (2 x-6)-e^{50}-9\right )+e^{50} x+9 x+\left (-x+e^{25}+3\right ) \log (x)\right ) \log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log \left (\log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )-x+\left (2 x-e^{25}-3\right ) \log (x)+e^{25}+3}{\left (x^3-6 x^2+e^{25} \left (6 x-2 x^2\right )+e^{x+1} \left (-x^2+6 x+e^{25} (2 x-6)-e^{50}-9\right )+e^{50} x+9 x+\left (-x+e^{25}+3\right ) \log (x)\right ) \log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )} \, dx\) |
| \(\Big \downarrow \) 6 |
| \(\displaystyle \int \frac {e^{x+1} \left (-x^3+7 x^2+e^{25} \left (2 x^2-8 x+6\right )-15 x+e^{50} (1-x)+9\right )+\left (x^3-6 x^2+e^{25} \left (6 x-2 x^2\right )+e^{x+1} \left (-x^2+6 x+e^{25} (2 x-6)-e^{50}-9\right )+e^{50} x+9 x+\left (-x+e^{25}+3\right ) \log (x)\right ) \log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log \left (\log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )-x+\left (2 x-e^{25}-3\right ) \log (x)+e^{25}+3}{\left (x^3-6 x^2+e^{25} \left (6 x-2 x^2\right )+e^{x+1} \left (-x^2+6 x+e^{25} (2 x-6)-e^{50}-9\right )+\left (9+e^{50}\right ) x+\left (-x+e^{25}+3\right ) \log (x)\right ) \log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )}dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-e^{x+1} \left (-x^3+7 x^2+e^{25} \left (2 x^2-8 x+6\right )-15 x+e^{50} (1-x)+9\right )-\left (x^3-6 x^2+e^{25} \left (6 x-2 x^2\right )+e^{x+1} \left (-x^2+6 x+e^{25} (2 x-6)-e^{50}-9\right )+e^{50} x+9 x+\left (-x+e^{25}+3\right ) \log (x)\right ) \log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log \left (\log \left (\frac {-x^2+e^{25} x+3 x}{-x^2+e^{25} x+3 x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )+x-\left (2 x-e^{25}-3\right ) \log (x)-3 \left (1+\frac {e^{25}}{3}\right )}{\left (-x+e^{25}+3\right ) \left (x^2-e^{x+1} x-3 \left (1+\frac {e^{25}}{3}\right ) x+3 \left (1+\frac {e^{25}}{3}\right ) e^{x+1}-\log (x)\right ) \log \left (\frac {\left (-x+e^{25}+3\right ) x}{-x^2+3 \left (1+\frac {e^{25}}{3}\right ) x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {\left (-x+e^{25}+3\right ) x}{-x^2+3 \left (1+\frac {e^{25}}{3}\right ) x+e^{x+1} \left (x-e^{25}-3\right )+\log (x)}\right )\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {x^4-7 \left (1+\frac {2 e^{25}}{7}\right ) x^3+15 \left (1+\frac {1}{15} e^{25} \left (8+e^{25}\right )\right ) x^2-x^2 \log (x)-8 \left (1+\frac {1}{8} e^{25} \left (6+e^{25}\right )\right ) x+2 \left (1+\frac {e^{25}}{2}\right ) x \log (x)-3 \left (1+\frac {e^{25}}{3}\right )}{\left (-x+e^{25}+3\right ) \left (x^2-e^{x+1} x-3 \left (1+\frac {e^{25}}{3}\right ) x+3 \left (1+\frac {e^{25}}{3}\right ) e^{x+1}-\log (x)\right ) \log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )}+\frac {x+\log \left (\frac {x \left (x-e^{25}-3\right )}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log \left (\log \left (\frac {x \left (x-e^{25}-3\right )}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )-1}{\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {x^4-7 \left (1+\frac {2 e^{25}}{7}\right ) x^3+15 \left (1+\frac {1}{15} e^{25} \left (8+e^{25}\right )\right ) x^2-x^2 \log (x)-8 \left (1+\frac {1}{8} e^{25} \left (6+e^{25}\right )\right ) x+2 \left (1+\frac {e^{25}}{2}\right ) x \log (x)-3 \left (1+\frac {e^{25}}{3}\right )}{\left (-x+e^{25}+3\right ) \left (x^2-e^{x+1} x-3 \left (1+\frac {e^{25}}{3}\right ) x+3 \left (1+\frac {e^{25}}{3}\right ) e^{x+1}-\log (x)\right ) \log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )}+\frac {x+\log \left (\frac {x \left (x-e^{25}-3\right )}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log \left (\log \left (\frac {x \left (x-e^{25}-3\right )}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )-1}{\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right ) \log ^2\left (\log \left (-\frac {\left (-x+e^{25}+3\right ) x}{\left (-x+e^{25}+3\right ) \left (e^{x+1}-x\right )-\log (x)}\right )\right )}\right )dx\) |
Int[(3 + E^25 - x + E^(1 + x)*(9 + E^50*(1 - x) - 15*x + 7*x^2 - x^3 + E^2 5*(6 - 8*x + 2*x^2)) + (-3 - E^25 + 2*x)*Log[x] + (9*x + E^50*x - 6*x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25*(-6 + 2 *x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x + E^25*x - x^2)/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]])/((9*x + E^50*x - 6 *x^2 + x^3 + E^25*(6*x - 2*x^2) + E^(1 + x)*(-9 - E^50 + 6*x - x^2 + E^25* (-6 + 2*x)) + (3 + E^25 - x)*Log[x])*Log[(3*x + E^25*x - x^2)/(3*x + E^25* x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]*Log[Log[(3*x + E^25*x - x^2 )/(3*x + E^25*x - x^2 + E^(1 + x)*(-3 - E^25 + x) + Log[x])]]^2),x]
3.11.8.3.1 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]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.30 (sec) , antiderivative size = 453, normalized size of antiderivative = 14.16
\[\frac {x}{\ln \left (\ln \left (x \right )+\ln \left ({\mathrm e}^{25}+3-x \right )-\ln \left (-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x \right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right ) \left (-\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )+\operatorname {csgn}\left (i \left ({\mathrm e}^{25}+3-x \right )\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )+\operatorname {csgn}\left (\frac {i}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )\right )}{2}-\frac {i \pi \,\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right ) \left (-\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )+\operatorname {csgn}\left (i x \right )\right ) \left (-\operatorname {csgn}\left (\frac {i x \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )+\operatorname {csgn}\left (\frac {i \left ({\mathrm e}^{25}+3-x \right )}{-{\mathrm e}^{x +26}+x \,{\mathrm e}^{25}+x \,{\mathrm e}^{1+x}-x^{2}+\ln \left (x \right )-3 \,{\mathrm e}^{1+x}+3 x}\right )\right )}{2}\right )}\]
int((((exp(25)+3-x)*ln(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(1+x)+ x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)*ln((x*exp(25)-x^2+3*x)/(ln (x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))*ln(ln((x*exp(25)-x^2+3*x)/ (ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))+(-exp(25)+2*x-3)*ln(x) +((1-x)*exp(25)^2+(2*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp(1+x)+exp(25) +3-x)/((exp(25)+3-x)*ln(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*exp(1+x) +x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/ln((x*exp(25)-x^2+3*x)/(l n(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))/ln(ln((x*exp(25)-x^2+3*x) /(ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))^2,x)
x/ln(ln(x)+ln(exp(25)+3-x)-ln(-exp(x+26)+x*exp(25)+x*exp(1+x)-x^2+ln(x)-3* exp(1+x)+3*x)-1/2*I*Pi*csgn(I*(exp(25)+3-x)/(-exp(x+26)+x*exp(25)+x*exp(1+ x)-x^2+ln(x)-3*exp(1+x)+3*x))*(-csgn(I*(exp(25)+3-x)/(-exp(x+26)+x*exp(25) +x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+3*x))+csgn(I*(exp(25)+3-x)))*(-csgn(I*(ex p(25)+3-x)/(-exp(x+26)+x*exp(25)+x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+3*x))+csg n(I/(-exp(x+26)+x*exp(25)+x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+3*x)))-1/2*I*Pi* csgn(I*x/(-exp(x+26)+x*exp(25)+x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+3*x)*(exp(2 5)+3-x))*(-csgn(I*x/(-exp(x+26)+x*exp(25)+x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+ 3*x)*(exp(25)+3-x))+csgn(I*x))*(-csgn(I*x/(-exp(x+26)+x*exp(25)+x*exp(1+x) -x^2+ln(x)-3*exp(1+x)+3*x)*(exp(25)+3-x))+csgn(I*(exp(25)+3-x)/(-exp(x+26) +x*exp(25)+x*exp(1+x)-x^2+ln(x)-3*exp(1+x)+3*x))))
Time = 0.25 (sec) , antiderivative size = 50, normalized size of antiderivative = 1.56 \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\frac {x}{\log \left (\log \left (\frac {x^{2} - x e^{25} - 3 \, x}{x^{2} - x e^{25} - {\left (x - e^{25} - 3\right )} e^{\left (x + 1\right )} - 3 \, x - \log \left (x\right )}\right )\right )} \]
integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*ex p(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+ 3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))*log(log((x*exp(25 )-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))+(-exp(25)+ 2*x-3)*log(x)+((1-x)*exp(25)^2+(2*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp (1+x)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6 *x-9)*exp(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp( 25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))/log(log(( x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))^2, x, algorithm=\
Timed out. \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\text {Timed out} \]
integrate((((exp(25)+3-x)*ln(x)+(-exp(25)**2+(2*x-6)*exp(25)-x**2+6*x-9)*e xp(1+x)+x*exp(25)**2+(-2*x**2+6*x)*exp(25)+x**3-6*x**2+9*x)*ln((x*exp(25)- x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x**2+3*x))*ln(ln((x*exp (25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x**2+3*x)))+(-exp( 25)+2*x-3)*ln(x)+((1-x)*exp(25)**2+(2*x**2-8*x+6)*exp(25)-x**3+7*x**2-15*x +9)*exp(1+x)+exp(25)+3-x)/((exp(25)+3-x)*ln(x)+(-exp(25)**2+(2*x-6)*exp(25 )-x**2+6*x-9)*exp(1+x)+x*exp(25)**2+(-2*x**2+6*x)*exp(25)+x**3-6*x**2+9*x) /ln((x*exp(25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x**2+3*x ))/ln(ln((x*exp(25)-x**2+3*x)/(ln(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x** 2+3*x)))**2,x)
Time = 28.50 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.59 \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\frac {x}{\log \left (-\log \left (x^{2} - x {\left (e^{25} + 3\right )} - {\left (x e - e^{26} - 3 \, e\right )} e^{x} - \log \left (x\right )\right ) + \log \left (x - e^{25} - 3\right ) + \log \left (x\right )\right )} \]
integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*ex p(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+ 3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))*log(log((x*exp(25 )-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))+(-exp(25)+ 2*x-3)*log(x)+((1-x)*exp(25)^2+(2*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp (1+x)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6 *x-9)*exp(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp( 25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))/log(log(( x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))^2, x, algorithm=\
x/log(-log(x^2 - x*(e^25 + 3) - (x*e - e^26 - 3*e)*e^x - log(x)) + log(x - e^25 - 3) + log(x))
Timed out. \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=\text {Timed out} \]
integrate((((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6*x-9)*ex p(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)*log((x*exp(25)-x^2+ 3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))*log(log((x*exp(25 )-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))+(-exp(25)+ 2*x-3)*log(x)+((1-x)*exp(25)^2+(2*x^2-8*x+6)*exp(25)-x^3+7*x^2-15*x+9)*exp (1+x)+exp(25)+3-x)/((exp(25)+3-x)*log(x)+(-exp(25)^2+(2*x-6)*exp(25)-x^2+6 *x-9)*exp(1+x)+x*exp(25)^2+(-2*x^2+6*x)*exp(25)+x^3-6*x^2+9*x)/log((x*exp( 25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x))/log(log(( x*exp(25)-x^2+3*x)/(log(x)+(-exp(25)+x-3)*exp(1+x)+x*exp(25)-x^2+3*x)))^2, x, algorithm=\
Timed out. \[ \int \frac {3+e^{25}-x+e^{1+x} \left (9+e^{50} (1-x)-15 x+7 x^2-x^3+e^{25} \left (6-8 x+2 x^2\right )\right )+\left (-3-e^{25}+2 x\right ) \log (x)+\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log \left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )}{\left (9 x+e^{50} x-6 x^2+x^3+e^{25} \left (6 x-2 x^2\right )+e^{1+x} \left (-9-e^{50}+6 x-x^2+e^{25} (-6+2 x)\right )+\left (3+e^{25}-x\right ) \log (x)\right ) \log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right ) \log ^2\left (\log \left (\frac {3 x+e^{25} x-x^2}{3 x+e^{25} x-x^2+e^{1+x} \left (-3-e^{25}+x\right )+\log (x)}\right )\right )} \, dx=-\int \frac {x-{\mathrm {e}}^{25}+{\mathrm {e}}^{x+1}\,\left (15\,x-{\mathrm {e}}^{25}\,\left (2\,x^2-8\,x+6\right )+{\mathrm {e}}^{50}\,\left (x-1\right )-7\,x^2+x^3-9\right )+\ln \left (x\right )\,\left ({\mathrm {e}}^{25}-2\,x+3\right )-\ln \left (\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \left (x\right )-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\right )\,\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \left (x\right )-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\,\left (9\,x-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{50}-6\,x+x^2-{\mathrm {e}}^{25}\,\left (2\,x-6\right )+9\right )+{\mathrm {e}}^{25}\,\left (6\,x-2\,x^2\right )+x\,{\mathrm {e}}^{50}-6\,x^2+x^3+\ln \left (x\right )\,\left ({\mathrm {e}}^{25}-x+3\right )\right )-3}{{\ln \left (\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \left (x\right )-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\right )}^2\,\ln \left (\frac {3\,x+x\,{\mathrm {e}}^{25}-x^2}{3\,x+\ln \left (x\right )-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{25}-x+3\right )+x\,{\mathrm {e}}^{25}-x^2}\right )\,\left (9\,x-{\mathrm {e}}^{x+1}\,\left ({\mathrm {e}}^{50}-6\,x+x^2-{\mathrm {e}}^{25}\,\left (2\,x-6\right )+9\right )+{\mathrm {e}}^{25}\,\left (6\,x-2\,x^2\right )+x\,{\mathrm {e}}^{50}-6\,x^2+x^3+\ln \left (x\right )\,\left ({\mathrm {e}}^{25}-x+3\right )\right )} \,d x \]
int(-(x - exp(25) + exp(x + 1)*(15*x - exp(25)*(2*x^2 - 8*x + 6) + exp(50) *(x - 1) - 7*x^2 + x^3 - 9) + log(x)*(exp(25) - 2*x + 3) - log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2)))*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*(9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(2 5)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 + log( x)*(exp(25) - x + 3)) - 3)/(log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2)))^2*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*( 9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*( 6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 + log(x)*(exp(25) - x + 3))),x)
-int((x - exp(25) + exp(x + 1)*(15*x - exp(25)*(2*x^2 - 8*x + 6) + exp(50) *(x - 1) - 7*x^2 + x^3 - 9) + log(x)*(exp(25) - 2*x + 3) - log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2)))*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*(9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(2 5)*(2*x - 6) + 9) + exp(25)*(6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 + log( x)*(exp(25) - x + 3)) - 3)/(log(log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2)))^2*log((3*x + x*exp(25) - x^2)/(3*x + log(x) - exp(x + 1)*(exp(25) - x + 3) + x*exp(25) - x^2))*( 9*x - exp(x + 1)*(exp(50) - 6*x + x^2 - exp(25)*(2*x - 6) + 9) + exp(25)*( 6*x - 2*x^2) + x*exp(50) - 6*x^2 + x^3 + log(x)*(exp(25) - x + 3))), x)