Integrand size = 432, antiderivative size = 28 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )} \]
Time = 0.44 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.00 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right )} \]
Integrate[(E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(2*x - 75*x^2 - 75*x^ 2*Log[x] + (75*x^2*Log[x] - x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]) + Lo g[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]*(-75*x^3*Log[x] + x^2*Log [x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-7 5*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2 + E^(x/(-x + Log[-75 *x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Lo g[-75*x*Log[x] + Log[x^2]]^2)))/(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log [x^2]]))]^2*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2 ])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[ x] + Log[x^2]]^2 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[ x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log [x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^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.
| \(\displaystyle \int \frac {e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}} \left (-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )+2 x\right )+\log \left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )+e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}} \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )\right )}{\log ^2\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )+e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}} \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )\right )} \, dx\) |
| \(\Big \downarrow \) 7292 |
| \(\displaystyle \int \frac {-e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}} \left (-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )+2 x\right )-\log \left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )+e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}} \left (-75 x^3 \log (x)+\left (\log \left (x^2\right )-75 x \log (x)\right ) \log ^2\left (\log \left (x^2\right )-75 x \log (x)\right )+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )\right )}{\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \log ^2\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )^2}dx\) |
| \(\Big \downarrow \) 7239 |
| \(\displaystyle \int \frac {\log \left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right )-\frac {x \left (75 x \log (x) \left (\log \left (\log \left (x^2\right )-75 x \log (x)\right )-1\right )-\log \left (x^2\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )-75 x+2\right )}{\left (e^{\frac {x}{x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )}}+1\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )^2}}{\log ^2\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right )}dx\) |
| \(\Big \downarrow \) 7293 |
| \(\displaystyle \int \left (\frac {1}{\log \left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right )}-\frac {x \left (75 x \log (x) \log \left (\log \left (x^2\right )-75 x \log (x)\right )-\log \left (x^2\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )-75 x-75 x \log (x)+2\right )}{\left (e^{\frac {x}{x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )}}+1\right ) \log ^2\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )^2}\right )dx\) |
| \(\Big \downarrow \) 7299 |
| \(\displaystyle \int \left (\frac {1}{\log \left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right )}-\frac {x \left (75 x \log (x) \log \left (\log \left (x^2\right )-75 x \log (x)\right )-\log \left (x^2\right ) \log \left (\log \left (x^2\right )-75 x \log (x)\right )-75 x-75 x \log (x)+2\right )}{\left (e^{\frac {x}{x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )}}+1\right ) \log ^2\left (e^{\frac {x}{\log \left (\log \left (x^2\right )-75 x \log (x)\right )-x}}+1\right ) \left (75 x \log (x)-\log \left (x^2\right )\right ) \left (x-\log \left (\log \left (x^2\right )-75 x \log (x)\right )\right )^2}\right )dx\) |
Int[(E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(2*x - 75*x^2 - 75*x^2*Log[ x] + (75*x^2*Log[x] - x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]) + Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))]*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Lo g[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2 + E^(x/(-x + Log[-75*x*Log [x] + Log[x^2]]))*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*L og[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75* x*Log[x] + Log[x^2]]^2)))/(Log[1 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]] ))]^2*(-75*x^3*Log[x] + x^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log [-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + L og[x^2]]^2 + E^(x/(-x + Log[-75*x*Log[x] + Log[x^2]]))*(-75*x^3*Log[x] + x ^2*Log[x^2] + (150*x^2*Log[x] - 2*x*Log[x^2])*Log[-75*x*Log[x] + Log[x^2]] + (-75*x*Log[x] + Log[x^2])*Log[-75*x*Log[x] + Log[x^2]]^2))),x]
3.8.6.3.1 Defintions of rubi rules used
Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; Simpl erIntegrandQ[v, u, x]]
Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.48 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.04
\[\frac {x}{\ln \left ({\mathrm e}^{-\frac {x}{-\ln \left (2 \ln \left (x \right )-\frac {i \pi \,\operatorname {csgn}\left (i x^{2}\right ) {\left (-\operatorname {csgn}\left (i x^{2}\right )+\operatorname {csgn}\left (i x \right )\right )}^{2}}{2}-75 x \ln \left (x \right )\right )+x}}+1\right )}\]
int(((((ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+150*x^2 *ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))*exp(x/(ln(ln(x^2) -75*x*ln(x))-x))+(ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^ 2)+150*x^2*ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))*ln(exp( x/(ln(ln(x^2)-75*x*ln(x))-x))+1)+((-x*ln(x^2)+75*x^2*ln(x))*ln(ln(x^2)-75* x*ln(x))-75*x^2*ln(x)-75*x^2+2*x)*exp(x/(ln(ln(x^2)-75*x*ln(x))-x)))/(((ln (x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+150*x^2*ln(x))*ln (ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))*exp(x/(ln(ln(x^2)-75*x*ln(x ))-x))+(ln(x^2)-75*x*ln(x))*ln(ln(x^2)-75*x*ln(x))^2+(-2*x*ln(x^2)+150*x^2 *ln(x))*ln(ln(x^2)-75*x*ln(x))+x^2*ln(x^2)-75*x^3*ln(x))/ln(exp(x/(ln(ln(x ^2)-75*x*ln(x))-x))+1)^2,x)
Time = 0.44 (sec) , antiderivative size = 27, normalized size of antiderivative = 0.96 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (e^{\left (-\frac {x}{x - \log \left (-{\left (75 \, x - 2\right )} \log \left (x\right )\right )}\right )} + 1\right )} \]
integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log( x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x)) *exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2)- 75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^ 2*log(x^2)-75*x^3*log(x))*log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x *log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^2+2* x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log( x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x ))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x ^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x) )*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log (x^2)-75*x*log(x))-x))+1)^2,x, algorithm=\
Timed out. \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\text {Timed out} \]
integrate(((((ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*ln(x))**2+(-2*x*ln(x** 2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x**2)-75*x**3*ln(x))*ex p(x/(ln(ln(x**2)-75*x*ln(x))-x))+(ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*ln (x))**2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x** 2)-75*x**3*ln(x))*ln(exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+1)+((-x*ln(x**2)+7 5*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))-75*x**2*ln(x)-75*x**2+2*x)*exp(x/(ln (ln(x**2)-75*x*ln(x))-x)))/(((ln(x**2)-75*x*ln(x))*ln(ln(x**2)-75*x*ln(x)) **2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln(x))+x**2*ln(x**2)-7 5*x**3*ln(x))*exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+(ln(x**2)-75*x*ln(x))*ln( ln(x**2)-75*x*ln(x))**2+(-2*x*ln(x**2)+150*x**2*ln(x))*ln(ln(x**2)-75*x*ln (x))+x**2*ln(x**2)-75*x**3*ln(x))/ln(exp(x/(ln(ln(x**2)-75*x*ln(x))-x))+1) **2,x)
Leaf count of result is larger than twice the leaf count of optimal. 59 vs. \(2 (28) = 56\).
Time = 0.75 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.11 \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\frac {x}{\log \left (e + e^{\left (-\frac {\log \left (-75 \, x + 2\right )}{x - \log \left (-75 \, x + 2\right ) - \log \left (\log \left (x\right )\right )} - \frac {\log \left (\log \left (x\right )\right )}{x - \log \left (-75 \, x + 2\right ) - \log \left (\log \left (x\right )\right )}\right )}\right ) - 1} \]
integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log( x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x)) *exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2)- 75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^ 2*log(x^2)-75*x^3*log(x))*log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x *log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^2+2* x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log( x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x ))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x ^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x) )*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log (x^2)-75*x*log(x))-x))+1)^2,x, algorithm=\
x/(log(e + e^(-log(-75*x + 2)/(x - log(-75*x + 2) - log(log(x))) - log(log (x))/(x - log(-75*x + 2) - log(log(x))))) - 1)
\[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx =\text {Too large to display} \]
integrate(((((log(x^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log( x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x)) *exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x^2)-75*x*log(x))*log(log(x^2)- 75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x))+x^ 2*log(x^2)-75*x^3*log(x))*log(exp(x/(log(log(x^2)-75*x*log(x))-x))+1)+((-x *log(x^2)+75*x^2*log(x))*log(log(x^2)-75*x*log(x))-75*x^2*log(x)-75*x^2+2* x)*exp(x/(log(log(x^2)-75*x*log(x))-x)))/(((log(x^2)-75*x*log(x))*log(log( x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x))*log(log(x^2)-75*x*log(x ))+x^2*log(x^2)-75*x^3*log(x))*exp(x/(log(log(x^2)-75*x*log(x))-x))+(log(x ^2)-75*x*log(x))*log(log(x^2)-75*x*log(x))^2+(-2*x*log(x^2)+150*x^2*log(x) )*log(log(x^2)-75*x*log(x))+x^2*log(x^2)-75*x^3*log(x))/log(exp(x/(log(log (x^2)-75*x*log(x))-x))+1)^2,x, algorithm=\
Timed out. \[ \int \frac {e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (2 x-75 x^2-75 x^2 \log (x)+\left (75 x^2 \log (x)-x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )\right )+\log \left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )}{\log ^2\left (1+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}}\right ) \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )+e^{\frac {x}{-x+\log \left (-75 x \log (x)+\log \left (x^2\right )\right )}} \left (-75 x^3 \log (x)+x^2 \log \left (x^2\right )+\left (150 x^2 \log (x)-2 x \log \left (x^2\right )\right ) \log \left (-75 x \log (x)+\log \left (x^2\right )\right )+\left (-75 x \log (x)+\log \left (x^2\right )\right ) \log ^2\left (-75 x \log (x)+\log \left (x^2\right )\right )\right )\right )} \, dx=\int \frac {\ln \left ({\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}+1\right )\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^2\,\ln \left (x\right )-2\,x+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (x\,\ln \left (x^2\right )-75\,x^2\,\ln \left (x\right )\right )+75\,x^2\right )}{{\ln \left ({\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}+1\right )}^2\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+{\mathrm {e}}^{-\frac {x}{x-\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}}\,\left (75\,x^3\,\ln \left (x\right )-x^2\,\ln \left (x^2\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )+\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\,\left (2\,x\,\ln \left (x^2\right )-150\,x^2\,\ln \left (x\right )\right )-{\ln \left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )}^2\,\left (\ln \left (x^2\right )-75\,x\,\ln \left (x\right )\right )\right )} \,d x \]
int((log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)*(75*x^3*log(x) - x ^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))*(75*x^3*log(x) - x ^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2) - 75*x*log(x) )^2*(log(x^2) - 75*x*log(x))) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))* (75*x^2*log(x) - 2*x + log(log(x^2) - 75*x*log(x))*(x*log(x^2) - 75*x^2*lo g(x)) + 75*x^2))/(log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)^2*(75 *x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))*(75 *x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 1 50*x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2 ) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x)))),x)
int((log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)*(75*x^3*log(x) - x ^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))*(75*x^3*log(x) - x ^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2) - 75*x*log(x) )^2*(log(x^2) - 75*x*log(x))) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))* (75*x^2*log(x) - 2*x + log(log(x^2) - 75*x*log(x))*(x*log(x^2) - 75*x^2*lo g(x)) + 75*x^2))/(log(exp(-x/(x - log(log(x^2) - 75*x*log(x)))) + 1)^2*(75 *x^3*log(x) - x^2*log(x^2) + exp(-x/(x - log(log(x^2) - 75*x*log(x))))*(75 *x^3*log(x) - x^2*log(x^2) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 1 50*x^2*log(x)) - log(log(x^2) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x))) + log(log(x^2) - 75*x*log(x))*(2*x*log(x^2) - 150*x^2*log(x)) - log(log(x^2 ) - 75*x*log(x))^2*(log(x^2) - 75*x*log(x)))), x)