Integral de (x)/(x(1+lnx)^5) dx

                              /                                                                      
                             |                                                                       
                             |     1                                                                 
                             | ---------- dx                                                         
  /                          | 1 + log(x)                                                            
 |                           |                                   3                          2        
 |        x                 /                       -10*x - x*log (x) - 7*x*log(x) - 4*x*log (x)     
 | --------------- dx = C + ---------------- + ------------------------------------------------------
 |               5                 24                     4            3                         2   
 | x*(1 + log(x))                              24 + 24*log (x) + 96*log (x) + 96*log(x) + 144*log (x)
 |                                                                                                   
/                                                                                                    

$$\int \frac{x}{x \left(\log{\left(x \right)} + 1\right)^{5}}\, dx = C + \frac{- x \log{\left(x \right)}^{3} - 4 x \log{\left(x \right)}^{2} - 7 x \log{\left(x \right)} - 10 x}{24 \log{\left(x \right)}^{4} + 96 \log{\left(x \right)}^{3} + 144 \log{\left(x \right)}^{2} + 96 \log{\left(x \right)} + 24} + \frac{\int \frac{1}{\log{\left(x \right)} + 1}\, dx}{24}$$

Simplificar