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Resolución de integrales/ x^2+x/ x^3+x/ (lnx)^2/ (((lnx)^2)-1)/(x^3+x^2+x)

Integral de (((lnx)^2)-1)/(x^3+x^2+x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  -1              
 e                
  /               
 |                
 |     2          
 |  log (x) - 1   
 |  ----------- dx
 |   3    2       
 |  x  + x  + x   
 |                
/                 
0
∫0e−1log⁡(x)2−1x+(x3+x2) dx\int\limits_{0}^{e^{-1}} \frac{\log{\left(x \right)}^{2} - 1}{x + \left(x^{3} + x^{2}\right)}\, dx 
Integral((log(x)^2 - 1)/(x^3 + x^2 + x), (x, 0, exp(-1)))
Respuesta (Indefinida) [src] 
  /                                                          /    ___          \     /                 
 |                                                   ___     |2*\/ 3 *(1/2 + x)|    |                  
 |    2                    /         2\            \/ 3 *atan|-----------------|    |       2          
 | log (x) - 1          log\1 + x + x /                      \        3        /    |    log (x)       
 | ----------- dx = C + --------------- - log(x) + ----------------------------- +  | -------------- dx
 |  3    2                     2                                 3                  |   /         2\   
 | x  + x  + x                                                                      | x*\1 + x + x /   
 |                                                                                  |                  
/                                                                                  /
∫log⁡(x)2−1x+(x3+x2) dx=C−log⁡(x)+log⁡(x2+x+1)2+3atan⁡(23(x+12)3)3+∫log⁡(x)2x(x2+x+1) dx\int \frac{\log{\left(x \right)}^{2} - 1}{x + \left(x^{3} + x^{2}\right)}\, dx = C - \log{\left(x \right)} + \frac{\log{\left(x^{2} + x + 1 \right)}}{2} + \frac{\sqrt{3} \operatorname{atan}{\left(\frac{2 \sqrt{3} \left(x + \frac{1}{2}\right)}{3} \right)}}{3} + \int \frac{\log{\left(x \right)}^{2}}{x \left(x^{2} + x + 1\right)}\, dx
Simplificar
Respuesta [src] 
  -1                             
 e                               
  /                              
 |                               
 |  (1 + log(x))*(-1 + log(x))   
 |  -------------------------- dx
 |          /         2\         
 |        x*\1 + x + x /         
 |                               
/                                
0
∫0e−1(log⁡(x)−1)(log⁡(x)+1)x(x2+x+1) dx\int\limits_{0}^{e^{-1}} \frac{\left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}{x \left(x^{2} + x + 1\right)}\, dx 
=
= 
  -1                             
 e                               
  /                              
 |                               
 |  (1 + log(x))*(-1 + log(x))   
 |  -------------------------- dx
 |          /         2\         
 |        x*\1 + x + x /         
 |                               
/                                
0
∫0e−1(log⁡(x)−1)(log⁡(x)+1)x(x2+x+1) dx\int\limits_{0}^{e^{-1}} \frac{\left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)} + 1\right)}{x \left(x^{2} + x + 1\right)}\, dx 
Integral((1 + log(x))*(-1 + log(x))/(x*(1 + x + x^2)), (x, 0, exp(-1)))
Respuesta numérica [src] 
30510.9331293798
30510.9331293798

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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