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Resolución de integrales/ lnx/[x*(lnx-1)*((lnx^2)-2)]

Integral de lnx/[x*(lnx-1)*((lnx^2)-2)] dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                                
  /                                
 |                                 
 |             log(x)              
 |  ---------------------------- dx
 |                 /   2       \   
 |  x*(log(x) - 1)*\log (x) - 2/   
 |                                 
/                                  
0
∫01log⁡(x)x(log⁡(x)−1)(log⁡(x)2−2) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx 
Integral(log(x)/(((x*(log(x) - 1))*(log(x)^2 - 2))), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                                                  //            /  ___       \                  \
                                                                                  ||   ___      |\/ 2 *log(x)|                  |
                                                                                  ||-\/ 2 *acoth|------------|                  |
  /                                                                               ||            \     2      /          2       |
 |                                          /        2   \                        ||---------------------------  for log (x) > 2|
 |            log(x)                     log\-2 + log (x)/                        ||             2                              |
 | ---------------------------- dx = C + ----------------- - log(-1 + log(x)) + 2*|<                                            |
 |                /   2       \                  2                                ||            /  ___       \                  |
 | x*(log(x) - 1)*\log (x) - 2/                                                   ||   ___      |\/ 2 *log(x)|                  |
 |                                                                                ||-\/ 2 *atanh|------------|                  |
/                                                                                 ||            \     2      /          2       |
                                                                                  ||---------------------------  for log (x) < 2|
                                                                                  \\             2                              /
∫log⁡(x)x(log⁡(x)−1)(log⁡(x)2−2) dx=C+2({−2acoth⁡(2log⁡(x)2)2for log⁡(x)2>2−2atanh⁡(2log⁡(x)2)2for log⁡(x)2<2)−log⁡(log⁡(x)−1)+log⁡(log⁡(x)2−2)2\int \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx = C + 2 \left(\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\frac{\sqrt{2} \log{\left(x \right)}}{2} \right)}}{2} & \text{for}\: \log{\left(x \right)}^{2} > 2 \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\frac{\sqrt{2} \log{\left(x \right)}}{2} \right)}}{2} & \text{for}\: \log{\left(x \right)}^{2} < 2 \end{cases}\right) - \log{\left(\log{\left(x \right)} - 1 \right)} + \frac{\log{\left(\log{\left(x \right)}^{2} - 2 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Trazar el gráfico f(x)
Respuesta [src] 
  1                                  
  /                                  
 |                                   
 |              log(x)               
 |  ------------------------------ dx
 |                  /        2   \   
 |  x*(-1 + log(x))*\-2 + log (x)/   
 |                                   
/                                    
0
∫01log⁡(x)x(log⁡(x)−1)(log⁡(x)2−2) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx 
=
= 
  1                                  
  /                                  
 |                                   
 |              log(x)               
 |  ------------------------------ dx
 |                  /        2   \   
 |  x*(-1 + log(x))*\-2 + log (x)/   
 |                                   
/                                    
0
∫01log⁡(x)x(log⁡(x)−1)(log⁡(x)2−2) dx\int\limits_{0}^{1} \frac{\log{\left(x \right)}}{x \left(\log{\left(x \right)} - 1\right) \left(\log{\left(x \right)}^{2} - 2\right)}\, dx 
Integral(log(x)/(x*(-1 + log(x))*(-2 + log(x)^2)), (x, 0, 1))
Respuesta numérica [src] 
0.679845038203365
0.679845038203365

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

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