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Resolución de integrales/ ln(x)/ (x+1)/ (x-1)/ ((x+1)ln(x))/(x-1)

Integral de ((x+1)ln(x))/(x-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  0                  
  /                  
 |                   
 |  (x + 1)*log(x)   
 |  -------------- dx
 |      x - 1        
 |                   
/                    
0
∫00(x+1)log⁡(x)x−1 dx\int\limits_{0}^{0} \frac{\left(x + 1\right) \log{\left(x \right)}}{x - 1}\, dx 
Integral(((x + 1)*log(x))/(x - 1), (x, 0, 0))
Respuesta (Indefinida) [src] 
                               //                         -polylog(2, x) + pi*I*log(x)                           for |x| < 1\                                                        
  /                            ||                                                                                           |                                                        
 |                             ||                                                  /1\                                1     |                                                        
 | (x + 1)*log(x)              ||                         -polylog(2, x) - pi*I*log|-|                           for --- < 1|          /             pi*I\                           
 | -------------- dx = C - x - |<                                                  \x/                               |x|    | - polylog\2, (-1 + x)*e    / + (x + log(-1 + x))*log(x)
 |     x - 1                   ||                                                                                           |                                                        
 |                             ||                       __0, 2 /1, 1       |  \         __2, 0 /      1, 1 |  \             |                                                        
/                              ||-polylog(2, x) + pi*I*/__     |           | x| - pi*I*/__     |           | x|   otherwise |                                                        
                               \\                      \_|2, 2 \      0, 0 |  /        \_|2, 2 \0, 0       |  /             /
∫(x+1)log⁡(x)x−1 dx=C−x+(x+log⁡(x−1))log⁡(x)−{iπlog⁡(x)−Li⁡2(x)for ∣x∣<1−iπlog⁡(1x)−Li⁡2(x)for 1∣x∣<1−iπG2,22,0(1,10,0|x)+iπG2,20,2(1,10,0|x)−Li⁡2(x)otherwise−Li⁡2((x−1)eiπ)\int \frac{\left(x + 1\right) \log{\left(x \right)}}{x - 1}\, dx = C - x + \left(x + \log{\left(x - 1 \right)}\right) \log{\left(x \right)} - \begin{cases} i \pi \log{\left(x \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \left|{x}\right| < 1 \\- i \pi \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- i \pi {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} + i \pi {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} - \operatorname{Li}_{2}\left(x\right) & \text{otherwise} \end{cases} - \operatorname{Li}_{2}\left(\left(x - 1\right) e^{i \pi}\right)
Simplificar
Respuesta [src] 
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Respuesta numérica [src] 
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    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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