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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   2                         
  e                          
   /                         
  |                          
  |   /1 + log(x - 1)    \   
  |   |-------------- - 1| dx
  |   \      x           /   
  |                          
 /                           
1 + E
∫1+ee2(−1+log⁡(x−1)+1x) dx\int\limits_{1 + e}^{e^{2}} \left(-1 + \frac{\log{\left(x - 1 \right)} + 1}{x}\right)\, dx 
Integral((1 + log(x - 1))/x - 1, (x, 1 + E, exp(2)))
Respuesta (Indefinida) [src] 
                                     //                         -polylog(2, x) + pi*I*log(x)                           for |x| < 1\         
  /                                  ||                                                                                           |         
 |                                   ||                                                  /1\                                1     |         
 | /1 + log(x - 1)    \              ||                         -polylog(2, x) - pi*I*log|-|                           for --- < 1|         
 | |-------------- - 1| dx = C - x + |<                                                  \x/                               |x|    | + log(x)
 | \      x           /              ||                                                                                           |         
 |                                   ||                       __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       |  /             /
∫(−1+log⁡(x−1)+1x) dx=C−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+log⁡(x)\int \left(-1 + \frac{\log{\left(x - 1 \right)} + 1}{x}\right)\, dx = C - x + \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} + \log{\left(x \right)}
Simplificar
Gráfica
4.04.55.05.56.06.57.0-0.8-0.4
Trazar el gráfico f(x)
Respuesta [src] 
         2                       /    2\                                               
3 + E - e  - log(1 + E) - polylog\2, e / + 2*pi*I - pi*I*log(1 + E) + polylog(2, 1 + E)
−e2−log⁡(1+e)+e+3−iπlog⁡(1+e)+Li⁡2(1+e)−Li⁡2(e2)+2iπ- e^{2} - \log{\left(1 + e \right)} + e + 3 - i \pi \log{\left(1 + e \right)} + \operatorname{Li}_{2}\left(1 + e\right) - \operatorname{Li}_{2}\left(e^{2}\right) + 2 i \pi 
=
= 
         2                       /    2\                                               
3 + E - e  - log(1 + E) - polylog\2, e / + 2*pi*I - pi*I*log(1 + E) + polylog(2, 1 + E)
−e2−log⁡(1+e)+e+3−iπlog⁡(1+e)+Li⁡2(1+e)−Li⁡2(e2)+2iπ- e^{2} - \log{\left(1 + e \right)} + e + 3 - i \pi \log{\left(1 + e \right)} + \operatorname{Li}_{2}\left(1 + e\right) - \operatorname{Li}_{2}\left(e^{2}\right) + 2 i \pi 
3 + E - exp(2) - log(1 + E) - polylog(2, exp(2)) + 2*pi*i - pi*i*log(1 + E) + polylog(2, 1 + E)
Respuesta numérica [src] 
-1.99573306002061
-1.99573306002061

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

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