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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2                    
  /                    
 |                     
 |  x - x*log(x) - 1   
 |  ---------------- dx
 |     x*(x - 1)       
 |                     
/                      
1
∫12(−xlog⁡(x)+x)−1x(x−1) dx\int\limits_{1}^{2} \frac{\left(- x \log{\left(x \right)} + x\right) - 1}{x \left(x - 1\right)}\, dx 
Integral((x - x*log(x) - 1)/((x*(x - 1))), (x, 1, 2))
Respuesta (Indefinida) [src] 
                                                                                           //                         -polylog(2, x) + pi*I*log(x)                           for |x| < 1\
  /                                                                                        ||                                                                                           |
 |                                         / 2    \                                        ||                                                  /1\                                1     |
 | x - x*log(x) - 1          log(2*x)   log\x  - x/   log(-2 + 2*x)                        ||                         -polylog(2, x) - pi*I*log|-|                           for --- < 1|
 | ---------------- dx = C + -------- + ----------- - ------------- - log(x)*log(-1 + x) + |<                                                  \x/                               |x|    |
 |    x*(x - 1)                 2            2              2                              ||                                                                                           |
 |                                                                                         ||                       __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       |  /             /
∫(−xlog⁡(x)+x)−1x(x−1) dx=C+{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)log⁡(x−1)+log⁡(2x)2−log⁡(2x−2)2+log⁡(x2−x)2\int \frac{\left(- x \log{\left(x \right)} + x\right) - 1}{x \left(x - 1\right)}\, dx = C + \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)} \log{\left(x - 1 \right)} + \frac{\log{\left(2 x \right)}}{2} - \frac{\log{\left(2 x - 2 \right)}}{2} + \frac{\log{\left(x^{2} - x \right)}}{2}
Simplificar
Respuesta numérica [src] 
-0.129319852864168
-0.129319852864168

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

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