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Resolución de integrales/ (x+2)/ ln(x+2)/x

Integral de ln(x+2)/x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  2              
  /              
 |               
 |  log(x + 2)   
 |  ---------- dx
 |      x        
 |               
/                
-1
∫−12log⁡(x+2)x dx\int\limits_{-1}^{2} \frac{\log{\left(x + 2 \right)}}{x}\, dx 
Integral(log(x + 2)/x, (x, -1, 2))
Respuesta (Indefinida) [src] 
                       //                                   /      pi*I\                                                       \
                       ||                                   |   x*e    |                                                       |
                       ||                          - polylog|2, -------| + log(2)*log(x)                            for |x| < 1|
                       ||                                   \      2   /                                                       |
  /                    ||                                                                                                      |
 |                     ||                                   /      pi*I\                                                       |
 | log(x + 2)          ||                                   |   x*e    |             /1\                                 1     |
 | ---------- dx = C + |<                          - polylog|2, -------| - log(2)*log|-|                            for --- < 1|
 |     x               ||                                   \      2   /             \x/                                |x|    |
 |                     ||                                                                                                      |
/                      ||         /      pi*I\                                                                                 |
                       ||         |   x*e    |           __0, 2 /1, 1       |  \           __2, 0 /      1, 1 |  \             |
                       ||- polylog|2, -------| + log(2)*/__     |           | x| - log(2)*/__     |           | x|   otherwise |
                       ||         \      2   /          \_|2, 2 \      0, 0 |  /          \_|2, 2 \0, 0       |  /             |
                       \\                                                                                                      /
∫log⁡(x+2)x dx=C+{log⁡(2)log⁡(x)−Li⁡2(xeiπ2)for ∣x∣<1−log⁡(2)log⁡(1x)−Li⁡2(xeiπ2)for 1∣x∣<1−G2,22,0(1,10,0|x)log⁡(2)+G2,20,2(1,10,0|x)log⁡(2)−Li⁡2(xeiπ2)otherwise\int \frac{\log{\left(x + 2 \right)}}{x}\, dx = C + \begin{cases} \log{\left(2 \right)} \log{\left(x \right)} - \operatorname{Li}_{2}\left(\frac{x e^{i \pi}}{2}\right) & \text{for}\: \left|{x}\right| < 1 \\- \log{\left(2 \right)} \log{\left(\frac{1}{x} \right)} - \operatorname{Li}_{2}\left(\frac{x e^{i \pi}}{2}\right) & \text{for}\: \frac{1}{\left|{x}\right|} < 1 \\- {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} + {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x} \right)} \log{\left(2 \right)} - \operatorname{Li}_{2}\left(\frac{x e^{i \pi}}{2}\right) & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
nan
NaN\text{NaN} 
=
= 
nan
NaN\text{NaN} 
nan
Respuesta numérica [src] 
82.9187403629937
82.9187403629937

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

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