Sr Examen

Otras calculadoras

Resolución de integrales/ (x+5)/ (x+1)/ log(x+5)/(x+1)

Integral de log(x+5)/(x+1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |  log(x + 5)   
 |  ---------- dx
 |    x + 1      
 |               
/                
0
∫01log⁡(x+5)x+1 dx\int\limits_{0}^{1} \frac{\log{\left(x + 5 \right)}}{x + 1}\, dx 
Integral(log(x + 5)/(x + 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                       //                                      /            pi*I\                                                                    \
                       ||                                      |   (1 + x)*e    |                                                                    |
                       ||                             - polylog|2, -------------| + 2*log(2)*log(1 + x)                               for |1 + x| < 1|
                       ||                                      \         4      /                                                                    |
  /                    ||                                                                                                                            |
 |                     ||                                      /            pi*I\                                                                    |
 | log(x + 5)          ||                                      |   (1 + x)*e    |               /  1  \                                      1       |
 | ---------- dx = C + |<                             - polylog|2, -------------| - 2*log(2)*log|-----|                               for ------- < 1|
 |   x + 1             ||                                      \         4      /               \1 + x/                                   |1 + x|    |
 |                     ||                                                                                                                            |
/                      ||         /            pi*I\                                                                                                 |
                       ||         |   (1 + x)*e    |             __2, 0 /      1, 1 |      \             __0, 2 /1, 1       |      \                 |
                       ||- polylog|2, -------------| - 2*log(2)*/__     |           | 1 + x| + 2*log(2)*/__     |           | 1 + x|     otherwise   |
                       ||         \         4      /            \_|2, 2 \0, 0       |      /            \_|2, 2 \      0, 0 |      /                 |
                       \\                                                                                                                            /
∫log⁡(x+5)x+1 dx=C+{2log⁡(2)log⁡(x+1)−Li⁡2((x+1)eiπ4)for ∣x+1∣<1−2log⁡(2)log⁡(1x+1)−Li⁡2((x+1)eiπ4)for 1∣x+1∣<1−2G2,22,0(1,10,0|x+1)log⁡(2)+2G2,20,2(1,10,0|x+1)log⁡(2)−Li⁡2((x+1)eiπ4)otherwise\int \frac{\log{\left(x + 5 \right)}}{x + 1}\, dx = C + \begin{cases} 2 \log{\left(2 \right)} \log{\left(x + 1 \right)} - \operatorname{Li}_{2}\left(\frac{\left(x + 1\right) e^{i \pi}}{4}\right) & \text{for}\: \left|{x + 1}\right| < 1 \\- 2 \log{\left(2 \right)} \log{\left(\frac{1}{x + 1} \right)} - \operatorname{Li}_{2}\left(\frac{\left(x + 1\right) e^{i \pi}}{4}\right) & \text{for}\: \frac{1}{\left|{x + 1}\right|} < 1 \\- 2 {G_{2, 2}^{2, 0}\left(\begin{matrix} & 1, 1 \\0, 0 & \end{matrix} \middle| {x + 1} \right)} \log{\left(2 \right)} + 2 {G_{2, 2}^{0, 2}\left(\begin{matrix} 1, 1 & \\ & 0, 0 \end{matrix} \middle| {x + 1} \right)} \log{\left(2 \right)} - \operatorname{Li}_{2}\left(\frac{\left(x + 1\right) e^{i \pi}}{4}\right) & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
                         2                      
-polylog(2, -1/2) + 2*log (2) + polylog(2, -1/4)
Li⁡2(−14)−Li⁡2(−12)+2log⁡(2)2\operatorname{Li}_{2}\left(- \frac{1}{4}\right) - \operatorname{Li}_{2}\left(- \frac{1}{2}\right) + 2 \log{\left(2 \right)}^{2} 
=
= 
                         2                      
-polylog(2, -1/2) + 2*log (2) + polylog(2, -1/4)
Li⁡2(−14)−Li⁡2(−12)+2log⁡(2)2\operatorname{Li}_{2}\left(- \frac{1}{4}\right) - \operatorname{Li}_{2}\left(- \frac{1}{2}\right) + 2 \log{\left(2 \right)}^{2} 
-polylog(2, -1/2) + 2*log(2)^2 + polylog(2, -1/4)
Respuesta numérica [src] 
1.17341993707379
1.17341993707379

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

    © Sr Examen – Калькулятор