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Resolución de integrales/ ln(c1*x+c2)

Integral de ln(c1*x+c2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                  
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 |  log(c1*x + c2) dx
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0
∫01log⁡(c1x+c2) dx\int\limits_{0}^{1} \log{\left(c_{1} x + c_{2} \right)}\, dx 
Integral(log(c1*x + c2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                        //-c2 + (c1*x + c2)*log(c1*x + c2) - c1*x             \
 |                         ||---------------------------------------  for c1 != 0|
 | log(c1*x + c2) dx = C + |<                   c1                               |
 |                         ||                                                    |
/                          \\               x*log(c2)                  otherwise /
∫log⁡(c1x+c2) dx=C+{−c1x−c2+(c1x+c2)log⁡(c1x+c2)c1for c1≠0xlog⁡(c2)otherwise\int \log{\left(c_{1} x + c_{2} \right)}\, dx = C + \begin{cases} \frac{- c_{1} x - c_{2} + \left(c_{1} x + c_{2}\right) \log{\left(c_{1} x + c_{2} \right)}}{c_{1}} & \text{for}\: c_{1} \neq 0 \\x \log{\left(c_{2} \right)} & \text{otherwise} \end{cases}
Simplificar
Respuesta [src] 
     /1    c2*log(c1 + c2)\   c2*log(c2)               
- c1*|-- - ---------------| - ---------- + log(c1 + c2)
     |c1           2      |       c1                   
     \           c1       /
−c1(1c1−c2log⁡(c1+c2)c12)+log⁡(c1+c2)−c2log⁡(c2)c1- c_{1} \left(\frac{1}{c_{1}} - \frac{c_{2} \log{\left(c_{1} + c_{2} \right)}}{c_{1}^{2}}\right) + \log{\left(c_{1} + c_{2} \right)} - \frac{c_{2} \log{\left(c_{2} \right)}}{c_{1}} 
=
= 
     /1    c2*log(c1 + c2)\   c2*log(c2)               
- c1*|-- - ---------------| - ---------- + log(c1 + c2)
     |c1           2      |       c1                   
     \           c1       /
−c1(1c1−c2log⁡(c1+c2)c12)+log⁡(c1+c2)−c2log⁡(c2)c1- c_{1} \left(\frac{1}{c_{1}} - \frac{c_{2} \log{\left(c_{1} + c_{2} \right)}}{c_{1}^{2}}\right) + \log{\left(c_{1} + c_{2} \right)} - \frac{c_{2} \log{\left(c_{2} \right)}}{c_{1}} 
-c1*(1/c1 - c2*log(c1 + c2)/c1^2) - c2*log(c2)/c1 + log(c1 + c2)

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

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