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Resolución de integrales/ (x+2)/ (x-3)/ log3((x-3)/(x+2))

Integral de log3((x-3)/(x+2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |     /x - 3\   
 |  log|-----|   
 |     \x + 2/   
 |  ---------- dx
 |    log(3)     
 |               
/                
0
$$\int\limits_{0}^{1} \frac{\log{\left(\frac{x - 3}{x + 2} \right)}}{\log{\left(3 \right)}}\, dx$$ 
Integral(log((x - 3)/(x + 2))/log(3), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                
 |                                                                 
 |    /x - 3\                                               /x - 3\
 | log|-----|          -3*log(-3 + x) - 2*log(2 + x) + x*log|-----|
 |    \x + 2/                                               \x + 2/
 | ---------- dx = C + --------------------------------------------
 |   log(3)                               log(3)                   
 |                                                                 
/
$$\int \frac{\log{\left(\frac{x - 3}{x + 2} \right)}}{\log{\left(3 \right)}}\, dx = C + \frac{x \log{\left(\frac{x - 3}{x + 2} \right)} - 3 \log{\left(x - 3 \right)} - 2 \log{\left(x + 2 \right)}}{\log{\left(3 \right)}}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
     pi*I + log(2/3)   3*(pi*I + log(2))   2*log(2)   3*(pi*I + log(3))
-2 + --------------- - ----------------- + -------- + -----------------
          log(3)             log(3)         log(3)          log(3)
$$-2 + \frac{2 \log{\left(2 \right)}}{\log{\left(3 \right)}} - \frac{3 \left(\log{\left(2 \right)} + i \pi\right)}{\log{\left(3 \right)}} + \frac{\log{\left(\frac{2}{3} \right)} + i \pi}{\log{\left(3 \right)}} + \frac{3 \left(\log{\left(3 \right)} + i \pi\right)}{\log{\left(3 \right)}}$$ 
=
= 
     pi*I + log(2/3)   3*(pi*I + log(2))   2*log(2)   3*(pi*I + log(3))
-2 + --------------- - ----------------- + -------- + -----------------
          log(3)             log(3)         log(3)          log(3)
$$-2 + \frac{2 \log{\left(2 \right)}}{\log{\left(3 \right)}} - \frac{3 \left(\log{\left(2 \right)} + i \pi\right)}{\log{\left(3 \right)}} + \frac{\log{\left(\frac{2}{3} \right)} + i \pi}{\log{\left(3 \right)}} + \frac{3 \left(\log{\left(3 \right)} + i \pi\right)}{\log{\left(3 \right)}}$$ 
-2 + (pi*i + log(2/3))/log(3) - 3*(pi*i + log(2))/log(3) + 2*log(2)/log(3) + 3*(pi*i + log(3))/log(3)
Respuesta numérica [src] 
(-1.89009377493234e-23 + 2.85960086738013j)
(-1.89009377493234e-23 + 2.85960086738013j)

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

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