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Resolución de integrales/ (x+5)/ x/((x+5)^2ln^2)

Integral de x/((x+5)^2ln^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                    
  /                    
 |                     
 |         x           
 |  ---------------- dx
 |         2    2      
 |  (x + 5) *log (x)   
 |                     
/                      
2
$$\int\limits_{2}^{\infty} \frac{x}{\left(x + 5\right)^{2} \log{\left(x \right)}^{2}}\, dx$$ 
Integral(x/(((x + 5)^2*log(x)^2)), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                               /                                                                                
 |                               |                                                                      2          
 |        x                      |                          x                                          x           
 | ---------------- dx = C + 10* | --------------------------------------------------- dx - -----------------------
 |        2    2                 |               3              2                           /      2       \       
 | (x + 5) *log (x)              | 125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x)      \25 + x  + 10*x/*log(x)
 |                               |                                                                                 
/                               /
$$\int \frac{x}{\left(x + 5\right)^{2} \log{\left(x \right)}^{2}}\, dx = C - \frac{x^{2}}{\left(x^{2} + 10 x + 25\right) \log{\left(x \right)}} + 10 \int \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx$$
Simplificar
Respuesta [src] 
    oo                                                                   
     /                                                                   
    |                                                                    
    |                           x                                   4    
10* |  --------------------------------------------------- dx + ---------
    |                3              2                           49*log(2)
    |  125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x)               
    |                                                                    
   /                                                                     
   2
$$10 \int\limits_{2}^{\infty} \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx + \frac{4}{49 \log{\left(2 \right)}}$$ 
=
= 
    oo                                                                   
     /                                                                   
    |                                                                    
    |                           x                                   4    
10* |  --------------------------------------------------- dx + ---------
    |                3              2                           49*log(2)
    |  125*log(x) + x *log(x) + 15*x *log(x) + 75*x*log(x)               
    |                                                                    
   /                                                                     
   2
$$10 \int\limits_{2}^{\infty} \frac{x}{x^{3} \log{\left(x \right)} + 15 x^{2} \log{\left(x \right)} + 75 x \log{\left(x \right)} + 125 \log{\left(x \right)}}\, dx + \frac{4}{49 \log{\left(2 \right)}}$$ 
10*Integral(x/(125*log(x) + x^3*log(x) + 15*x^2*log(x) + 75*x*log(x)), (x, 2, oo)) + 4/(49*log(2))

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

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