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Resolución de integrales/ (1+ln(x))/(x+sqrt(4+(lnx)^2))

Integral de (1+ln(x))/(x+sqrt(4+(lnx)^2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |       1 + log(x)        
 |  -------------------- dx
 |         _____________   
 |        /        2       
 |  x + \/  4 + log (x)    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 1}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx$$ 
Integral((1 + log(x))/(x + sqrt(4 + log(x)^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                /                            /                       
 |                                |                            |                        
 |      1 + log(x)                |          1                 |        log(x)          
 | -------------------- dx = C +  | -------------------- dx +  | -------------------- dx
 |        _____________           |        _____________       |        _____________   
 |       /        2               |       /        2           |       /        2       
 | x + \/  4 + log (x)            | x + \/  4 + log (x)        | x + \/  4 + log (x)    
 |                                |                            |                        
/                                /                            /
$$\int \frac{\log{\left(x \right)} + 1}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx = C + \int \frac{\log{\left(x \right)}}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx + \int \frac{1}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx$$
Simplificar
Respuesta [src] 
  1                        
  /                        
 |                         
 |       1 + log(x)        
 |  -------------------- dx
 |         _____________   
 |        /        2       
 |  x + \/  4 + log (x)    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 1}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx$$ 
=
= 
  1                        
  /                        
 |                         
 |       1 + log(x)        
 |  -------------------- dx
 |         _____________   
 |        /        2       
 |  x + \/  4 + log (x)    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{\log{\left(x \right)} + 1}{x + \sqrt{\log{\left(x \right)}^{2} + 4}}\, dx$$ 
Integral((1 + log(x))/(x + sqrt(4 + log(x)^2)), (x, 0, 1))
Respuesta numérica [src] 
0.0269163657404893
0.0269163657404893

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

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