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Resolución de integrales/ ln(x)/ (sin(2*ln(x))+ln2x)/x

Integral de (sin(2*ln(x))+ln2x)/x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                            
  /                            
 |                             
 |  sin(2*log(x)) + log(2*x)   
 |  ------------------------ dx
 |             x               
 |                             
/                              
0
$$\int\limits_{0}^{1} \frac{\log{\left(2 x \right)} + \sin{\left(2 \log{\left(x \right)} \right)}}{x}\, dx$$ 
Integral((sin(2*log(x)) + log(2*x))/x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                         
 |                                      2                                   
 | sin(2*log(x)) + log(2*x)          log (x)   cos(2*log(x))                
 | ------------------------ dx = C + ------- - ------------- + log(2)*log(x)
 |            x                         2            2                      
 |                                                                          
/
$$\int \frac{\log{\left(2 x \right)} + \sin{\left(2 \log{\left(x \right)} \right)}}{x}\, dx = C + \frac{\log{\left(x \right)}^{2}}{2} + \log{\left(2 \right)} \log{\left(x \right)} - \frac{\cos{\left(2 \log{\left(x \right)} \right)}}{2}$$
Simplificar
Respuesta [src] 
  1                            
  /                            
 |                             
 |  log(2*x) + sin(2*log(x))   
 |  ------------------------ dx
 |             x               
 |                             
/                              
0
$$\int\limits_{0}^{1} \frac{\log{\left(2 x \right)} + \sin{\left(2 \log{\left(x \right)} \right)}}{x}\, dx$$ 
=
= 
  1                            
  /                            
 |                             
 |  log(2*x) + sin(2*log(x))   
 |  ------------------------ dx
 |             x               
 |                             
/                              
0
$$\int\limits_{0}^{1} \frac{\log{\left(2 x \right)} + \sin{\left(2 \log{\left(x \right)} \right)}}{x}\, dx$$ 
Integral((log(2*x) + sin(2*log(x)))/x, (x, 0, 1))
Respuesta numérica [src] 
-941.373402825431
-941.373402825431

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

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