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Resolución de integrales/ log(x)/ sin(log(x))^2/x

Integral de sin(log(x))^2/x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |     2           
 |  sin (log(x))   
 |  ------------ dx
 |       x         
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$ 
Integral(sin(log(x))^2/x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                 
 |                                                                             /log(x)\                              3/log(x)\                        4/log(x)\                              2/log(x)\              
 |    2                                                                   2*tan|------|                         2*tan |------|                     tan |------|*log(x)                  2*tan |------|*log(x)       
 | sin (log(x))                         log(x)                                 \  2   /                               \  2   /                         \  2   /                               \  2   /              
 | ------------ dx = C + ----------------------------------- - ----------------------------------- + ----------------------------------- + ----------------------------------- + -----------------------------------
 |      x                         4/log(x)\        2/log(x)\            4/log(x)\        2/log(x)\            4/log(x)\        2/log(x)\            4/log(x)\        2/log(x)\            4/log(x)\        2/log(x)\
 |                       2 + 2*tan |------| + 4*tan |------|   2 + 2*tan |------| + 4*tan |------|   2 + 2*tan |------| + 4*tan |------|   2 + 2*tan |------| + 4*tan |------|   2 + 2*tan |------| + 4*tan |------|
/                                  \  2   /         \  2   /             \  2   /         \  2   /             \  2   /         \  2   /             \  2   /         \  2   /             \  2   /         \  2   /
$$\int \frac{\sin^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx = C + \frac{\log{\left(x \right)} \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{2 \log{\left(x \right)} \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{\log{\left(x \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} + \frac{2 \tan^{3}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2} - \frac{2 \tan{\left(\frac{\log{\left(x \right)}}{2} \right)}}{2 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 4 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 2}$$
Simplificar
Respuesta [src] 
  1                
  /                
 |                 
 |     2           
 |  sin (log(x))   
 |  ------------ dx
 |       x         
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$ 
=
= 
  1                
  /                
 |                 
 |     2           
 |  sin (log(x))   
 |  ------------ dx
 |       x         
 |                 
/                  
0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(\log{\left(x \right)} \right)}}{x}\, dx$$ 
Integral(sin(log(x))^2/x, (x, 0, 1))
Respuesta numérica [src] 
21.9871048302453
21.9871048302453

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

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