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Resolución de integrales/ ln(sin(x))*ln(abs(cos(x)))/sin(x)/cos(x)

Integral de ln(sin(x))*ln(abs(cos(x)))/sin(x)/cos(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                               
  /                               
 |                                
 |  /log(sin(x))*log(|cos(x)|)\   
 |  |-------------------------|   
 |  \          sin(x)         /   
 |  --------------------------- dx
 |             cos(x)             
 |                                
/                                 
0
∫0πlog⁡(sin⁡(x))log⁡(∣cos⁡(x)∣)1sin⁡(x)cos⁡(x) dx\int\limits_{0}^{\pi} \frac{\log{\left(\sin{\left(x \right)} \right)} \log{\left(\left|{\cos{\left(x \right)}}\right| \right)} \frac{1}{\sin{\left(x \right)}}}{\cos{\left(x \right)}}\, dx 
Integral(((log(sin(x))*log(Abs(cos(x))))/sin(x))/cos(x), (x, 0, pi))
Respuesta (Indefinida) [src] 
  /                                                                    
 |                                                                     
 | /log(sin(x))*log(|cos(x)|)\            /                            
 | |-------------------------|           |                             
 | \          sin(x)         /           | log(|cos(x)|)*log(sin(x))   
 | --------------------------- dx = C +  | ------------------------- dx
 |            cos(x)                     |       cos(x)*sin(x)         
 |                                       |                             
/                                       /
∫log⁡(sin⁡(x))log⁡(∣cos⁡(x)∣)1sin⁡(x)cos⁡(x) dx=C+∫log⁡(sin⁡(x))log⁡(∣cos⁡(x)∣)sin⁡(x)cos⁡(x) dx\int \frac{\log{\left(\sin{\left(x \right)} \right)} \log{\left(\left|{\cos{\left(x \right)}}\right| \right)} \frac{1}{\sin{\left(x \right)}}}{\cos{\left(x \right)}}\, dx = C + \int \frac{\log{\left(\sin{\left(x \right)} \right)} \log{\left(\left|{\cos{\left(x \right)}}\right| \right)}}{\sin{\left(x \right)} \cos{\left(x \right)}}\, dx
Simplificar
Respuesta numérica [src] 
-2.58597612732067e-17
-2.58597612732067e-17

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

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