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Integral de (sin(x)+sin^3(x))/cos(2x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                    
  /                    
 |                     
 |              3      
 |  sin(x) + sin (x)   
 |  ---------------- dx
 |      cos(2*x)       
 |                     
/                      
0                      
$$\int\limits_{0}^{1} \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
Integral((sin(x) + sin(x)^3)/cos(2*x), (x, 0, 1))
Respuesta (Indefinida) [src]
                             /   ___      /  ___       \                                                
                             |-\/ 2 *acoth\\/ 2 *cos(x)/          2                                     
                             |---------------------------  for cos (x) > 1/2                            
                             |             2                                                            
                             <                                                                          
  /                          |   ___      /  ___       \                                                
 |                           |-\/ 2 *atanh\\/ 2 *cos(x)/          2                         /           
 |             3             |---------------------------  for cos (x) < 1/2               |            
 | sin(x) + sin (x)          \             2                                   cos(x)      |  sin(x)    
 | ---------------- dx = C + ----------------------------------------------- + ------ + 2* | -------- dx
 |     cos(2*x)                                     2                            2         | cos(2*x)   
 |                                                                                         |            
/                                                                                         /             
$$\int \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx = C + \frac{\begin{cases} - \frac{\sqrt{2} \operatorname{acoth}{\left(\sqrt{2} \cos{\left(x \right)} \right)}}{2} & \text{for}\: \cos^{2}{\left(x \right)} > \frac{1}{2} \\- \frac{\sqrt{2} \operatorname{atanh}{\left(\sqrt{2} \cos{\left(x \right)} \right)}}{2} & \text{for}\: \cos^{2}{\left(x \right)} < \frac{1}{2} \end{cases}}{2} + \frac{\cos{\left(x \right)}}{2} + 2 \int \frac{\sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
Respuesta [src]
  1                    
  /                    
 |                     
 |     3               
 |  sin (x) + sin(x)   
 |  ---------------- dx
 |      cos(2*x)       
 |                     
/                      
0                      
$$\int\limits_{0}^{1} \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
=
=
  1                    
  /                    
 |                     
 |     3               
 |  sin (x) + sin(x)   
 |  ---------------- dx
 |      cos(2*x)       
 |                     
/                      
0                      
$$\int\limits_{0}^{1} \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{\cos{\left(2 x \right)}}\, dx$$
Integral((sin(x)^3 + sin(x))/cos(2*x), (x, 0, 1))
Respuesta numérica [src]
-1.58209170525304
-1.58209170525304

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