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Integral de 1/(sin^2(3x)(2+ctg(3x))) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                            
  /                            
 |                             
 |             1               
 |  ------------------------ dx
 |     2                       
 |  sin (3*x)*(2 + cot(3*x))   
 |                             
/                              
0                              
$$\int\limits_{0}^{1} \frac{1}{\left(\cot{\left(3 x \right)} + 2\right) \sin^{2}{\left(3 x \right)}}\, dx$$
Integral(1/(sin(3*x)^2*(2 + cot(3*x))), (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                    /                           
 |                                    |                            
 |            1                       |            1               
 | ------------------------ dx = C +  | ------------------------ dx
 |    2                               |                   2        
 | sin (3*x)*(2 + cot(3*x))           | (2 + cot(3*x))*sin (3*x)   
 |                                    |                            
/                                    /                             
$$\int \frac{1}{\left(\cot{\left(3 x \right)} + 2\right) \sin^{2}{\left(3 x \right)}}\, dx = C + \int \frac{1}{\left(\cot{\left(3 x \right)} + 2\right) \sin^{2}{\left(3 x \right)}}\, dx$$
Respuesta [src]
  1                            
  /                            
 |                             
 |             1               
 |  ------------------------ dx
 |                    2        
 |  (2 + cot(3*x))*sin (3*x)   
 |                             
/                              
0                              
$$\int\limits_{0}^{1} \frac{1}{\left(\cot{\left(3 x \right)} + 2\right) \sin^{2}{\left(3 x \right)}}\, dx$$
=
=
  1                            
  /                            
 |                             
 |             1               
 |  ------------------------ dx
 |                    2        
 |  (2 + cot(3*x))*sin (3*x)   
 |                             
/                              
0                              
$$\int\limits_{0}^{1} \frac{1}{\left(\cot{\left(3 x \right)} + 2\right) \sin^{2}{\left(3 x \right)}}\, dx$$
Integral(1/((2 + cot(3*x))*sin(3*x)^2), (x, 0, 1))
Respuesta numérica [src]
14.0969830891352
14.0969830891352

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