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Resolución de integrales/ (2*exp^(2*x)*(2+3*cos(x)))/(1-(cos(x))^2)

Integral de (2*exp^(2*x)*(2+3*cos(x)))/(1-(cos(x))^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |     2*x                  
 |  2*E   *(2 + 3*cos(x))   
 |  --------------------- dx
 |              2           
 |       1 - cos (x)        
 |                          
/                           
0
$$\int\limits_{0}^{1} \frac{2 e^{2 x} \left(3 \cos{\left(x \right)} + 2\right)}{1 - \cos^{2}{\left(x \right)}}\, dx$$ 
Integral(((2*E^(2*x))*(2 + 3*cos(x)))/(1 - cos(x)^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                   /                                    /                             
 |                                   |                                    |                              
 |    2*x                            |                2*x                 |             2*x              
 | 2*E   *(2 + 3*cos(x))             |        cos(x)*e                    |            e                 
 | --------------------- dx = C - 6* | -------------------------- dx - 4* | -------------------------- dx
 |             2                     | (1 + cos(x))*(-1 + cos(x))         | (1 + cos(x))*(-1 + cos(x))   
 |      1 - cos (x)                  |                                    |                              
 |                                  /                                    /                               
/
$$\int \frac{2 e^{2 x} \left(3 \cos{\left(x \right)} + 2\right)}{1 - \cos^{2}{\left(x \right)}}\, dx = C - 4 \int \frac{e^{2 x}}{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right)}\, dx - 6 \int \frac{e^{2 x} \cos{\left(x \right)}}{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right)}\, dx$$
Simplificar
Respuesta [src] 
      1                       1                 
      /                       /                 
     |                       |                  
     |        2*x            |            2*x   
     |     2*e               |  3*cos(x)*e      
- 2* |  ------------ dx - 2* |  ------------- dx
     |          2            |           2      
     |  -1 + cos (x)         |   -1 + cos (x)   
     |                       |                  
    /                       /                   
    0                       0
$$- 2 \int\limits_{0}^{1} \frac{2 e^{2 x}}{\cos^{2}{\left(x \right)} - 1}\, dx - 2 \int\limits_{0}^{1} \frac{3 e^{2 x} \cos{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx$$ 
=
= 
      1                       1                 
      /                       /                 
     |                       |                  
     |        2*x            |            2*x   
     |     2*e               |  3*cos(x)*e      
- 2* |  ------------ dx - 2* |  ------------- dx
     |          2            |           2      
     |  -1 + cos (x)         |   -1 + cos (x)   
     |                       |                  
    /                       /                   
    0                       0
$$- 2 \int\limits_{0}^{1} \frac{2 e^{2 x}}{\cos^{2}{\left(x \right)} - 1}\, dx - 2 \int\limits_{0}^{1} \frac{3 e^{2 x} \cos{\left(x \right)}}{\cos^{2}{\left(x \right)} - 1}\, dx$$ 
-2*Integral(2*exp(2*x)/(-1 + cos(x)^2), (x, 0, 1)) - 2*Integral(3*cos(x)*exp(2*x)/(-1 + cos(x)^2), (x, 0, 1))

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

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