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Resolución de integrales/ sec^2/ tan^2/ (sec^2x)/(sqrt(4-tan^2x))

Integral de (sec^2x)/(sqrt(4-tan^2x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |         2           
 |      sec (x)        
 |  ---------------- dx
 |     _____________   
 |    /        2       
 |  \/  4 - tan (x)    
 |                     
/                      
0
$$\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\sqrt{4 - \tan^{2}{\left(x \right)}}}\, dx$$ 
Integral(sec(x)^2/sqrt(4 - tan(x)^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                            /                                  
 |                            |                                   
 |        2                   |                2                  
 |     sec (x)                |             sec (x)               
 | ---------------- dx = C +  | ------------------------------- dx
 |    _____________           |   _____________________________   
 |   /        2               | \/ -(-2 + tan(x))*(2 + tan(x))    
 | \/  4 - tan (x)            |                                   
 |                           /                                    
/
$$\int \frac{\sec^{2}{\left(x \right)}}{\sqrt{4 - \tan^{2}{\left(x \right)}}}\, dx = C + \int \frac{\sec^{2}{\left(x \right)}}{\sqrt{- \left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} + 2\right)}}\, dx$$
Simplificar
Respuesta [src] 
  1                                   
  /                                   
 |                                    
 |                 2                  
 |              sec (x)               
 |  ------------------------------- dx
 |    _____________________________   
 |  \/ -(-2 + tan(x))*(2 + tan(x))    
 |                                    
/                                     
0
$$\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\sqrt{- \left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} + 2\right)}}\, dx$$ 
=
= 
  1                                   
  /                                   
 |                                    
 |                 2                  
 |              sec (x)               
 |  ------------------------------- dx
 |    _____________________________   
 |  \/ -(-2 + tan(x))*(2 + tan(x))    
 |                                    
/                                     
0
$$\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\sqrt{- \left(\tan{\left(x \right)} - 2\right) \left(\tan{\left(x \right)} + 2\right)}}\, dx$$ 
Integral(sec(x)^2/sqrt(-(-2 + tan(x))*(2 + tan(x))), (x, 0, 1))
Respuesta numérica [src] 
0.892597245537764
0.892597245537764

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

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