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Resolución de integrales/ sec^2/ tg^2x/ sec^2x/(tg^2x-9)

Integral de sec^2x/(tg^2x-9) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1               
  /               
 |                
 |       2        
 |    sec (x)     
 |  ----------- dx
 |     2          
 |  tan (x) - 9   
 |                
/                 
0
∫01sec⁡2(x)tan⁡2(x)−9 dx\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} - 9}\, dx 
Integral(sec(x)^2/(tan(x)^2 - 9), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                       /                             
 |                       |                              
 |      2                |             2                
 |   sec (x)             |          sec (x)             
 | ----------- dx = C +  | -------------------------- dx
 |    2                  | (-3 + tan(x))*(3 + tan(x))   
 | tan (x) - 9           |                              
 |                      /                               
/
∫sec⁡2(x)tan⁡2(x)−9 dx=C+∫sec⁡2(x)(tan⁡(x)−3)(tan⁡(x)+3) dx\int \frac{\sec^{2}{\left(x \right)}}{\tan^{2}{\left(x \right)} - 9}\, dx = C + \int \frac{\sec^{2}{\left(x \right)}}{\left(\tan{\left(x \right)} - 3\right) \left(\tan{\left(x \right)} + 3\right)}\, dx
Simplificar
Respuesta [src] 
  1                              
  /                              
 |                               
 |              2                
 |           sec (x)             
 |  -------------------------- dx
 |  (-3 + tan(x))*(3 + tan(x))   
 |                               
/                                
0
∫01sec⁡2(x)(tan⁡(x)−3)(tan⁡(x)+3) dx\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\left(\tan{\left(x \right)} - 3\right) \left(\tan{\left(x \right)} + 3\right)}\, dx 
=
= 
  1                              
  /                              
 |                               
 |              2                
 |           sec (x)             
 |  -------------------------- dx
 |  (-3 + tan(x))*(3 + tan(x))   
 |                               
/                                
0
∫01sec⁡2(x)(tan⁡(x)−3)(tan⁡(x)+3) dx\int\limits_{0}^{1} \frac{\sec^{2}{\left(x \right)}}{\left(\tan{\left(x \right)} - 3\right) \left(\tan{\left(x \right)} + 3\right)}\, dx 
Integral(sec(x)^2/((-3 + tan(x))*(3 + tan(x))), (x, 0, 1))
Respuesta numérica [src] 
-0.191718715674425
-0.191718715674425

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

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