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Resolución de integrales/ 1/x^2/ 9-x^2/ 1/x^2sqrt(9-x^2)

Integral de 1/x^2sqrt(9-x^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 sinh(2)              
    /                 
   |                  
   |       ________   
   |      /      2    
   |    \/  9 - x     
   |    ----------- dx
   |          2       
   |         x        
   |                  
  /                   
sinh(1)
$$\int\limits_{\sinh{\left(1 \right)}}^{\sinh{\left(2 \right)}} \frac{\sqrt{9 - x^{2}}}{x^{2}}\, dx$$ 
Integral(sqrt(9 - x^2)/x^2, (x, sinh(1), sinh(2)))
Respuesta (Indefinida) [src] 
  /                                          
 |                                           
 |    ________                       ________
 |   /      2                       /      2 
 | \/  9 - x                /x\   \/  9 - x  
 | ----------- dx = C - asin|-| - -----------
 |       2                  \3/        x     
 |      x                                    
 |                                           
/
$$\int \frac{\sqrt{9 - x^{2}}}{x^{2}}\, dx = C - \operatorname{asin}{\left(\frac{x}{3} \right)} - \frac{\sqrt{9 - x^{2}}}{x}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
                     ______________      ______________                
                    /         2         /         2                    
      /sinh(2)\   \/  9 - sinh (1)    \/  9 - sinh (2)        /sinh(1)\
- asin|-------| + ----------------- - ----------------- + asin|-------|
      \   3   /        sinh(1)             sinh(2)            \   3   /
$$\operatorname{asin}{\left(\frac{\sinh{\left(1 \right)}}{3} \right)} + \frac{\sqrt{9 - \sinh^{2}{\left(1 \right)}}}{\sinh{\left(1 \right)}} - \frac{\sqrt{9 - \sinh^{2}{\left(2 \right)}}}{\sinh{\left(2 \right)}} - \operatorname{asin}{\left(\frac{\sinh{\left(2 \right)}}{3} \right)}$$ 
=
= 
                     ______________      ______________                
                    /         2         /         2                    
      /sinh(2)\   \/  9 - sinh (1)    \/  9 - sinh (2)        /sinh(1)\
- asin|-------| + ----------------- - ----------------- + asin|-------|
      \   3   /        sinh(1)             sinh(2)            \   3   /
$$\operatorname{asin}{\left(\frac{\sinh{\left(1 \right)}}{3} \right)} + \frac{\sqrt{9 - \sinh^{2}{\left(1 \right)}}}{\sinh{\left(1 \right)}} - \frac{\sqrt{9 - \sinh^{2}{\left(2 \right)}}}{\sinh{\left(2 \right)}} - \operatorname{asin}{\left(\frac{\sinh{\left(2 \right)}}{3} \right)}$$ 
-asin(sinh(2)/3) + sqrt(9 - sinh(1)^2)/sinh(1) - sqrt(9 - sinh(2)^2)/sinh(2) + asin(sinh(1)/3)
Respuesta numérica [src] 
(1.18054511925678 + 0.0737457880827969j)
(1.18054511925678 + 0.0737457880827969j)

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

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