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Resolución de integrales/ ln^2x/ 4*ln^2/ 1/(x*(9-4*ln^2x)^(1/2))

Integral de 1/(x*(9-4*ln^2x)^(1/2)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                        
  /                        
 |                         
 |           1             
 |  -------------------- dx
 |       _______________   
 |      /          2       
 |  x*\/  9 - 4*log (x)    
 |                         
/                          
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{9 - 4 \log{\left(x \right)}^{2}}}\, dx$$ 
Integral(1/(x*sqrt(9 - 4*log(x)^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                /                                        
 |                                |                                         
 |          1                     |                   1                     
 | -------------------- dx = C +  | ------------------------------------- dx
 |      _______________           |     _________________________________   
 |     /          2               | x*\/ -(-3 + 2*log(x))*(3 + 2*log(x))    
 | x*\/  9 - 4*log (x)            |                                         
 |                               /                                          
/
$$\int \frac{1}{x \sqrt{9 - 4 \log{\left(x \right)}^{2}}}\, dx = C + \int \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 3\right) \left(2 \log{\left(x \right)} + 3\right)}}\, dx$$
Simplificar
Respuesta [src] 
  1                                         
  /                                         
 |                                          
 |                    1                     
 |  ------------------------------------- dx
 |      _________________________________   
 |  x*\/ -(-3 + 2*log(x))*(3 + 2*log(x))    
 |                                          
/                                           
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 3\right) \left(2 \log{\left(x \right)} + 3\right)}}\, dx$$ 
=
= 
  1                                         
  /                                         
 |                                          
 |                    1                     
 |  ------------------------------------- dx
 |      _________________________________   
 |  x*\/ -(-3 + 2*log(x))*(3 + 2*log(x))    
 |                                          
/                                           
0
$$\int\limits_{0}^{1} \frac{1}{x \sqrt{- \left(2 \log{\left(x \right)} - 3\right) \left(2 \log{\left(x \right)} + 3\right)}}\, dx$$ 
Integral(1/(x*sqrt(-(-3 + 2*log(x))*(3 + 2*log(x)))), (x, 0, 1))
Respuesta numérica [src] 
(0.717627550394306 - 2.06403892241411j)
(0.717627550394306 - 2.06403892241411j)

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

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