Sr Examen

Otras calculadoras

Resolución de integrales/ dx/x√(1-4ln²x)

Integral de dx/x√(1-4ln²x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                      
  /                      
 |                       
 |     _______________   
 |    /          2       
 |  \/  1 - 4*log (x)    
 |  ------------------ dx
 |          x            
 |                       
/                        
0
∫011−4log⁡(x)2x dx\int\limits_{0}^{1} \frac{\sqrt{1 - 4 \log{\left(x \right)}^{2}}}{x}\, dx 
Integral(sqrt(1 - 4*log(x)^2)/x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                     
 |                               /                                      
 |    _______________           |                                       
 |   /          2               |   _________________________________   
 | \/  1 - 4*log (x)            | \/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 | ------------------ dx = C +  | ----------------------------------- dx
 |         x                    |                  x                    
 |                              |                                       
/                              /
∫1−4log⁡(x)2x dx=C+∫−(2log⁡(x)−1)(2log⁡(x)+1)x dx\int \frac{\sqrt{1 - 4 \log{\left(x \right)}^{2}}}{x}\, dx = C + \int \frac{\sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}{x}\, dx
Simplificar
Respuesta [src] 
  1                                       
  /                                       
 |                                        
 |    _________________________________   
 |  \/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 |  ----------------------------------- dx
 |                   x                    
 |                                        
/                                         
0
∫01−(2log⁡(x)−1)(2log⁡(x)+1)x dx\int\limits_{0}^{1} \frac{\sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}{x}\, dx 
=
= 
  1                                       
  /                                       
 |                                        
 |    _________________________________   
 |  \/ -(1 + 2*log(x))*(-1 + 2*log(x))    
 |  ----------------------------------- dx
 |                   x                    
 |                                        
/                                         
0
∫01−(2log⁡(x)−1)(2log⁡(x)+1)x dx\int\limits_{0}^{1} \frac{\sqrt{- \left(2 \log{\left(x \right)} - 1\right) \left(2 \log{\left(x \right)} + 1\right)}}{x}\, dx 
Integral(sqrt(-(1 + 2*log(x))*(-1 + 2*log(x)))/x, (x, 0, 1))
Respuesta numérica [src] 
(0.393159803058362 + 1942.50922339667j)
(0.393159803058362 + 1942.50922339667j)

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

    © Sr Examen – Калькулятор