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Resolución de integrales/ (ln^2)/ ln3x/(1+((ln^2)3x))x

Integral de ln3x/(1+((ln^2)3x))x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                     
  /                     
 |                      
 |      log(3*x)        
 |  ---------------*x dx
 |         2            
 |  1 + log (x)*3*x     
 |                      
/                       
0
∫01xlog⁡(3x)x3log⁡(x)2+1 dx\int\limits_{0}^{1} x \frac{\log{\left(3 x \right)}}{x 3 \log{\left(x \right)}^{2} + 1}\, dx 
Integral((log(3*x)/(1 + (log(x)^2*3)*x))*x, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                           /  /                  \            /                  
 |                            | |                   |           |                   
 |     log(3*x)               | |        x          |           |     x*log(x)      
 | ---------------*x dx = C + | | --------------- dx|*log(3) +  | --------------- dx
 |        2                   | |            2      |           |            2      
 | 1 + log (x)*3*x            | | 1 + 3*x*log (x)   |           | 1 + 3*x*log (x)   
 |                            | |                   |           |                   
/                             \/                    /          /
∫xlog⁡(3x)x3log⁡(x)2+1 dx=C+log⁡(3)∫x3xlog⁡(x)2+1 dx+∫xlog⁡(x)3xlog⁡(x)2+1 dx\int x \frac{\log{\left(3 x \right)}}{x 3 \log{\left(x \right)}^{2} + 1}\, dx = C + \log{\left(3 \right)} \int \frac{x}{3 x \log{\left(x \right)}^{2} + 1}\, dx + \int \frac{x \log{\left(x \right)}}{3 x \log{\left(x \right)}^{2} + 1}\, dx
Simplificar
Respuesta [src] 
  1                       
  /                       
 |                        
 |  x*(log(3) + log(x))   
 |  ------------------- dx
 |               2        
 |    1 + 3*x*log (x)     
 |                        
/                         
0
∫01x(log⁡(x)+log⁡(3))3xlog⁡(x)2+1 dx\int\limits_{0}^{1} \frac{x \left(\log{\left(x \right)} + \log{\left(3 \right)}\right)}{3 x \log{\left(x \right)}^{2} + 1}\, dx 
=
= 
  1                       
  /                       
 |                        
 |  x*(log(3) + log(x))   
 |  ------------------- dx
 |               2        
 |    1 + 3*x*log (x)     
 |                        
/                         
0
∫01x(log⁡(x)+log⁡(3))3xlog⁡(x)2+1 dx\int\limits_{0}^{1} \frac{x \left(\log{\left(x \right)} + \log{\left(3 \right)}\right)}{3 x \log{\left(x \right)}^{2} + 1}\, dx 
Integral(x*(log(3) + log(x))/(1 + 3*x*log(x)^2), (x, 0, 1))
Respuesta numérica [src] 
0.27152135302515
0.27152135302515

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

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