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Resolución de integrales/ x×lnx/ (x+2)/ 1/((x+2)×lnx×lnx)

Integral de 1/((x+2)×lnx×lnx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                         
  /                         
 |                          
 |            1             
 |  --------------------- dx
 |  (x + 2)*log(x)*log(x)   
 |                          
/                           
0
∫011(x+2)log⁡(x)log⁡(x) dx\int\limits_{0}^{1} \frac{1}{\left(x + 2\right) \log{\left(x \right)} \log{\left(x \right)}}\, dx 
Integral(1/(((x + 2)*log(x))*log(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                   /                                                     
 |                                   |                                                      
 |           1                       |                 1                            x       
 | --------------------- dx = C + 2* | --------------------------------- dx - --------------
 | (x + 2)*log(x)*log(x)             |             2                          (2 + x)*log(x)
 |                                   | 4*log(x) + x *log(x) + 4*x*log(x)                    
/                                    |                                                      
                                    /
∫1(x+2)log⁡(x)log⁡(x) dx=C−x(x+2)log⁡(x)+2∫1x2log⁡(x)+4xlog⁡(x)+4log⁡(x) dx\int \frac{1}{\left(x + 2\right) \log{\left(x \right)} \log{\left(x \right)}}\, dx = C - \frac{x}{\left(x + 2\right) \log{\left(x \right)}} + 2 \int \frac{1}{x^{2} \log{\left(x \right)} + 4 x \log{\left(x \right)} + 4 \log{\left(x \right)}}\, dx
Simplificar
Respuesta [src] 
         1                                     
         /                                     
        |                                      
        |                  1                   
oo + 2* |  --------------------------------- dx
        |              2                       
        |  4*log(x) + x *log(x) + 4*x*log(x)   
        |                                      
       /                                       
       0
2∫011x2log⁡(x)+4xlog⁡(x)+4log⁡(x) dx+∞2 \int\limits_{0}^{1} \frac{1}{x^{2} \log{\left(x \right)} + 4 x \log{\left(x \right)} + 4 \log{\left(x \right)}}\, dx + \infty 
=
= 
         1                                     
         /                                     
        |                                      
        |                  1                   
oo + 2* |  --------------------------------- dx
        |              2                       
        |  4*log(x) + x *log(x) + 4*x*log(x)   
        |                                      
       /                                       
       0
2∫011x2log⁡(x)+4xlog⁡(x)+4log⁡(x) dx+∞2 \int\limits_{0}^{1} \frac{1}{x^{2} \log{\left(x \right)} + 4 x \log{\left(x \right)} + 4 \log{\left(x \right)}}\, dx + \infty 
oo + 2*Integral(1/(4*log(x) + x^2*log(x) + 4*x*log(x)), (x, 0, 1))
Respuesta numérica [src] 
4.60065203752215e+18
4.60065203752215e+18

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

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