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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                      
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |  / 2      \    3      
 |  \x  + 2*x/*log (x)   
 |                       
/                        
1
∫1∞1(x2+2x)log⁡(x)3 dx\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx 
Integral(1/((x^2 + 2*x)*log(x)^3), (x, 1, oo))
Respuesta (Indefinida) [src] 
                                 /                                                        /                                                                              
                                |                                                        |                                                                               
                                |                       -2                               |                        x                                                      
                                | ------------------------------------------------ dx +  | ------------------------------------------------ dx                           
                                |             3             2                            |             3             2                                                   
  /                             | 8*log(x) + x *log(x) + 6*x *log(x) + 12*x*log(x)       | 8*log(x) + x *log(x) + 6*x *log(x) + 12*x*log(x)                              
 |                              |                                                        |                                                                               
 |         1                   /                                                        /                                                           -2 - x + x*log(x)    
 | ------------------ dx = C + --------------------------------------------------------------------------------------------------------------- + ------------------------
 | / 2      \    3                                                                    2                                                          /       2      \    2   
 | \x  + 2*x/*log (x)                                                                                                                            \8 + 2*x  + 8*x/*log (x)
 |                                                                                                                                                                       
/
∫1(x2+2x)log⁡(x)3 dx=C+∫xx3log⁡(x)+6x2log⁡(x)+12xlog⁡(x)+8log⁡(x) dx+∫(−2x3log⁡(x)+6x2log⁡(x)+12xlog⁡(x)+8log⁡(x)) dx2+xlog⁡(x)−x−2(2x2+8x+8)log⁡(x)2\int \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx = C + \frac{\int \frac{x}{x^{3} \log{\left(x \right)} + 6 x^{2} \log{\left(x \right)} + 12 x \log{\left(x \right)} + 8 \log{\left(x \right)}}\, dx + \int \left(- \frac{2}{x^{3} \log{\left(x \right)} + 6 x^{2} \log{\left(x \right)} + 12 x \log{\left(x \right)} + 8 \log{\left(x \right)}}\right)\, dx}{2} + \frac{x \log{\left(x \right)} - x - 2}{\left(2 x^{2} + 8 x + 8\right) \log{\left(x \right)}^{2}}
Simplificar
Respuesta [src] 
 oo                      
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |  / 2      \    3      
 |  \x  + 2*x/*log (x)   
 |                       
/                        
1
∫1∞1(x2+2x)log⁡(x)3 dx\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx 
=
= 
 oo                      
  /                      
 |                       
 |          1            
 |  ------------------ dx
 |  / 2      \    3      
 |  \x  + 2*x/*log (x)   
 |                       
/                        
1
∫1∞1(x2+2x)log⁡(x)3 dx\int\limits_{1}^{\infty} \frac{1}{\left(x^{2} + 2 x\right) \log{\left(x \right)}^{3}}\, dx 
Integral(1/((x^2 + 2*x)*log(x)^3), (x, 1, oo))

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

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