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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 oo                         
  /                         
 |                          
 |            1             
 |  --------------------- dx
 |               2          
 |  (2*x + 3)*log (x + 1)   
 |                          
/                           
2
∫2∞1(2x+3)log⁡(x+1)2 dx\int\limits_{2}^{\infty} \frac{1}{\left(2 x + 3\right) \log{\left(x + 1 \right)}^{2}}\, dx 
Integral(1/((2*x + 3)*log(x + 1)^2), (x, 2, oo))
Respuesta (Indefinida) [src] 
  /                                                        /                        
 |                                                        |                         
 |           1                           -1 - x           |           1             
 | --------------------- dx = C + -------------------- +  | --------------------- dx
 |              2                 (3 + 2*x)*log(1 + x)    |          2              
 | (2*x + 3)*log (x + 1)                                  | (3 + 2*x) *log(1 + x)   
 |                                                        |                         
/                                                        /
∫1(2x+3)log⁡(x+1)2 dx=C+−x−1(2x+3)log⁡(x+1)+∫1(2x+3)2log⁡(x+1) dx\int \frac{1}{\left(2 x + 3\right) \log{\left(x + 1 \right)}^{2}}\, dx = C + \frac{- x - 1}{\left(2 x + 3\right) \log{\left(x + 1 \right)}} + \int \frac{1}{\left(2 x + 3\right)^{2} \log{\left(x + 1 \right)}}\, dx
Simplificar
Respuesta [src] 
            oo                         
             /                         
            |                          
   3        |            1             
-------- +  |  --------------------- dx
7*log(3)    |           2              
            |  (3 + 2*x) *log(1 + x)   
            |                          
           /                           
           2
∫2∞1(2x+3)2log⁡(x+1) dx+37log⁡(3)\int\limits_{2}^{\infty} \frac{1}{\left(2 x + 3\right)^{2} \log{\left(x + 1 \right)}}\, dx + \frac{3}{7 \log{\left(3 \right)}} 
=
= 
            oo                         
             /                         
            |                          
   3        |            1             
-------- +  |  --------------------- dx
7*log(3)    |           2              
            |  (3 + 2*x) *log(1 + x)   
            |                          
           /                           
           2
∫2∞1(2x+3)2log⁡(x+1) dx+37log⁡(3)\int\limits_{2}^{\infty} \frac{1}{\left(2 x + 3\right)^{2} \log{\left(x + 1 \right)}}\, dx + \frac{3}{7 \log{\left(3 \right)}} 
3/(7*log(3)) + Integral(1/((3 + 2*x)^2*log(1 + x)), (x, 2, oo))

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

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