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  • Identical expressions

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  • Similar expressions

  • 1/(x*(ln(x-1))^2)
Solving integrals/ 1/(x*(ln(x+1))^2)

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |       2          
 |  x*log (x + 1)   
 |                  
/                   
1
$$\int\limits_{1}^{\infty} \frac{1}{x \log{\left(x + 1 \right)}^{2}}\, dx$$ 
Integral(1/(x*log(x + 1)^2), (x, 1, oo))
The answer (Indefinite) [src] 
  /                         /                               
 |                         |                                
 |       1                 |       1               -1 - x   
 | ------------- dx = C -  | ------------- dx + ------------
 |      2                  |  2                 x*log(1 + x)
 | x*log (x + 1)           | x *log(1 + x)                  
 |                         |                                
/                         /
$$\int \frac{1}{x \log{\left(x + 1 \right)}^{2}}\, dx = C - \int \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{- x - 1}{x \log{\left(x + 1 \right)}}$$
Simplify
The answer [src] 
   oo                          
    /                          
   |                           
   |        1              2   
-  |  ------------- dx + ------
   |   2                 log(2)
   |  x *log(1 + x)            
   |                           
  /                            
  1
$$- \int\limits_{1}^{\infty} \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{2}{\log{\left(2 \right)}}$$ 
=
= 
   oo                          
    /                          
   |                           
   |        1              2   
-  |  ------------- dx + ------
   |   2                 log(2)
   |  x *log(1 + x)            
   |                           
  /                            
  1
$$- \int\limits_{1}^{\infty} \frac{1}{x^{2} \log{\left(x + 1 \right)}}\, dx + \frac{2}{\log{\left(2 \right)}}$$ 
-Integral(1/(x^2*log(1 + x)), (x, 1, oo)) + 2/log(2)

    Use the examples entering the upper and lower limits of integration.

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