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Integral of 4/(x(ln^2x+1)) dx

Limits of integration:

from to
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The graph:

from to

Piecewise:

The solution

You have entered [src]
 oo                   
  /                   
 |                    
 |         4          
 |  --------------- dx
 |    /   2       \   
 |  x*\log (x) + 1/   
 |                    
/                     
1                     
$$\int\limits_{1}^{\infty} \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
Integral(4/((x*(log(x)^2 + 1))), (x, 1, oo))
Detail solution
  1. The integral of a constant times a function is the constant times the integral of the function:

    1. Don't know the steps in finding this integral.

      But the integral is

    So, the result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                      
 |                                                                       
 |        4                          /   2                              \
 | --------------- dx = C + 4*RootSum\4*z  + 1, i -> i*log(2*i + log(x))/
 |   /   2       \                                                       
 | x*\log (x) + 1/                                                       
 |                                                                       
/                                                                        
$$\int \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + 4 \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$$
The graph
The answer [src]
   oo                   
    /                   
   |                    
   |         1          
4* |  --------------- dx
   |    /       2   \   
   |  x*\1 + log (x)/   
   |                    
  /                     
  1                     
$$4 \int\limits_{1}^{\infty} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
=
=
   oo                   
    /                   
   |                    
   |         1          
4* |  --------------- dx
   |    /       2   \   
   |  x*\1 + log (x)/   
   |                    
  /                     
  1                     
$$4 \int\limits_{1}^{\infty} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
4*Integral(1/(x*(1 + log(x)^2)), (x, 1, oo))

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