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Similar expressions
4/(x(ln^2x-1))

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

The solution

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 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

The integral of a constant times a function is the constant times the integral of the function:

$\int \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = 4 \int \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$
So, the result is: $4 \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$
Now simplify:

$- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}$
Add the constant of integration:

$- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}+ \mathrm{constant}$

The answer is:

$- 2 i \log{\left(\log{\left(x \right)} - i \right)} + 2 i \log{\left(\log{\left(x \right)} + i \right)}+ \mathrm{constant}$

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/                                                       
 |                                                                       
/

$$\int \frac{4}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx = C + 4 \operatorname{RootSum} {\left(4 z^{2} + 1, \left( i \mapsto i \log{\left(2 i + \log{\left(x \right)} \right)} \right)\right)}$$

Simplify

The graph

Plot the graph f(x)

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.

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

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Piecewise:

The solution