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Integral of 1/(x((lnx^2)+1)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  1                     
  /                     
 |                      
 |           1          
 |  1*--------------- dx
 |      /   2       \   
 |    x*\log (x) + 1/   
 |                      
/                       
0                       
$$\int\limits_{0}^{1} 1 \cdot \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
Integral(1/(x*(log(x)^2 + 1)), (x, 0, 1))
The answer (Indefinite) [src]
  /                                                                      
 |                                                                       
 |          1                        /   2                              \
 | 1*--------------- dx = C + RootSum\4*z  + 1, i -> i*log(2*i + log(x))/
 |     /   2       \                                                     
 |   x*\log (x) + 1/                                                     
 |                                                                       
/                                                                        
$$\arctan \log x$$
The answer [src]
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |    /       2   \   
 |  x*\1 + log (x)/   
 |                    
/                     
0                     
$${{\pi}\over{2}}$$
=
=
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |    /       2   \   
 |  x*\1 + log (x)/   
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \frac{1}{x \left(\log{\left(x \right)}^{2} + 1\right)}\, dx$$
Numerical answer [src]
1.54812002707698
1.54812002707698

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