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Solving integrals/ 1/(x*(ln^2x+16))

Integral of 1/(x*(ln^2x+16)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                    
  /                    
 |                     
 |         1           
 |  ---------------- dx
 |    /   2        \   
 |  x*\log (x) + 16/   
 |                     
/                      
0
∫011x(log⁡(x)2+16) dx\int\limits_{0}^{1} \frac{1}{x \left(\log{\left(x \right)}^{2} + 16\right)}\, dx 
Integral(1/(x*(log(x)^2 + 16)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                       
 |                                                                        
 |        1                         /    2                               \
 | ---------------- dx = C + RootSum\64*z  + 1, i -> i*log(32*i + log(x))/
 |   /   2        \                                                       
 | x*\log (x) + 16/                                                       
 |                                                                        
/
∫1x(log⁡(x)2+16) dx=C+RootSum⁡(64z2+1,(i↦ilog⁡(32i+log⁡(x))))\int \frac{1}{x \left(\log{\left(x \right)}^{2} + 16\right)}\, dx = C + \operatorname{RootSum} {\left(64 z^{2} + 1, \left( i \mapsto i \log{\left(32 i + \log{\left(x \right)} \right)} \right)\right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90200-100
Plot the graph f(x)
The answer [src] 
  1                    
  /                    
 |                     
 |         1           
 |  ---------------- dx
 |    /        2   \   
 |  x*\16 + log (x)/   
 |                     
/                      
0
∫011x(log⁡(x)2+16) dx\int\limits_{0}^{1} \frac{1}{x \left(\log{\left(x \right)}^{2} + 16\right)}\, dx 
=
= 
  1                    
  /                    
 |                     
 |         1           
 |  ---------------- dx
 |    /        2   \   
 |  x*\16 + log (x)/   
 |                     
/                      
0
∫011x(log⁡(x)2+16) dx\int\limits_{0}^{1} \frac{1}{x \left(\log{\left(x \right)}^{2} + 16\right)}\, dx 
Integral(1/(x*(16 + log(x)^2)), (x, 0, 1))
Numerical answer [src] 
0.370080806610993
0.370080806610993

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

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