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  • Identical expressions

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  • (1/(2*pi))*exp(-((ln(x)*ln(x)))/2)/xdx

  • Similar expressions

  • (1/(2*pi))*exp(((ln(x)*ln(x)))/2)/x
Solving integrals/ (1/(2*pi))*exp(-((ln(x)*ln(x)))/2)/x

Integral of (1/(2*pi))*exp(-((ln(x)*ln(x)))/2)/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

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

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