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1/(x*sqrt(ln(x/x)))dx

Integral of 1/(x*sqrt(ln(x/x))) dx

The solution

You have entered [src]

  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |        ________   
 |       /    /x\    
 |  x*  /  log|-|    
 |    \/      \x/    
 |                   
/                    
E

$$\int\limits_{e}^{1} \frac{1}{x \sqrt{\log{\left(\frac{x}{x} \right)}}}\, dx$$

Integral(1/(x*sqrt(log(x/x))), (x, E, 1))

Detail solution

Let $u = x \sqrt{\log{\left(\frac{x}{x} \right)}}$ .

Then let $du = \sqrt{\log{\left(\frac{x}{x} \right)}} dx$ and substitute $\tilde{\infty} du$ :

$\int \frac{\tilde{\infty}}{u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \tilde{\infty} \int \frac{1}{u}\, du$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\tilde{\infty} \log{\left(u \right)}$
Now substitute $u$ back in:

$\tilde{\infty} \log{\left(x \sqrt{\log{\left(\frac{x}{x} \right)}} \right)}$
Now simplify:

$\tilde{\infty}$
Add the constant of integration:

$\tilde{\infty}+ \mathrm{constant}$

The answer is:

$\tilde{\infty}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                               
 |                                /      ________\
 |       1                        |     /    /x\ |
 | -------------- dx = C + zoo*log|x*  /  log|-| |
 |       ________                 \  \/      \x/ /
 |      /    /x\                                  
 | x*  /  log|-|                                  
 |   \/      \x/                                  
 |                                                
/

$$\int \frac{1}{x \sqrt{\log{\left(\frac{x}{x} \right)}}}\, dx = C + \tilde{\infty} \log{\left(x \sqrt{\log{\left(\frac{x}{x} \right)}} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

nan

$$\text{NaN}$$

nan

$$\text{NaN}$$

nan

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

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Identical expressions

Integral of 1/(x*sqrt(ln(x/x))) dx

Limits of integration:

The graph:

Piecewise:

The solution