Integral of 2dx/(xlnx) dx

The solution

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  E            
  /            
 |             
 |     2       
 |  -------- dx
 |  x*log(x)   
 |             
/              
1

$$\int\limits_{1}^{e} \frac{2}{x \log{\left(x \right)}}\, dx$$

Integral(2/((x*log(x))), (x, 1, E))

Detail solution

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

$\int \frac{2}{x \log{\left(x \right)}}\, dx = 2 \int \frac{1}{x \log{\left(x \right)}}\, dx$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $\log{\left(\log{\left(x \right)} \right)}$
So, the result is: $2 \log{\left(\log{\left(x \right)} \right)}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                               
 |                                
 |    2                           
 | -------- dx = C + 2*log(log(x))
 | x*log(x)                       
 |                                
/

$$\int \frac{2}{x \log{\left(x \right)}}\, dx = C + 2 \log{\left(\log{\left(x \right)} \right)}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

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$$\infty$$

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$$\infty$$

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Numerical answer [src]

87.0984741687787

87.0984741687787

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

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Identical expressions

Integral of 2dx/(xlnx) dx

Limits of integration:

The graph:

Piecewise:

The solution