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Solving integrals/ tan(1/x)

Integral of tan(1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1          
  /          
 |           
 |     /1\   
 |  tan|-| dx
 |     \x/   
 |           
/            
0
$$\int\limits_{0}^{1} \tan{\left(\frac{1}{x} \right)}\, dx$$ 
Integral(tan(1/x), (x, 0, 1))
Detail solution

  1. Rewrite the integrand:

  2. Don't know the steps in finding this integral.

    But the integral is

  3. Now simplify:

  4. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
                     /         
                    |          
  /                 |    /1\   
 |                  | sin|-|   
 |    /1\           |    \x/   
 | tan|-| dx = C +  | ------ dx
 |    \x/           |    /1\   
 |                  | cos|-|   
/                   |    \x/   
                    |          
                   /
$$\int \tan{\left(\frac{1}{x} \right)}\, dx = C + \int \frac{\sin{\left(\frac{1}{x} \right)}}{\cos{\left(\frac{1}{x} \right)}}\, dx$$
Simplify
The answer [src] 
  1          
  /          
 |           
 |     /1\   
 |  tan|-| dx
 |     \x/   
 |           
/            
0
$$\int\limits_{0}^{1} \tan{\left(\frac{1}{x} \right)}\, dx$$ 
=
= 
  1          
  /          
 |           
 |     /1\   
 |  tan|-| dx
 |     \x/   
 |           
/            
0
$$\int\limits_{0}^{1} \tan{\left(\frac{1}{x} \right)}\, dx$$ 
Integral(tan(1/x), (x, 0, 1))
Numerical answer [src] 
344.20968320909
344.20968320909

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

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