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Solving integrals/ sin(1/x)/x

Integral of sin(1/x)/x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  pi           
  --           
  2            
   /           
  |            
  |      /1\   
  |   sin|-|   
  |      \x/   
  |   ------ dx
  |     x      
  |            
 /             
1/100
$$\int\limits_{\frac{1}{100}}^{\frac{\pi}{2}} \frac{\sin{\left(\frac{1}{x} \right)}}{x}\, dx$$ 
Integral(sin(1/x)/x, (x, 1/100, pi/2))
Detail solution

  1. Let .

    Then let and substitute :

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

        SiRule(a=1, b=0, context=sin(_u)/_u, symbol=_u)

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                     
 |                      
 |    /1\               
 | sin|-|               
 |    \x/            /1\
 | ------ dx = C - Si|-|
 |   x               \x/
 |                      
/
$$\int \frac{\sin{\left(\frac{1}{x} \right)}}{x}\, dx = C - \operatorname{Si}{\left(\frac{1}{x} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    /2 \          
- Si|--| + Si(100)
    \pi/
$$- \operatorname{Si}{\left(\frac{2}{\pi} \right)} + \operatorname{Si}{\left(100 \right)}$$ 
=
= 
    /2 \          
- Si|--| + Si(100)
    \pi/
$$- \operatorname{Si}{\left(\frac{2}{\pi} \right)} + \operatorname{Si}{\left(100 \right)}$$ 
-Si(2/pi) + Si(100)
Numerical answer [src] 
0.939766625101071
0.939766625101071

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

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