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Solving integrals/ x*sin(1/x)

Integral of x*sin(1/x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1            
  /            
 |             
 |       /1\   
 |  x*sin|-| dx
 |       \x/   
 |             
/              
0
$$\int\limits_{0}^{1} x \sin{\left(\frac{1}{x} \right)}\, dx$$ 
Integral(x*sin(1/x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                    /1\        /1\    2    /1\
 |                   Si|-|   x*cos|-|   x *sin|-|
 |      /1\            \x/        \x/         \x/
 | x*sin|-| dx = C + ----- + -------- + ---------
 |      \x/            2        2           2    
 |                                               
/
$$\int x \sin{\left(\frac{1}{x} \right)}\, dx = C + \frac{x^{2} \sin{\left(\frac{1}{x} \right)}}{2} + \frac{x \cos{\left(\frac{1}{x} \right)}}{2} + \frac{\operatorname{Si}{\left(\frac{1}{x} \right)}}{2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
Si(1)   cos(1)   sin(1)   pi
----- + ------ + ------ - --
  2       2        2      4
$$- \frac{\pi}{4} + \frac{\cos{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)}}{2} + \frac{\operatorname{Si}{\left(1 \right)}}{2}$$ 
=
= 
Si(1)   cos(1)   sin(1)   pi
----- + ------ + ------ - --
  2       2        2      4
$$- \frac{\pi}{4} + \frac{\cos{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)}}{2} + \frac{\operatorname{Si}{\left(1 \right)}}{2}$$ 
Si(1)/2 + cos(1)/2 + sin(1)/2 - pi/4
Numerical answer [src] 
0.378558237367188
0.378558237367188

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

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