Интеграл x*cos(w*x) (dx)

Вы ввели

  1              
  /              
 |               
 |  x*cos(w*x) dx
 |               
/                
0                

$$\int_{0}^{1} x \cos{\left (w x \right )}\, dx$$

Ответ

  1                 /         1/2            for w = 0
  /                 |                                 
 |                  |  1    sin(w)   cos(w)           
 |  x*cos(w*x) dx = <- -- + ------ + ------  otherwise
 |                  |   2     w         2             
/                   |  w               w              
0                   \                                 

$${{w\,\sin w+\cos w}\over{w^2}}-{{1}\over{w^2}}$$