Mister Exam

Integral of x*cos(nx) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1              
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 |  x*cos(n*x) dx
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$$\int\limits_{0}^{1} x \cos{\left(n x \right)}\, dx$$
Integral(x*cos(n*x), (x, 0, 1))
The answer (Indefinite) [src]
                       //           2                      \                           
                       ||          x                       |                           
                       ||          --             for n = 0|                           
                       ||          2                       |                           
  /                    ||                                  |     //   x      for n = 0\
 |                     ||/-cos(n*x)                        |     ||                   |
 | x*cos(n*x) dx = C - |<|----------  for n != 0           | + x*|
            
$${{n\,x\,\sin \left(n\,x\right)+\cos \left(n\,x\right)}\over{n^2}}$$
The answer [src]
/  1    sin(n)   cos(n)                                  
|- -- + ------ + ------  for And(n > -oo, n < oo, n != 0)
|   2     n         2                                    
<  n               n                                     
|                                                        
|         1/2                       otherwise            
\                                                        
$${{n\,\sin n+\cos n}\over{n^2}}-{{1}\over{n^2}}$$
=
=
/  1    sin(n)   cos(n)                                  
|- -- + ------ + ------  for And(n > -oo, n < oo, n != 0)
|   2     n         2                                    
<  n               n                                     
|                                                        
|         1/2                       otherwise            
\                                                        
$$\begin{cases} \frac{\sin{\left(n \right)}}{n} + \frac{\cos{\left(n \right)}}{n^{2}} - \frac{1}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{2} & \text{otherwise} \end{cases}$$

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