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Solving integrals/ xcosnx

Integral of xcosnx dx

Limits of integration:

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The solution

You have entered [src] 
  1              
  /              
 |               
 |  x*cos(n*x) dx
 |               
/                
0
∫01xcos⁡(nx) dx\int\limits_{0}^{1} x \cos{\left(n x \right)}\, dx
Simplify
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⁡(n x)+cos⁡(n x)n2{{n\,x\,\sin \left(n\,x\right)+\cos \left(n\,x\right)}\over{n^2}}
Simplify
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⁡nn2−1n2{{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            
\
{sin⁡(n)n+cos⁡(n)n2−1n2for n>−∞∧n<∞∧n≠012otherwise\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}
Simplify

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

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