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Solving integrals/ x*cos(k*x)

Integral of x*cos(k*x) dx

Limits of integration:

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The solution

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

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

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