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Solving integrals/ (x-1)*cos(n*x)

Integral of (x-1)*cos(n*x) dx

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The solution

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

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

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