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Solving integrals/ x*sin(kx)

Integral of x*sin(kx) dx

Limits of integration:

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Piecewise:

The solution

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

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

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