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Solving integrals/ x*sin(n*x)*dx

Integral of x*sin(n*x)*dx dx

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The solution

You have entered [src] 
  1                
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 |  x*sin(n*x)*1 dx
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0
∫01xsin⁡(nx)1 dx\int\limits_{0}^{1} x \sin{\left(n x \right)} 1\, dx 
Integral(x*sin(n*x)*1, (x, 0, 1))
The answer (Indefinite) [src] 
                         //            0              for n = 0\                             
                         ||                                    |                             
  /                      || //sin(n*x)            \            |     //    0       for n = 0\
 |                       || ||--------  for n != 0|            |     ||                     |
 | x*sin(n*x)*1 dx = C - |<-|<   n                |            | + x*|<-cos(n*x)            |
 |                       || ||                    |            |     ||----------  otherwise|
/                        || \\   x      otherwise /            |     \\    n                /
                         ||-------------------------  otherwise|                             
                         \\            n                       /
sin⁡(n x)−n x cos⁡(n x)n2{{\sin \left(n\,x\right)-n\,x\,\cos \left(n\,x\right)}\over{n^2}}
Simplify
The answer [src] 
/sin(n)   cos(n)                                  
|------ - ------  for And(n > -oo, n < oo, n != 0)
|   2       n                                     
<  n                                              
|                                                 
|       0                    otherwise            
\
sin⁡n−n cos⁡nn2{{\sin n-n\,\cos n}\over{n^2}} 
=
= 
/sin(n)   cos(n)                                  
|------ - ------  for And(n > -oo, n < oo, n != 0)
|   2       n                                     
<  n                                              
|                                                 
|       0                    otherwise            
\
{−cos⁡(n)n+sin⁡(n)n2for n>−∞∧n<∞∧n≠00otherwise\begin{cases} - \frac{\cos{\left(n \right)}}{n} + \frac{\sin{\left(n \right)}}{n^{2}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\0 & \text{otherwise} \end{cases}
Simplify

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

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