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Solving integrals/ (x^2)*(cos(nx))

Integral of (x^2)*(cos(nx)) dx

Limits of integration:

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The solution

You have entered [src] 
  1               
  /               
 |                
 |   2            
 |  x *cos(n*x) dx
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0
∫01x2cos⁡(nx) dx\int\limits_{0}^{1} x^{2} \cos{\left(n x \right)}\, dx
Simplify
The answer (Indefinite) [src] 
                          //                 3                           \                            
                          ||                x                            |                            
                          ||                --                  for n = 0|                            
                          ||                3                            |                            
  /                       ||                                             |                            
 |                        ||/sin(n*x)   x*cos(n*x)                       |      //   x      for n = 0\
 |  2                     |||-------- - ----------  for n != 0           |    2 ||                   |
 | x *cos(n*x) dx = C - 2*|<|    2          n                            | + x *|
(n2 x2−2) sin⁡(n x)+2 n x cos⁡(n x)n3{{\left(n^2\,x^2-2\right)\,\sin \left(n\,x\right)+2\,n\,x\,\cos \left(n\,x\right)}\over{n^3}}
Simplify
The answer [src] 
/sin(n)   2*sin(n)   2*cos(n)                                  
|------ - -------- + --------  for And(n > -oo, n < oo, n != 0)
|  n          3          2                                     
<            n          n                                      
|                                                              
|            1/3                          otherwise            
\
(n2−2) sin⁡n+2 n cos⁡nn3{{\left(n^2-2\right)\,\sin n+2\,n\,\cos n}\over{n^3}} 
=
= 
/sin(n)   2*sin(n)   2*cos(n)                                  
|------ - -------- + --------  for And(n > -oo, n < oo, n != 0)
|  n          3          2                                     
<            n          n                                      
|                                                              
|            1/3                          otherwise            
\
{sin⁡(n)n+2cos⁡(n)n2−2sin⁡(n)n3for n>−∞∧n<∞∧n≠013otherwise\begin{cases} \frac{\sin{\left(n \right)}}{n} + \frac{2 \cos{\left(n \right)}}{n^{2}} - \frac{2 \sin{\left(n \right)}}{n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{3} & \text{otherwise} \end{cases}
Simplify

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

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