Mister Exam

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

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### The solution

You have entered [src]
  1
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|   2
|  x *cos(n*x) dx
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0                 
$$\int\limits_{0}^{1} x^{2} \cos{\left(n x \right)}\, dx$$
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 *|

$${{\left(n^2\,x^2-2\right)\,\sin \left(n\,x\right)+2\,n\,x\,\cos \left(n\,x\right)}\over{n^3}}$$
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
\                                                              
$${{\left(n^2-2\right)\,\sin n+2\,n\,\cos n}\over{n^3}}$$
=
=
/sin(n)   2*sin(n)   2*cos(n)
|------ - -------- + --------  for And(n > -oo, n < oo, n != 0)
|  n          3          2
<            n          n
|
|            1/3                          otherwise
\                                                              
$$\begin{cases} \frac{\sin{\left(n \right)}}{n} + \frac{2 \cos{\left(n \right)}}{n^{2}} - \frac{2 \sin{\left(n \right)}}{n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{3} & \text{otherwise} \end{cases}$$

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