Integral de sin(ax)cos(nx) dx

                              //                     0                       for And(a = 0, n = 0)\
                              ||                                                                  |
                              ||                    2                                             |
                              ||                -sin (n*x)                                        |
                              ||                -----------                       for a = -n      |
                              ||                    2*n                                           |
  /                           ||                                                                  |
 |                            ||                    2                                             |
 | sin(a*x)*cos(n*x) dx = C + |<                 sin (n*x)                                        |
 |                            ||                 ---------                         for a = n      |
/                             ||                    2*n                                           |
                              ||                                                                  |
                              ||  a*cos(a*x)*cos(n*x)   n*sin(a*x)*sin(n*x)                       |
                              ||- ------------------- - -------------------        otherwise      |
                              ||         2    2                2    2                             |
                              ||        a  - n                a  - n                              |
                              \\                                                                  /

$$\int \sin{\left(a x \right)} \cos{\left(n x \right)}\, dx = C + \begin{cases} 0 & \text{for}\: a = 0 \wedge n = 0 \\- \frac{\sin^{2}{\left(n x \right)}}{2 n} & \text{for}\: a = - n \\\frac{\sin^{2}{\left(n x \right)}}{2 n} & \text{for}\: a = n \\- \frac{a \cos{\left(a x \right)} \cos{\left(n x \right)}}{a^{2} - n^{2}} - \frac{n \sin{\left(a x \right)} \sin{\left(n x \right)}}{a^{2} - n^{2}} & \text{otherwise} \end{cases}$$

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