詳解：\(\sin Ax\cos Bx = \frac{1}{2}\left[ {\sin (A + B)x + \sin (A - B)x} \right]\)

\(\int {2\sin 10x\cos 8x\;dx}  = \int {\left( {\sin 18x + \sin 2x} \right)} dx\)

將兩項相乘的三角函數化為加法後可分開

\(\int {\left( {\sin 18x + \sin 2x} \right)} dx = \int {\sin 18x} dx + \int {\sin 2x} dx\)

成為兩項單純的積分

\(\int {\sin 18x} dx + \int {\sin 2x} dx = \frac{1}{{18}}( - \cos 18x) + \frac{1}{2}( - \cos 2x) + C\)