Contoh 01

\begin{equation*} \begin{split} & \int 6 \sin 3x \cos 2x \:dx\\\\ & 3 \int 2 \sin 3x \cos 2x \:dx\\\\ & {\color {blue} 2\sin A \cos B = \sin (A+B) + \sin (A - B) }\\\\ & 3 \int \sin (3x+2x) + \sin (3x - 2x) \:dx\\\\ & 3 \int \sin 5x + \sin x \:dx\\\\ & 3 \int \sin 5x \: \frac {d(5x)}{5} + 3 \int \sin x \:dx\\\\ & \bbox[5px, border: 2px solid magenta] {- \frac{3}{5} \cos 5x - 3 \cos x + c} \end{split} \end{equation*}

Contoh 02

\begin{equation*} \begin{split} & \int \sin x \sin 5x \:dx\\\\ & -\frac{1}{2}\int -2\sin x \sin 5x \:dx\\\\ & {\color {blue} -2 \sin A \sin B = \cos (A+B) - \cos (A - B) }\\\\ & -\frac{1}{2}\int \cos (x+5x) - \cos (x - 5x) \:dx\\\\ & -\frac{1}{2}\int \cos 6x - \cos (-4x) \:dx\\\\ & -\frac{1}{2}\int \cos 6x - \cos 4x \:dx\\\\ & -\frac{1}{2}\int \cos 6x \: \frac {d(6x)}{6} + \frac 12 \cos 4x \: \frac{d(4x)}{4}\\\\ & \bbox[5px, border: 2px solid magenta] {-\frac{1}{12} \sin 6x + \frac{1}{8}\sin 4x + c} \end{split} \end{equation*}