sinとcosの積の不定積分

$${\hspace{10pt}\sin\alpha\cos\beta = \frac{1}{2}\{\sin(\alpha+\beta)+\sin(\alpha-\beta)\}\hspace{10pt}}$$

$$ \begin{aligned} \hspace{10pt}& \int \sin 3x \cos 2x \hspace{1pt}dx \\[1em] &= \frac{1}{2} \int (\sin 5x +\sin x ) \hspace{1pt}dx \\[1em] &= \frac{1}{2}\left(\left(-\frac{1}{5}\cos 5x \right) -\cos x \right)+C\hspace{10pt}\\[1em] &= -\frac{1}{10}\cos 5x - \frac{1}{2}\cos x+C\\[1em] \end{aligned} $$