Question

\[\int x \text{ sin 2x dx }\]

Answer 1

\[\int x \text{ sin 2x dx }\]
` "Taking x as the first function and sin 2x as the second function  " `.
\[ = x\int\text{ sin 2x dx} - \int\left\{ \frac{d}{dx}\left( x \right)\int\text{ sin 2x dx }\right\}dx\]
\[ = \frac{- x \cos 2x}{2} + \int\frac{\cos 2x}{2}dx\]
\[ = \frac{- x \cos 2x}{2} + \frac{\sin 2x}{4} + C\]