Question

\[\int x \cos x\ dx\]

Answer 1

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