Question

\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]

Answer 1

\[\int x\ {cosec}^2 \text{ x }\ \text{ dx }\]
`   "  Taking x as the first function and cosec"^2 x " as the second function " . `
\[ = x\int {cosec}^2 x\ dx - \int\left\{ \frac{d}{dx}\left( x \right)\int {cosec}^2 x\ dx \right\}dx\]
\[ = - x \text{ cot x } + \int\text{ cot x dx }\]
\[ = - x \text{ cot x }+ \text{ log }\left| \sin x \right| + c\]