∫ cosec^6 x d x is equal to

Let $I=\int cosec^6 x d x=\int cosec^4 x . cosec^2 x d x$

$=\int\left(1+\cot ^2 x\right)^2 . cosec^2 x d x=\int\left(1+\cot ^4 x+2 \cot ^2 x\right) . cosec^2 x d x$

∴  $I=-\cot x-\frac{\cot ^5 x}{5}-\frac{2}{3} \cot ^3 x+c$

Hence (1) is the correct answer.