$\begin{align*} \int e^x (1+\cot x + \cot^2 x)dx \end{align*}$ is equal to :

Question

( A ) $e^x \;\mathrm{cosec}\;x + c$
( B ) $e^x \; \cot x+c$
( C ) $-e^x \; \cot x+c$
( D ) $-e^x \;\mathrm{cosec}\;x + c$