Answer
$$x - \csc x + C$$
Work Step by Step
$$\eqalign{
& \int {\csc x\left( {\sin x + \cot x} \right)dx} \cr
& {\text{multiply}} \cr
& = \int {\left( {\csc x\sin x + \csc x\cot x} \right)dx} \cr
& {\text{basic trigonometric identities}} \cr
& = \int {\left( {\frac{1}{{\sin x}}\sin x + \csc x\cot x} \right)dx} \cr
& = \int {\left( {1 + \csc x\cot x} \right)dx} \cr
& = \int {dx} + \int {\csc x\cot x} dx \cr
& {\text{find the antiderivative}} \cr
& = x - \csc x + C \cr} $$
