Answer
$$\sec x+\cos x+C $$
Work Step by Step
We integrate as follows:
\begin{align*}
\int \frac{\tan ^{2} x}{\csc x} d x&=\int \frac{\sin ^{2} x}{\cos ^{2} x} \sin x d x\\
&=\int \frac{\left(1-\cos ^{2} x\right)}{\cos ^{2} x} \sin x d x\\
&=\int \frac{1}{\cos ^{2} x} \sin x d x -\int \frac{\cos^2 x}{\cos ^{2} x} \sin x d x\\
&=\int \sec x \tan x d x-\int \sin x d x\\
&=\sec x+\cos x+C
\end{align*}
