## Calculus with Applications (10th Edition)

$$- 4\cot x + C$$
\eqalign{ & \int {4{{\csc }^2}x} dx \cr & {\text{use multiple constant rule }} \cr & \int {4{{\csc }^2}x} dx = 4\int {{{\csc }^2}x} dx \cr & {\text{integrate by using the Basic Trigonometric integral }}\int {{{\csc }^2}x} dx = - \cot x + C \cr & then \cr & \int {4{{\csc }^2}x} dx = - 4\cot x + C \cr}