Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 415: 23

$ - 3\cot x + C$

$$\eqalign{ & \text{ Let }I=\int {3{{\csc }^2}t} dt \cr & {\text{Pull out the constant}}{\text{, apply }}\int {cf\left( x \right)} dx = c\int {f\left( x \right)} dx \cr & I = 3\int {{{\csc }^2}t} dt \cr & {\text{From the table of indefinite integrals }} \cr & \int {{{\csc }^2}x} dx = - \cot x + C,{\text{ then}} \cr & I=3\int {{{\csc }^2}t} dt = 3\left( { - \cot x} \right) + C \cr & = - 3\cot x + C \cr} $$