Practical Class 11. The Method of Change of Variable (Substitution) in the Indefinite Integral

This practical session focuses on the change of variable (substitution) method for indefinite integrals. It begins with a theoretical review and a table of basic differentials that students must memorize. The session is divided into three blocks: bringing under the differential sign, nonlinear substitutions (including eliminating irrationalities with roots of different degrees and exponential substitutions), and integrating expressions containing a quadratic trinomial by completing the square. Each block includes detailed examples and practice exercises. Three versions of independent work with answers are provided, along with additional challenging problems. The session concludes with homework instructions and a summary of key skills for choosing effective substitutions.