«Methodical instructions for solving problems on integrals with the parameter: Educational and methodical manual» is an indispensable assistant for students, teachers and everyone who seeks to understand and master the most complex aspects of integral calculus, especially problems in which the parameter is present. Created by a team of authors, this manual is a carefully designed learning resource that turns theory into a practical skill, making teaching mathematics fun and effective. The book focuses on the method of solving problems on integrals with a parameter, which is one of the most important and complex topics in the course of mathematical analysis. The authors not only collected theoretical foundations, but also offered a rich set of practical recommendations, algorithms and step-by-step solutions that help to understand how to properly approach analysis and problem solving, where parameters can radically change the nature of the integral. This manual is a real guide to the maze of complex calculations, allowing students and teachers not only to master the basic methods, but also to develop intuition to find optimal solutions. The book is perfect for students studying mathematics at the undergraduate and graduate levels, as well as for teachers looking for teaching materials for classes and preparation for exams . It will be useful for those who are faced with problems in integrals within the courses of mathematical analysis, higher mathematics, as well as for specialists working in the field of applied sciences, where integrals with a parameter are found in modeling and analysis of complex systems. The peculiarity of this teaching aid is the clarity and consistency of the presentation . The authors tried to make the material as accessible as possible, breaking down complex topics into understandable blocks, accompanying them with illustrations and examples, which contributes not only to the assimilation of theory, but also to the development of analytical thinking. The book discusses in detail the different types of tasks, methods for solving them, as well as typical mistakes that should be avoided. This approach makes the manual a valuable tool for self-employment and exam preparation. The topics raised in the book cover a wide range of issues: from the basic properties of integrals with a parameter to more complex methods of calculating them, analyzing behavior when changing a parameter and applying it in various fields of science and technology. Particular attention is paid to practical aspects, which makes the book not only a theoretical manual, but also a practical guide to solving specific problems. This makes it especially relevant for those who want not only to understand mathematics, but to learn how to apply it in real situations. The style of the authors is distinguished by clarity, logic and pragmatism. They are able to explain complex concepts in simple words, making the material available even to those who are just beginning to learn mathematics. In their other well-known works, such as textbooks on mathematical analysis and methods of teaching higher mathematics, their desire to make mathematics understandable and interesting is traced. This manual is a continuation of their mission to help students and teachers discover all the richness and beauty of integral calculus. If you are looking for a reliable teaching material that will help you systematize knowledge, prepare for exams or simply expand your horizons in the field of mathematical analysis, “Methodological guidelines for solving problems on integrals with the parameter: Educational and Methodological Guide” will become your indispensable companion . This is a book that not only teaches, but also inspires new discoveries in the world of mathematics, making the complex understandable and accessible.