קורס אינטגרלים -שיעור 8-האינטגרל של פונקציה רציונלית

Summary: In the eighth lesson in the Integrals series, we will learn how to perform an integral for a rational function when there is a number in the numerator and an expression with x in the denominator. We will learn the technique of raising the denominator to a power with a sign change, and using the general exponent formula. In addition, we will see how to deal with more complex expressions by factoring fractions to a common denominator and using abbreviated multiplication formulas to bring the function into a form that can be easily integrated. The full course on the Kibinimatika website: https://kibinimatika.org/2020/10/09/%... Timestamps: 0:00 - Introduction: When to use the method and when to use the substitution method 1:11 - Example 1: Integral of 4 parts x squared (raising to a power in the numerator) 3:16 - Example 2: Handling a negative coefficient in the numerator 4:20 - Example 3: Common mistake - separating the coefficient from the power in the denominator 5:40 - Example 4: Integral of a sum of functions (polynomial and rational) 7:09 - Example 5: Integral of a complex function with a linear expression in the denominator 9:14 - Example 6: Technique for factoring a fraction into a common denominator when there is x in the numerator 11:30 - Example 7: Opening parentheses (shortened multiplication) and reducing expressions before integration 14:40 - Summary and what awaits us in the next lessons Tags: #mathematics #matriculation #integrals #rational_function #addition #4units #5units #loving_worker