How to Integrate With Speed ~ Recognise and Use the Chain Rule Pattern

If you have difficulty with integrating functions (calculus), I hope you will find that my three videos will help you.

● In the previous video I explained the SIX BASIC PATTERNS that you need to master. I also explained why you may have been confused about two of the patterns, and then demonstrated how to find 'simple' integrals using a few examples.

● In THIS video I will show you how to integrate using the reverse of the CHAIN RULE. I will demonstrate a particular way of integrating that may appeal to you and make the process less confusing.

● In my next video I will explain 'INTEGRATE BY PARTS.' This is the inverse of the PRODUCT RULE that we learn and use when differentiating. I will demonstrate the use of this pattern using a number of examples.

In none of these videos do I use substitution. I was taught these methods using substitution, and it is important that you know the process of substitution but ... when there is a recognisable pattern, I find that the substitution method 'bogs' students down in unnecessary detail and they get lost or make mistakes.

My method of teaching involves helping students understand PATTERNS rather than rules. This is not to say that the rules aren't important. We need these to be convinced of the truth/validity of a process, and to understand it thoroughly. It is the PATTERN, however, that allows us to recognise and use a technique with ease and with a smaller risk of making careless mistakes. It is also MUCH FASTER!

My experience is that many students get 'bogged down' in detail and lose sight of the overall strategy that they are following (or the overall structure of the problem). By teaching students to recognise and follow patterns, I find that their confidence, speed and accuracy (and understanding) all improve significantly. I hope these videos will help you in the same way.

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Best wishes for your study and your mathematics!

Thank you.