How to Integrate Quickly ~ 5 Speedy Integrals Using Basic Patterns

Do you want to complete most integrals within 30 seconds or so?
Note that this is not a guarantee ... simply a guideline :-).

This video may help you do just that! It may not make sense to you, however, unless you have seen my earlier (explanatory) video    • How to Integrate With Speed! ~ Mastering t...  .

I recently produced three videos describing three basic methods of integration. I have now produced three corresponding videos in which I demonstrate the process of integration. This is the first of them ...

● In this video I integrate five elementary integrals using the method and principles described in the first instruction video. Learn your basic six patterns! To see the video that it is based on (the one with all the explanations), visit    • How to Integrate With Speed! ~ Mastering t...  .

● In my next video I will integrate a number of functions using the the method and principles based on reversing the CHAIN RULE.

● In my third video I will integrate a number of functions using the the method and principles based on reversing the PRODUCT RULE ... a process that we call "INTEGRATION BY PARTS."

Some subscribers have asked for these demonstration videos. They are much shorter and will allow you to study the methods in action.

The integrals are:
00:32 ~ ∫(6x²+5√x³).dx
02:04 ~ ∫(5e^x/3).dx
02:37 ~ ∫2/(3x).dx
03:02 ~ ∫3sinx.dx
03:40 ~ ∫(sec²x/2).dx

The method that I demonstrate here involves understanding PATTERNS rather than the rules upon which they are based. It also means that you do not need to use substitution ... so using this method allows you to integrate function more directly and (often) much more rapidly than if you used substitution!

My experience is that many students get 'bogged down' in detail (when substituting) and lose sight of the overall structure of the problem that they are solving. 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.