General question: How do you organise your knowledge on Integration?

[Al-Layth]

so far have split it into:

1- The base integrals of elementary functions
(trig, polynomial, hyperbolic, expolog, )

2 - General rules for evaluating
(by parts, reduction formulae, f(ax+b) rule, the f^n f rule, the inverse f rule ,| feynman technique, contour integration, symmetric limit odd function argument,

3 - general modification techniques
(general algebraic operations, function specific identities, Rules of Bioche, series subs, transformations, basic substitution rules, trig phase shifting,

4 - Collection of Analysed Structures
- Rational functions (partial fraction decomp, ostogradsky rule,
- Trig rational functions (weierstrass, Rules of Bioche)
- Radicalled quadratics (euler sub, trigsub, hyperbolicsub)
-

what do you think? is this an appropriate way to organise my study of symbolic integration

 

[mario99]

I don't understand your question

But if you mean that you have a lot of skills that you can apply to solve an integral, but you don't know which technique to apply first, the answer is simply: don't worry, your brain will tell you automatically how to solve the problem.

 

[khansaheb]

so far have split it into:

1- The base integrals of elementary functions
(trig, polynomial, hyperbolic, expolog, )

2 - General rules for evaluating
(by parts, reduction formulae, f(ax+b) rule, the f^n f rule, the inverse f rule ,| feynman technique, contour integration, symmetric limit odd function argument,

3 - general modification techniques
(general algebraic operations, function specific identities, Rules of Bioche, series subs, transformations, basic substitution rules, trig phase shifting,

4 - Collection of Analysed Structures
- Rational functions (partial fraction decomp, ostogradsky rule,
- Trig rational functions (weierstrass, Rules of Bioche)
- Radicalled quadratics (euler sub, trigsub, hyperbolicsub)
-

what do you think? is this an appropriate way to organise my study of symbolic integration

I think that is an excellent way to organize your thoughts. But do not be too rigid about it. Learning is categorizing. We learn to categorize by subjects (e.g.literature, math, history, etc.), then sub-categorize (math into algebra, geometry, etc.) then further categorizing (differential calculus, integral calculus, etc.).
Don't worry if your list does not match exactly with someone else's list.

It is early in the morning - I cannot think of anything else to add to your list - yet.