Complete ALGO to solve a indefinite integral ( classroom questions )

[amitjnkp]

Helo everyone,
can somebody post the best algorithm/strategy to solve indefinite integral questions which are usually asked to undergraduates. The most general set of steps that can be applied to every question one encounters in the classroom.
Algo that though may be proved to be inconvenient for some problems( eg. it may take more time to solve a question with that algo ) but it must lead to the correct solution....


thanks

 

[HallsofIvy]

You mean you want to be able to mechanically apply an algorithm rather than "thinking"? I 'm afraid integrals just don't work that way!

 

[CRGreathouse]

I imagine that an algorithm that could integrate indefinite integrals, or classify them as not closed-form integrable (for a usual definition of closed form) would be able to solve the halting problem.

 

[Gib Z]

You could possible do it for a certain class of known functions. Such an algorithm could convert the integrand into its Taylor series, integrate term by term and if you want to get more advanced, it could compare it to a library of other series to recognise it as another known function. However this is only applicable to entire functions ie functions that are equal to their taylor series everywhere.

 

[neutrino]

Actually there is an algorithm attributed to Feynman which can be applied to any function. I'm sure many here have heard about it.

Write down the problem - think really hard - write down the answer.

 

[amitjnkp]

hmm can anyone post a little example with their sample algo that can detect a flawed step in solving a integral or is the guess and try (or try all if one doesnot work) the only process ?

What i am feeling about this indefinite integral calculus(classroom questions (undergraduate level)) is that one has just to do as much as possible questions to do it well. its mostly the memorising power. though some argue that we analyse the question and give answer but how often does one take 1 minute to solve a problem of a type that he never encountered before. It seems one is memorising the prototypes and applying them to question. it doesnot seem to be a good way, something is lacking deeply in me. atleast my textbooks do not give any strategy.

This is how the teach me..
they give many questions which can be solved through substitution ( remember you already know they shall use substitution only)
and so on for other methods...Then i try to solve some mixed up questions and its not so obvios that the question can be solved through what way. and when though my guesses i solve the question taking much time. but hey now i remember the way and the prototype if there is a similar question i can solve it in less time..
If some like this never encountered question is asked to me i will spend all of my time in that question. ( the question which we tell tricky)I really want some sort of strategy to approach a question in a better way.