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what Integration technique should I be using?

It tends to be quite difficult when trying to figure out what technique(reverse chain rule, substitution, partial fractions, parts etc.) I need to use in order to integrate an equation.

What should I be looking out for and how do I know what integration technique I should be using in a question? Differentiation is so much easier man kmt
Reply 1
Original post by MannyNFM
It tends to be quite difficult when trying to figure out what technique(reverse chain rule, substitution, partial fractions, parts etc.) I need to use in order to integrate an equation.

What should I be looking out for and how do I know what integration technique I should be using in a question? Differentiation is so much easier man kmt


Even if you can help by posting a useful website/video that would be much appreciated
Reply 2
I think the best thing you can do is practise. But generally what i tend to do when i get an integration question is literally go though all the possible options in my head. Start with reverse chain, look at the function and just think if i differentiate one of these could i get the other part of the function, if yes then there you go. keep on moving down the list, with things like partial fractions its obviously quite easy to rule out if there are no fractions involved then's its unlikely to be partial. Parts tends to only happen between an algebraic function and some kind of trig function plus things like e^x and lnx. Substitution is sometimes more difficult to spot, however do enough questions and you'll find that there is just are only a few certain type of question that they can ask you and trust me soon enough you will be able to look at it and just tell if it is sub or not, but a general rule is that if it looks like a reverse chain but too hard to do in one step its likely to be a substitution. There are lots of videos online but my main advise would be to practise.
Reply 3
Original post by ate3
I think the best thing you can do is practise. But generally what i tend to do when i get an integration question is literally go though all the possible options in my head. Start with reverse chain, look at the function and just think if i differentiate one of these could i get the other part of the function, if yes then there you go. keep on moving down the list, with things like partial fractions its obviously quite easy to rule out if there are no fractions involved then's its unlikely to be partial. Parts tends to only happen between an algebraic function and some kind of trig function plus things like e^x and lnx. Substitution is sometimes more difficult to spot, however do enough questions and you'll find that there is just are only a few certain type of question that they can ask you and trust me soon enough you will be able to look at it and just tell if it is sub or not, but a general rule is that if it looks like a reverse chain but too hard to do in one step its likely to be a substitution. There are lots of videos online but my main advise would be to practise.

Thanks a lot man
Hi! It's always good to have an idea of all the tools at your disposal to deal with an integral question. Sometimes, it's also great to know 'by heart' what is the most efficient technique to use for a particular 'textbook' integral problem. Here is an 8-page document from dr frost maths that compiles all the A-level techniques that are taught and when they are useful

https://www.drfrostmaths.com/uploads/JFrost/files/C4CheatSheet.pdf

At the bottom, there is a one-page cheatsheet which summarises the document nicely

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