Integration identification

Is there some sort of clue whether to integrate something by parts, substitution, reverse chain rule etc.
Providing that the question doesn't tell you which one to do or is it just purely what you prefer/ a guess?
I was wondering if there was some sort of hack to make things easier

Reply 1

mqb2766

Original post by cherrycosmos

The integration section in
https://www.drfrostmaths.com/uploads/JFrost/files/C4CheatSheet.pdf
is decent though if there isnt any direction in the question, its useful to list the different techniques and think a couple of steps ahead to see if its going to give. So something like integrating (2022 paper)
x^3 ln(x)
is the product of functions so reverse chain (simple substitution) or by parts are obvious candidates. Reverse chain / substitution isnt going to go anywhere, but by parts would give as
ln(x) <-> 1/x
and youd have a standard x^n integral to end up with. So even without actually doing the numbers, you can see by parts will work.