I am not sure if Mathematics Stack Exchange allows this kind of questions. But I do think there are some who can guide me through this.
I am working on Indefinite Integrals for quite a long time and I have developed some of my own methods to evaluate long integrals like $\tan^nx$, $\sec^nx$ and $\cot^nx.$ I know we have reduction formulas for these integrals, but personally I don't find it useful for two obvious reasons:
1.It's hard to keep in mind.
2.It takes quite a long time, specially if you are dealing with $\tan^{20}x$ or something like that.
Besides this I have my own methods for integrals like $\tan x$,$\sec x$,$\cot x$,$\csc x$ and some of my own results on integrals.
Are they worth sending to some research society? Where can I do the same?
UPDATE: As pointed out by Joanpemo,I would like to show my one of my works. But since I don't know if these results have been derived in the past, I am posting one of my questions.I will show my work after seeing the answers.
$1. \int \tan^{13}x dx$