How to get credit for a mathematics discovery?

Glype11
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I figure out a way to evaluate an integral with an antiderivative with elementary functions which had previously only been defined by an anitderivative that was not an elementary function. Everything checks outs. I used 3 regular substitutions and a trigonometric substitution and I just have to go back and insert the original variables. Although the antiderivative maybe somewhat involved it will certainly be elementary.

I only did some algebraic manipulations and and used an initial substitution, and proceeded from there. I didn't discover a new method yet the antiderirvate was thought to be impossible to express in elementary functions and if I can proof that it can, how big of deal would that be? Before I show my results, I want to make sure I get credit for my work so no one can steal the idea as their own.

How does one get proper recognition for a discovery such as this?
 
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I want to know more about that. too.
Here is some information about what I do know:
You must write a paper to a journal, you can check:
ijma.info , before creating a paper, read author guidelines and some other papers/issues to understand how the journal works.
 
You could submit a paper to arxiv. First you got to register for arxiv. https://arxiv.org/help/registerhelp
And/or you could submit a paper to a peer reviewed journal.
 
The Liouville theorem and the Risch algorithm specify exactly which functions have an elementary primitive and a way to find. And if it has no elementary primitive, it provides a proof of this. So your discovery is sadly useless since the Liouville theorem and Risch algorithm already do what you invented (and they do it for general functions).
 
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