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Well back to work for me and an endless see of integrals... Anyway last night might have been a dead end but I think I have a good solution to try today
This is Mur 
@mur2501 Looks a lot like my notebook right now.
@freemo
what kind of integrals you deal with?
@mur2501 the integrals themselves arent all that fancy... the issue is that i have a particularly complex graph that has speicifc properties but can be represented by dozens of different actual equations... i need to find an equation that gives the intended graph with the desired properties but is actually integratable (no taylor series or numerical integration).... Most forms I try are not integratable
The only difficult part here is that im kinda working in reverse. Instead of given an equation and asked to integrate it I know what sort of result I need and need to figure out the equation.
@freemo
As long as the function is continuos it is integratable in the formal sense. I have no idea what exactly you said here but if you are going in reverse then you should be differentiating.
@mur2501 I dont need unlimited precision. But there is a certain minimal level of acceptable precision. The more difficult aspect is delivering the level of needed precision while requiring minimal level of computation to get there.
@freemo
Ahh I see computation limitations though even with a symbolic answer that could be a problem as you can't expect the answer would come out to be a simple equation.
One thing you can do is try to find the numerical integration answers with very high precision and then find a fitting function for the results that approximates it to your required want and is not computationally costly
@mur2501 yea closed form is not garunteed to be computationally simple. But they do stand a better chance at at it. Sadly thats why its a tricky problem, i cant avoid at least some degree of trial and error. I've had some closed forms I had to reject as well.
Finding a fitting function could work. In a sensethe problem is already pretty much just me manually trying to find an efficient fitting function working backwards from a known graph.
@freemo
Yes though if you aim for unlimited precision then maybe change of perspective can help in symbolic answers