So it becomes a determined process to integrate. And as the two forms of integration closure are known, the process can be extended as any integration has closed form if the series converge. Integration by parts to a series. So why? The end points can have good integral estimates, and many in-between values of the function do not need evaluation. Series acceleration should be enough. Imagine an integral from zero to (m to power a times n to power b) which equals m times n. If for some a not equal b, the factor of m or n becomes obvious? The calculation would be log of the upper limit in polytime, not linear.
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Think about the f+c as integral of f plus a rectangle making f always positive when offset by c to give defined sign and hence binary search opportunity.
It wasn’t specifically developed to crack public key things, and the motivation was for simplified solutions to differential equations. Anyone who’s done DE solving knows the problem with them. That problem is integration and closing it to be algorithmic is a useful thing. That kind of leaves the Lambert W kind of collection of variables problem for real analytical DEs. Good.
It also sets a complexity limit on integration in terms of an analytic function and series of differential orders. The try a power series multiplied by ln x is seen as good advice, but lacking. Hypergeometric series can be reseen as useful to approach the series of this closure. It maybe helpful to decompose these closures into more fundamental sums of new special operators. And do some cancellation. If you find yourself pedantic about dx or plus C, then might I suggest you forget it and blunder on.