- Problem Statement
- I've been doing maths for fun (I've only learned calculus 1 in university yet, but I love experimenting) and I've found the formula for integration by parts can be generalized as an infinite series.
- Relevant Equations
- I'm not well educated in infinite series, this is an amateur attempt but it works in most cases. Can someone tell me if this is right? I know in most cases it only makes things more complicated. I've tried it with simpler functions and it seems to work, more complicated ones are sometimes a problem. Here d^0/dx^0 f(x)=f(x)
For example integral of f(x)=sqrt(1-x^2) from 0 to 1 is a problem, since the derivative of the function is -x/sqrt(1-x^2) so putting in 1 in the place of x ruins the whole thing.
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