- #1

fazekasgergely

- 3

- 0

- Homework 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.