Question

Can anybody figure out how to solve the equation in the comments?

Answer 1

\[E _{p}=k _{e}\lambda R (x _{p}\int\limits_{0}^{2\pi}\frac{ d \theta }{ (x _{p}^{2}-2Rx _{p} \cos \theta +R ^{2})^{3/2}}-R \int\limits_{0}^{2\pi}\frac{ \cos \theta d \theta }{ (x _{p}^{2}-2Rx _{p}\cos \theta +R ^{2})^{3/2} })\]

Answer 2

first integral is easy to solve (power rule) and the second is non-elementary so It can't be solved by hand. It can only be approximated with computers. The more precise answer you get depends on how much computation power and time you have for it.

Answer 3

How do you know if an integral is non-elementary?

Answer 4

pretty much by looking at it.
Most "chain" functions aren't unless they are set-up so that they are. for example:

Elementary:
\[2xe^{x^2}\]Non-Elementary:
\[e^{x^2}\]

You can integrate the elementary one but not the non-elementary one.

You might want to look up the official definition for a clearer interpretation.

And I may have spoken too quickly, you don't absolutely need a computer unless your want a very precise answer. Although very possible to do, nobody has time to do these integrals by hand using the numerical algorithms that the computer will perform in fractions of seconds