Is there any book or any website that let you learn integration techniques? I'm not talking about the standard ones like integration by
- Parts
- Substitution (trigonometric)
- Partial fractions
- Order
- Reduction formulae
- recurrence
but I'm talking at ones like in this question here, or the ones used by Ron Gordon or the user Chris'iss or Integrals or robjohn.
Thanks in advance.
Best Answer
In college. $($Math, physics, engineering, etc$)$.
Yes: college books.$($Math, physics, engineering, etc$)$.
That question does not require any fancy integration techniques, but merely exploiting the basic properties of some good old fashioned elementary functions.
User Ron Gordon always uses the same complex integration technique, based on contour integrals exploiting Cauchy's integral formula and his famous residue theorem. They are pretty standard and are taught in college.
See “Ron Gordon”. Also, familiarizing oneself with the properties of certain special functions, like the Gamma, Beta and Zeta functions, Wallis and Fresnel integrals, polylogarithms, hypergeometric series, etc. would probably not be such a bad idea either. In fact, there's an entire site about them.
Other users to watch out for are Achille Hui, sos$440$, Felix Marin, Random Variable, Tunk Fey, Vladimir Reshetnikov, Kirill, Pranav Arora, Cleo, Integrals and Series, Laila Podlesny, Olivier Oloa, etc.