Where to learn integration techniques?

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.

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Where to learn integration techniques?

In college. $($Math, physics, engineering, etc$)$.

Is there any book that let you learn integration techniques?

Yes: college books.$($Math, physics, engineering, etc$)$.

I’m talking at ones like in this question here

That question does not require any fancy integration techniques, but merely exploiting the basic properties of some good old fashioned elementary functions.

the ones used by Ron Gordon

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.

or the user Chris’s sis or Integrals or robjohn.

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.

I recommend the following books:

(1) The Handbook of Integration by Daniel Zwillinger;

and

(2) Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals by George Boros and Victor Moll.