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Is there any other method of integration besides the best known as:

  • Substitution,
  • Integration by parts,
  • Trigonometric,
  • Trigonometric Substitutions,
  • Partial Fractions,
  • Improper Integrals, and
  • Laplace?

Some method that is taught in doctorates etc...

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  • $\begingroup$ The question is a bit broad. $\endgroup$ – copper.hat Mar 30 '19 at 0:28
  • $\begingroup$ You could read about "differentiating under the integral sign". See e.g. math.stackexchange.com/questions/2157226/…. $\endgroup$ – Minus One-Twelfth Mar 30 '19 at 0:29
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    $\begingroup$ If $$f(x) = \sum_{k=0}^{\infty}(-1)^k c_k x^{2k}$$ then $$\int_0^{\infty}f(x)dx = \frac{\pi}{2}c_{-\frac{1}{2}}$$ $\endgroup$ – Count Iblis Mar 30 '19 at 0:35
  • $\begingroup$ @CountIblis is that a special case of Ramanujan's master theorem? $\endgroup$ – clathratus Mar 30 '19 at 1:50
  • $\begingroup$ @clathratus Yes! $\endgroup$ – Count Iblis Mar 30 '19 at 4:32
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Integration by differentiating under the integral, integration by residue theorem, integration by complexification etc. There are of course a large number of fields of which integration covers.

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