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...
Asked
Active
Viewed 175 times
1
MarianD
- 2,953
-
The question is a bit broad. – copper.hat Mar 30 '19 at 00:28
-
You could read about "differentiating under the integral sign". See e.g. https://math.stackexchange.com/questions/2157226/interesting-examples-of-differentiation-under-the-integral-sign. – Minus One-Twelfth Mar 30 '19 at 00:29
-
1If $$f(x) = \sum_{k=0}^{\infty}(-1)^k c_k x^{2k}$$ then $$\int_0^{\infty}f(x)dx = \frac{\pi}{2}c_{-\frac{1}{2}}$$ – Count Iblis Mar 30 '19 at 00:35
-
@CountIblis is that a special case of Ramanujan's master theorem? – clathratus Mar 30 '19 at 01:50
-
@clathratus Yes! – Count Iblis Mar 30 '19 at 04:32
1 Answers
5
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.
Peter Foreman
- 19,947