Hello could any one tell me some unusual or advanced integration techniques, I am already familiar with the standard ones like u-substitution, integration by parts, trig substitution, partial fractions, Feynman technique (differentiation under the integral), integrating the inverse, Laplace transforms In the integral and matrix inversion so I was wondering if anyone knew some rare ones (definite or indefinite)
Please do not answer with any already listed Otherwise Any help is appreciated Thanks in advance
Two little known (perhaps?) methods for finding indefinite integrals are:
The Rules of Bioche - Are rules used to guide one towards the most effective trigonometric substitution to use in integrals of the form $$\int f(\sin x, \cos x) \, dx,$$ where $f$ is a rational function of sine and cosine. For more details, see here or here.
Ostrogradsky's Method - Is a method that finds the rational part of $$\int \frac{P(x)}{Q(x)} \, dx,$$ without having to find a factorisation for $Q$ and without having to decompose the integrand into partial fractions. Here $P$ and $Q$ are polynomials such that $\deg P < \deg Q$. For more details, see here.