tell me some exotic integration techniques !

[Al-Layth]

i want to expand my repertoire of integration techniques and tools . please recommend me any useful, exotic lesser known techniques not on this list

Here is what I have​

For Rules of Evaluation I have:

integration by parts

The specific quotient rule [imath]\int{\frac{f'(x)}{f(x)} }dx = \ln |{f(x)}| +c[/imath]

Reduction formula for trig terms

The specific composition rule: [imath]\int {f(ax+b)}dx = \frac{1}{a}F(ax+b)[/imath] +c

Ostogradsky rule for rational functions

The Feynman Trick

The Inverse function integral Rule




For techniques of Modifying and Simplifying integrands I have:

The basic algebraic operations

Algebraic Identities specific to each group of functions (trig identities, hyperbolic identities, log identities etc)

Euler's Identity

U - Substitution and its variants

Trigonometric Substitution

Hyperbolic Substitution

Weierstrass Substitution for rational functions of trig terms

Partial Fraction Decomposition of Rational Functions

The expression of trig terms as complex exponentials

 

[Steven G]

I think that you should start with learning the integrals on a typical integral table. These are found in every calculus textbook and I suspect on line as well.

 

[Al-Layth]

I think that you should start with learning the integrals on a typical integral table. These are found in every calculus textbook and I suspect on line as well.

i only memorised the differentials and integrals of the standard functions

the polynomial

sin,cos,tan,sec,csc,cot etc

same for hyperbolic

exponential

logarithm

I didn't want to turn it into a memorisation task

also i think learning integral tables is not really an integration technique.

 

[topsquark]

i only memorised the differentials and integrals of the standard functions

the polynomial

sin,cos,tan,sec,csc,cot etc

same for hyperbolic

exponential

logarithm

I didn't want to turn it into a memorisation task

also i think learning integral tables is not really an integration technique.

Yes, but working out each integral in the table is really really good practice! It will teach you a lot about integration techniques.

-Dan

 

[Al-Layth]

Yes, but working out each integral in the table is really really good practice! It will teach you a lot about integration techniques.

-Dan

this is crazy
i asked for integration techniques i don't know already and im being told to do some "really really good practise" .

 

[topsquark]

this is crazy
i asked for integration techniques i don't know already and im being told to do some "really really good practise" .

I'm not trying to insult you but, honestly, asking a bunch of questions like "Can this general form be integrated?" without apparently trying to see if there is any sort of form yourself is a bit crazy. If you don't find it on Google then it isn't likely to be integrable. That's why you work the examples... to get used to how the integrals act and see what can be done with the ones you already know. And trust me, going through a table like that will teach you new techniques. Some of the integrals in the tables can be rather challenging.

-Dan

 

[Otis]

any useful, exotic lesser known techniques

I haven't reviewed the following information, and I'm not sure how useful your search topic is, but maybe you'll see something that you find interesting.

Really advanced techniques of integration (definite or indefinite)

Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? E...

math.stackexchange.com

Contour integration - Wikipedia

en.wikipedia.org

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