Intereting Posts

$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
Proving a set is an abelian group.
$ \int \frac{1}{\sqrt{1 – x^2}} \text{exp}\left(-\frac{1}{2} \frac{a^2 + b x}{1 – x^2}\right) dx$
Equivalence of the definition of the Subbasis of a Topology
How to reproduce the Mathematica solution for $\int(\cos x)^{\frac23}dx$?
Prove or find a counter example to the claim that for all sets A,B,C if A ∩ B = B ∩ C = A ∩ C = Ø then A∩B∩C ≠ Ø
The complement of every countable set in the plane is path connected
$f(x)$ monotonic integrable function and $\lim_{x\to \infty}\frac{1}{x}\int_{0}^{x}f(t)dt=a$, Prove: $\lim_{x\to \infty}f(x)=a$
Fermat's little theorem's proof for a negative integer
Solve the equation. e and natural logs
Show that these two numbers have the same number of digits
Absolute continuity on an open interval of the real line?
Calculate $\lim_{n \to \infty}\binom{2n}{n}$ without using L'Hôpital's rule.
Concept of Random Walk
Complex analysis book for Algebraic Geometers

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.

- How to prove for $s<1,|a+b|^s\le|a|^s+|b|^s$
- Sum of the infinite series $\frac16+\frac{5}{6\cdot 12} + \frac{5\cdot8}{6\cdot12\cdot18} + \dots$
- Inequality constraints in calculus of variations
- What is infinity divided by infinity?
- What is the average length of 2 points on a circle, with generalizations
- Evaluation of $\sum^{\infty}_{n=0}\frac{1}{16^n}\binom{2n}{n}.$

- Is there a proof for the following series to diverge/converge?
- Integral $\int_{1}^{2011} \frac{\sqrt{x}}{\sqrt{2012 - x} + \sqrt{x}}dx$
- function $f(x)=x^{-(1/3)}$ , please check whether my solution is correct?
- Prove that if $\alpha, \beta, \gamma$ are angles in triangle, then $(tan(\frac{\alpha}{2}))^2+(tan(\frac{\beta}{2}))^2+(tan(\frac{\gamma}{2}))^2\geq1$
- What is the minimum value of $(1 + a_1)(1 + a_2). . .(1 + a_n)$?
- What is operator calculus?
- Help with epsilon delta definition
- Does $\int_{0}^{\infty}\frac{dx}{1+(x\sin5x)^2}$ converge?
- Is this “theorem” true in Optimization Theory?
- Guide to mathematical physics?

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.

- Function that is both midpoint convex and concave
- Mean curvature in terms of Christoffel symbols
- Markov process vs. markov chain vs. random process vs. stochastic process vs. collection of random variables
- Why $S^1\times S^{2m-1}$ carries a complex structure.
- $\epsilon$-$\delta$ limits of functions question
- Is local isomorphism totally determined by local rings?
- Is “locally linear” an appropriate description of a differentiable function?
- Linear independence of fractional powers
- Proof by induction – correct inductive step?
- Does every Banach space admit a continuous injection to a non-closed subspace of another Banach space?
- The sum of two continuous periodic functions is periodic if and only if the ratio of their periods is rational?
- Why metrizable group requires continuity of inverse?
- Suppose that $G$ is a group with the property that for every choice of elements in $G$, $axb=cxd$ implies $ab=cd$. Prove that $G$ is Abelian.
- Monkeys and Typewriters
- Computing $\lim\limits_{n\to\infty} \frac{\sqrt{n}}{4^{n}}\sum\limits_{k=1}^{n} \binom{2n-1}{n-k}\frac{ 1}{(2k-1)^2+\pi^2}$