Intereting Posts

calculation of $\int_{0}^{1}\tan^{-1}(1-x+x^2)dx$
Combining probabilities from different sample spaces
Can the following triple integral be computed via elementary calculus methods?
Spectral Measures: Multi Version (III)
Computing the homology groups.
Is there a systematic way to solve in $\bf Z$: $x_1^2+x_2^3+…+x_{n}^{n+1}=z^{n+2}$ for all $n$?
How to begin self study of Mathematics?
Prove $ \sin(A+B)\sin(A-B)=\sin^2A-\sin^2B $
Rank-nullity theorem for free $\mathbb Z$-modules
Burgers equation with initial data $u(x,0) = x^2$
A multiple integral question
Question on Groups $G=\langle x,y|x^4=y^4=e,xyxy^{-1}=e\rangle$
Why in an inconsistent axiom system every statement is true? (For Dummies)
Covectors and Vectors
A bridge hand void in one suit

I am searching for two kinds of books.

(1)Comprehensivebooks thatcollect,explain, and provide manyexamples(that is, fully worked problems) ofadvancedintegration techniques (that is,

something at the level of difficulty of the tables written by

Gradshteyn and Ryzhik, but obviously with explanations, examples and

proofs).

(2)Comprehensivebooks thatcollect,explain, and provide manyexamples(that is, fully worked problems) ofreallyunusualandslickintegration

techniques (which may however not be so advanced or use special

functions).

- sum of series using mean value theorem
- Deciding whether two metrics are topologically equivalent in the space $C^1()$
- Laplacian in polar coordinates
- Negation of uniform convergence
- Is there a non-compact metric space, every open cover of which has a Lebesgue number?
- Why is the Daniell integral not so popular?

Can you point out some good references?

**Related question:** “Really advanced techniques of integration (definite or indefinite)”.

**Remark:** Clearly, an answer should add some references that *have not been mentioned yet* (either in the comments or in the related thread),.

- Why does an infinite limit not exist?
- Computing $\int (1 - \frac{3}{x^4})\exp(-\frac{x^{2}}{2}) dx$
- How many roots have a complex number with irrational exponent?
- If $f(a)=f(b)=0$, Show that $\int_a^b xf(x)f'(x)dx=-\frac 12\int^2dx$
- Prove that $f(x)=0$ has no repeated roots
- Can you prove this property?
- How to prove that two non-zero linear functionals defined on the same vector space and having the same null-space are proportional?
- Slick proofs that if $\sum\limits_{k=1}^\infty \frac{a_k}{k}$ converges then $\lim\limits_{n\to\infty} \frac{1}{n}\sum\limits_{k=1}^n a_k=0$
- Looking for examples of Discrete / Continuous complementary approaches
- Prove $\frac{1}{\sqrt{x}}\geq \frac{\ln x}{x-1}$

I think the collected works of Ron Gordon on math.stackexchange is definitely worth mentioning!!

- Exciting games and material to motivate children to math
- Serre duality as a right adjoint functor
- Number of ways to choose 6 objects when they are of 11 different kinds
- Orthogonal complement of a Hilbert Space
- probabilistically what can we say about the next throw of a coin after n throws
- A convex function that is bounded on a neighborhood is Lipschitz
- Proof involving Cyclic group, generator and GCD
- Find all integers satisfying $m^2=n_1^2+n_1n_2+n_2^2$
- Find all critical points of $f(x,y) = x^3 – 12xy + 8y^3$ and state maximum, minimum, or saddle points.
- Determine the coefficients of an unknown black-box polynomial
- How to calculate the gradient of log det matrix inverse?
- Why is the Koch curve homeomorphic to $$?
- Colored Blocks Factorial
- Chess Master Problem
- Transpose of block matrix