20 Number which is simultaneously sum of 2 and 3 squares 5 A closed form for: $\int_{0}^{\infty} \frac{1}{(x-\log x)^2}dx$ 4 The sum of the series $\cos(x)-\cos(2x)+\cos(3x)-…$ 4 Special properties of the number $146$ 3 Proof of a Zeta function identity

### Reputation (2,136)

 +10 show $\int \frac{1}{\cosh(x)}dx = \arctan(\sinh(x))$ using the substitution $u=\sinh(x)$ +10 Closed form solution for this integral? +15 Numerical integration of oscilating functions (Python) +10 Show that for any natural number n between $n^2$ and$(n+1)^2$ there exist 3 distinct natural numbers a, b, c, so that $a^2+b^2$ is divisible by c

### Questions (19)

 7 Analogous “Dark Sector” Trigonometric (and Hyperbolic) Functions 7 Integrating $\int_0^{\frac{\pi}{2}} x (\log\tan x)^{2n+1}\;dx$ 5 Applying the Beukers-like irrationality proof for $\zeta(2)$/$\zeta(3)$ to Catalan's Constant: Where does it fail? 3 Hyperbolic “Fourier” type infinite series for $\log(\sinh x)$ and $\log(\cosh x)$ 3 Understanding when the Multiplication of two Definite Integrals gives Unity

### Tags (109)

 39 integration × 33 13 elementary-number-theory × 16 29 calculus × 19 10 closed-form × 4 28 number-theory × 10 9 real-analysis × 10 22 sequences-and-series × 22 9 special-functions × 7 19 definite-integrals × 18 8 hypergeometric-function × 5