Intereting Posts

Structure Descriptions (GAP) in semigroups
Algorithm for scrolling through different orbits in a permutation group
A question regarding the hitting time formula in brownian motion
Characters of the symmetric group corresponding to partitions into two parts
Three pythagorean triples
Prove that $f=x^4-4x^2+16\in\mathbb{Q}$ is irreducible
How to write “there exists an infinite number of”?
Equivalence relations and power sets.
eigen decomposition of an interesting matrix
Abelian Group Element Orders
Show that $\left | \sin a – \sin b \right | \leq \left | a-b \right |$
Let $ 0 \preceq A \preceq I$ can we relate $Tr( (I-A) B+A C)$ to $Tr(I-A)Tr(B)+Tr(A) Tr(C)$
Dilogarithm integral $\int^x_0 \frac{\operatorname{Li}_2(1-t)\log(1-t)}{t}\, dt$
Show a Cubic Polynomial over $\Bbb C$ can be factored as a product of linear terms
Computing Quotient Groups $\mathbb{Z}_4 \times \mathbb{Z}_{10} / \langle (2, 4) \rangle$, $\mathbb{Z} \times \mathbb{Z}_{6}/ \langle (1, 2) \rangle$

I seem to have seen quite a lot of integrals in the form:

$$\int_0^\infty \frac{\text{d}x}{e^x+(1+x^n)}$$

But none of those hold a closed forms (at least to my knowledge)

- Conjectured closed form for $\int_0^1x^{2\,q-1}\,K(x)^2dx$ where $K(x)$ is the complete elliptic integral of the 1ˢᵗ kind
- Integral $\int_0^1\frac{\ln x}{x-1}\ln\left(1+\frac1{\ln^2x}\right)dx$
- Tough Inverse Fourier Transform
- Find the closed form of $\sum_{n=1}^{\infty} \frac{H_{ n}}{2^nn^4}$
- Integral $\int_1^\infty\frac{\operatorname{arccot}\left(1+\frac{2\pi}{\operatorname{arcoth}x-\operatorname{arccsc}x}\right)}{\sqrt{x^2-1}}\mathrm dx$
- Evaluating $\int{ \frac{x^n}{1 + x + \frac{x^2}{2} + \cdots + \frac{x^n}{n!}}}dx$ using Pascal inversion

$$\Large\color\red{\int_0^\infty \frac{\text{d}x}{e^x+x^n}}$$

Does a closed form exist of this integral? (in terms of $n$)

- Looking for a Calculus Textbook
- Generating Function explicit formula
- Itzykson-Zuber integral over orthogonal groups
- Proving inequalities about integral approximation
- What's the fastest way to get an exact value for $\int_a^b{(1+x)^n dx}$?
- Integral remainder converges to 0
- Definite integral $\int_1^2 \sqrt{1+\left(-x^{-2}+x^2/4\right)^2}\,dx$
- Closed-from for the series: $\sum_{k=0}^{\infty} \frac{1}{(k!)!}$
- Definite Integral of square root of polynomial
- Evaluate $\int \sqrt{ \frac {\sin(x-\alpha)} {\sin(x+\alpha)} }\,\operatorname d\!x$?

- Not Skolem's Paradox – Part 3
- Deriving the inverse of $\mathbf{I}$+Idempotent matrix
- Let $n \geq 1$ be an odd integer. Show that $D_{2n}\cong \mathbb{Z}_2 \times D_n$.
- Is this equality true or it is not necessarily true?
- Homology of a co-h-space manifold
- Geometric interpretation of hyperbolic functions
- Order of element in multiplicative group modulo n, where n is not prime
- Why can't you count real numbers this way?
- Evaluate $\int_0^{\pi/4} \frac {\sin x} {x \cos^2 x} \mathrm d x$
- Computing $e^{isD}$ for a differential operator D
- prove that line bisect section
- Can the cardinality of continuum exceed all aleph numbers in ZF?
- Show $x^6 + 1.5x^5 + 3x – 4.5$ is irreducible in $\mathbb Q$.
- How is the notion of adjunction of two functors usefull?
- Proving a sequence defined by a recurrence relation converges