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How to evaluate $\int_{0}^{\frac{\pi}{2}} \ln ^{n}(\cos \theta) d \theta, \textrm{ where }n\in \mathbb{N}?$

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Lai

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Proving $\int_0^\infty \log\left (1-2\frac{\cos 2\theta}{x^2}+\frac{1}{x^4} \right)dx =2\pi \sin \theta$

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FDP

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If $C$ is a component of $Y$ and a component of $Z$, is it a component of $Y\cup Z$?

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Matt E

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Lasso - constraint form equivalent to penalty form

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travelingbones

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Manipulation of Tensors

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James S. Cook

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If $gf$ is an equalizer , is $f$ an equalizer?

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roman

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Can I use my powers for good? [closed]

Awarded Nov 27 at 8:27

gerrit

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Prove that $∫\limits_0^π \frac{\cos x \cos 4x}{(2 − \cos x)^2}\ \text dx\ =\ \frac π9 \left(2160 − 1247\sqrt3\right)$

Awarded Nov 27 at 7:19

Venus

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Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$

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Deusovi

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How do we know that the hessian will be positive definite for MLE of logistic regression parameters?

Awarded Nov 26 at 22:22

Jan Snajder

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Proving that $A\subseteq f^{-1}(f(A))$ and that if $f$ is injective $A=f^{-1}(f(A))$.

Awarded Nov 26 at 12:12

OBDA

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Configuration model for weighted graphs for use in modularity formula

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Splines

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Why isn't this a valid argument to the "proof" of the Axiom of Countable Choice?

Awarded Nov 26 at 12:12

Andrés E. Caicedo

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Modular exponentiation by hand ($a^b\bmod c$)

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phuclv

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Difficult coin weighing puzzle: 14 coins, 1 fake (heavier or lighter), 3 pre-determined weighings

Awarded Nov 26 at 1:10

Dodezv

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Square on graph of cubic

Awarded Nov 25 at 3:47

Jean Marie

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Solutions of an ode with Wronskian zero?

Awarded Nov 24 at 19:08

Rupadarshi Ray

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Calculating the integral $\int_0^\infty \frac{\cos x}{1+x^2}\, \mathrm{d}x$ without using complex analysis

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Tunk-Fey

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What are the disadvantages of non-standard analysis?

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Andreas

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Orthogonal projection onto an affine subspace

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Josh O'Brien

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A question on $k$-connected graphs

Awarded Nov 23 at 17:03

Robert

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Help solving $\int {\frac{8x^4+15x^3+16x^2+22x+4}{x(x+1)^2(x^2+2)}dx}$

Awarded Nov 23 at 9:42

Bill Dubuque

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Stable Kalman Filter estimator with given covariance matrices

Awarded Nov 22 at 23:52

Kwin van der Veen

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Integrate: $\int_0^{\pi} \log ( 1 - 2 r \cos \theta + r^2)d\theta$

Awarded Nov 22 at 16:33

Start wearing purple

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A characterization of AB5 and AB4 categories. Does this result show up in the literature?

Awarded Nov 21 at 19:08

Elías Guisado Villalgordo

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Mathematical writing: why should we not use the phrase "we have that"?

Awarded Nov 21 at 3:51

Brian M. Scott

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Complete omega-consistent theories

Awarded Nov 20 at 22:16

Burak

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Mathematical framework of the Koopman operator

Awarded Nov 19 at 20:06

Alp Uzman

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Interview riddle

Awarded Nov 18 at 19:42

hrkrshnn

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Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction

Awarded Nov 18 at 11:47

Stas Bushuev

1012 bronze badges

Closed form for Dirichlet series whose coefficients are the Möbius function times a geometric series

Awarded Nov 16 at 20:20

Gro-Tsen

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Calculating the mean distance of a point to all points on a circle, maybe with an integral?

Awarded Nov 15 at 20:38

Jacob

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A closed ball in a metric space is a closed set

Awarded Nov 15 at 16:19

Decaf-Math

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Why is learning modern algebraic geometry so complicated?

Awarded Nov 15 at 8:00

Georges Elencwajg

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What is your favorite application of the Pigeonhole Principle?

Awarded Nov 14 at 16:37

David E Speyer

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Find weak solution to Riemann problem for conservation law

Awarded Nov 14 at 3:31

EditPiAf

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Generators of the multiplicative group modulo $2^k$

Awarded Nov 13 at 23:33

Jyrki Lahtonen

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Finding center and radius of circumcircle

Awarded Nov 13 at 12:24

dxiv

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Evaluating $\int_{0}^{\frac{\pi}{2}} x^{2} \ln (\cos x) d x$

Awarded Nov 13 at 2:47

Lai

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Cardinality of set of normal functions $f \colon \omega_{\alpha} \to \omega_{\alpha}$

Awarded Nov 13 at 2:47

Philip Brooker

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A natural proof of the Cauchy-Schwarz inequality

Awarded Nov 12 at 12:32

littleO

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Multiplication in Permutation Groups Written in Cyclic Notation

Awarded Nov 11 at 23:27

James S. Cook

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Contour integration $ \int_0^\infty \ln(1+2\cos(x)+x^2) \frac{dx}{1+x^2} $

Awarded Nov 11 at 20:51

KStar

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Closed form solution for $x^n + x+ C = 0$

Awarded Nov 11 at 16:57

Kaira

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The free monoid functor is fully faithful?

Awarded Nov 10 at 21:06

Stefan Perko

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how to find null space basis directly by matrix calculation

Awarded Nov 10 at 17:24

James S. Cook

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Divisibility in an abelian group

Awarded Nov 9 at 23:58

Aryaman Maithani

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Why is it that linear fractional transformations cannot take the upper half-plane to the first quadrant?

Awarded Nov 9 at 23:58

Incnis Mrsi

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Black and white ball drawing without replacement expected number of ball color switches

Awarded Nov 9 at 23:58

drhab

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Why are two permutations conjugate iff they have the same cycle structure?

Awarded Nov 9 at 20:01

Shaun♦

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$a,b,c,d,e$ are positive real numbers such that $a+b+c+d+e=8$ and $a^2+b^2+c^2+d^2+e^2=16$, find the range of $e$.

Awarded Nov 9 at 2:37

Martin R

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polynomials such that $P(k)=Q(l)$ for all integer $k$

Awarded Nov 7 at 7:02

Bill Dubuque

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Prove $\, a,b,c, \sqrt{a}+ \sqrt{b}+\sqrt{c} \in\mathbb Q \implies \sqrt{a},\sqrt{b},\sqrt{c} \in\mathbb Q $ and generalization to $n$ summands.

Awarded Nov 6 at 6:27

Bill Dubuque

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Examples of mathematical induction

Awarded Nov 5 at 3:02

MJD

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How can I find $\gcd(a^m+1,a^n+1)$ with $a,m,n$ positive integers?

Awarded Nov 4 at 17:12

Bill Dubuque

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What is the difference between a variety and a manifold?

Awarded Nov 4 at 15:11

JCK

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Product of areas in a disk

Awarded Nov 4 at 11:05

Dan

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Information on permutation subgroups - symmetries of "Globe" like puzzle.

Awarded Nov 4 at 11:05

Alexander Chervov

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Number Theory: Calculating Norm.

Awarded Nov 4 at 9:28

Olivier Bégassat

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Riccati differential equation $y'=x^2+y^2$

Awarded Nov 3 at 10:46

Start wearing purple

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