7,128 reputation
21145
bio website
location Besançon, France
age 34
visits member for 2 years
seen 5 mins ago

Mathematics is a hobby for me, and MSE helps me not to forget too much what I learned in university (MS in applied mathematics at Lyon 1). I like especially real and complex analysis, trigonometry, numerical analysis, finite groups theory, number theory and combinatorics. I am not allergic to other fields.

Contact: arbautjc at gmail dot com


8m
comment Calculation of $\int_{0}^{\frac{\pi}{4}}\tan^{-1}\sqrt{\frac{\cos 2x }{2 \cos^2 x}}dx$
Your 1. is wrong: $$\int \frac {dt}{\cosh(2t)}=\mathrm{atan}(\tanh t)+C$$ Thus the first integral has value $$\mathrm{atan} (\tanh (\mathrm{asinh}\frac1{\sqrt{2}}))= \mathrm{atan} (\sqrt{\frac23}\cdot\frac1{\sqrt{2}})$$ $$=\mathrm{atan}\frac{1}{\sqrt 3}=\frac{\pi}6$$ Notice that $\mathrm{atanh} \sqrt{3}$ is not even defined.
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revised Using $x=\tan \theta$ to solve $\int x\sqrt{1+x^2}\,\mathrm dx$
deleted 43 characters in body; edited title
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reviewed Approve suggested edit on Distribution function for price of stock.
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reviewed No Action Needed Uniform convergence of Monte Carlo approximation
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reviewed Reviewed Question on Proof (Direct, Contrapositive, Contradiction)?
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reviewed Close integral with respect to Dirac measure
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reviewed Close Elementary Conditional Probability Question
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reviewed Close Show that the system has a solution.
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reviewed Leave Open Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist?
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reviewed Reject suggested edit on expectation equals 0 and probability.
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reviewed Reject suggested edit on Expected number of people getting their own hat given that at least one of them gets his hat.
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reviewed Reject suggested edit on How to prove that for all $x$ there exists some $y$ where $ (x^2 + y^2 \geq 0)$?
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revised Irrationality of reciprocal Fibonacci constant
edited title
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reviewed Approve suggested edit on $\lim_{x \to \infty} f$ of a piecewise function $f$
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reviewed Edit suggested edit on Simplify the algebraic expression
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revised Simplify the algebraic expression
missing symbol
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reviewed Reject suggested edit on How many bits are needed to encode the following data?
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reviewed Looks OK if the probability density of $x$ is given by
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reviewed Looks OK Complex Measures: Lebesgue Decomposition
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reviewed Close figure out $f(n)$ under given conditions