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 Nov 23 awarded Popular Question May 24 comment Given $|f(x)|=1$,how to construct an $f(x)$, such that $\int ^{+\infty }_{0}f\left( x\right) dx$ converges You can take $e^{i x^2}$. It's essentially what paul garrett wrote. See also [Fresnel integrals]( en.m.wikipedia.org/wiki/Fresnel_integral). May 24 revised Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$? added 67 characters in body May 24 revised Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$? added 162 characters in body May 24 awarded Yearling May 24 answered Counter example in Sobolev spaces: Is there a standard example for showing that $H^1(\mathbb{R}^2)\not\subset L^\infty(\mathbb R^2)$? May 9 comment Let $(a_n)$ be any sequence and $(b_n)=n(a_n-a_{n+1})$. If $\sum a_n$ and $\sum b_n$ converges then $\lim_{n\to \infty}na_n=0$ Summation by parts May 2 revised Relation between $\int_0^{\infty} \frac{e^{-ax}}{1+x^2}\,\,dx$ and $\int_0^{\infty} \frac{e^{-2ax}}{1+x^2}\,\,dx$ added 47 characters in body May 2 answered Relation between $\int_0^{\infty} \frac{e^{-ax}}{1+x^2}\,\,dx$ and $\int_0^{\infty} \frac{e^{-2ax}}{1+x^2}\,\,dx$ Dec 20 awarded Caucus Dec 14 revised Definite integral involving Error function improved formatting Dec 14 revised Definite integral involving Error function added 484 characters in body Dec 13 comment Definite integral involving Error function Yes, sure. But then you end up with an integral over powers of $erf$, which I do not know how to evaluate either. Dec 13 asked Definite integral involving Error function Jul 2 awarded Curious Jun 23 awarded Nice Question May 23 awarded Tumbleweed Feb 23 revised Closure of Schwartz space in homogeneous Besov space improved title Feb 23 asked Closure of Schwartz space in homogeneous Besov space Aug 5 awarded Nice Answer