Answer by Robert Z for Test $\int_{0}^{\infty}\frac{e^{ix}}{\log(x)},...
As regards the first one, the function $\frac{e^{ix}}{\log(x)}$ is not integrable in a neighbourhood of $1$. Why?For the second one, you are right, it diverges for $p\geq 1$ in $[0,1]$. For...
View ArticleTest $\int_{0}^{\infty}\frac{e^{ix}}{\log(x)},...
I need to test these integrals for convergence $\int_{0}^{\infty}\frac{e^{ix}}{\log(x)},\int_{0}^{\infty}\frac{\cos(x)}{x^p},\int_{0}^{\infty}\cos(x^2)$ with $p\in\mathbb{R}$. However I suck horribly...
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