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Found problems: 1

2019 District Olympiad, 4
Tags: improper integral , integral , calculus , limit
Let $a$ be a real number, $a>1.$ Find the real numbers $b \ge 1$ such that $$\lim_{x \to \infty} \int\limits_0^x (1+t^a)^{-b} \mathrm{d}t=1.$$