Is this improper integral convergent or divergent: $$\int_{0}^{1} \frac{5 \cos x}{x + \sqrt{x}}$$
I am not sure how I would find the answer to this question. I am trying to use the limit comparison test, but I don't see how I would get the answer.
2026-03-26 02:44:44.1774493084
Is this improper integral convergent or divergent?
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It is convergent, because$$\lim_{x\to0^+}\frac{\frac{5\cos x}{x+\sqrt x}}{\frac1{\sqrt x}}=5$$and the integral$$\int_0^1\frac1{\sqrt x}\,\mathrm dx$$converges.