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Problem 49 Hard Difficulty

Use the Comparison Theorem to determine whether the integral is convergent or divergent.

$ \displaystyle \int_0^\infty \frac{x}{x^3 + 1}\ dx $

Answer

convergent

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Video Transcript

Hello. Welcome to this lesson. In this lesson, we'll find a convergence good or divergence of the integration the comparison test. So let this be a function for backside is extra extra extra part three plus one. Let's have another function. Your ex That is X uber's the battery eggs. Oh, you have export to X over X two plus X last one. So for every value of X J of X is greater than f of X. Okay, but given the same same bounds, uh, converges in around almost one. Okay, Converges to 0.969 Okay, so F g of X is greater than f of x and Jim and Jane of X converges than f of X. Given the bounce in the integral. So it means that yeah. Of f of X Bull. Yeah, converges using the comparison tests. Sometimes your time is the end of the lesson.