(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Use the box and the behavior of rational and exponential functions as [tex] x \rightarrow \infty [/tex] to predict whether the integrals converge or diverge.

Here is the box:

[tex] \int^\infty_1 \frac{1}{x^p} dx [/tex] converges for p > 1 and diverges for p < 1.

[tex] \int^1_0 \frac{1}{x^p} dx [/tex] converges for p < 1 and diverges for p > 1.

[tex] \int^\infty_0 e^{-ax} dx [/tex] converges for a > 0.

Here is the problem I need help with:

[tex] \int^\infty_1 \frac{x^2+1}{x^3 + 3x + 2} dx [/tex]

2. Relevant equations

The box above.

3. The attempt at a solution

I know that this integral is less than [tex] \int^\infty_1 \frac{1}{x} dx [/tex]. I also know that [tex] \int^\infty_1 \frac{1}{x} dx [/tex] diverges. This does not help me though because I can not use a diverging integral to say that a smaller integral is also diverging. This is where I'm confused.

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# Homework Help: Another Comparison of Integrals

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