Improper integral question

In summary, an improper integral is an integral with either infinite limits of integration or an unbounded integrand within the interval of integration. A proper integral, on the other hand, has finite limits of integration and a bounded integrand. An integral can be determined as improper if it meets any of the following conditions: infinite interval of integration, unbounded integrand, or a discontinuity within the interval of integration. The two types of improper integrals are type 1 and type 2, with type 1 having infinite limits of integration and type 2 having an unbounded integrand or discontinuity within the interval of integration. To evaluate an improper integral, one can use the limit definition, split the integral, or use a comparison test
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This is my method, could you help me to continue?

 
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  • #2
note ...

$\dfrac{x\sqrt{x}}{x^2-1} > \dfrac{1}{\sqrt{x}}$

and $\displaystyle \int_2^\infty \dfrac{dx}{\sqrt{x}}$ is divergent.
 

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