I'm struggling with improper integrals in the context of definite integrals that become undefined within the limits of integration (I believe that this is Type II). For example, $$\int_0^1 \frac{x^2 dx}{x-1}$$ I've tried to utilize the comparison test, but I am having trouble determining a suitable function that is larger than this function to compare its convergence. Is there a set of rules I should be aware of when generating corresponding integers to test for convergence? Thank you!
2026-04-11 20:12:26.1775938346
Convergence of definite integral
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$\frac{x^2}{x-1}=x+1+\frac{1}{x-1}$