Find the improper integral of te^-st dt from 0 to b where the limit of b approaches to positive infinity.

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please i need a formal proof of comparison test for improper integrals..

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How do I integrate 4x^2/(x^3-8) from 0 to 8 It is an improper integral and I know it diverges but I don't know why i found u=x^3-8 but am getting stuck after that ...

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I have this problem: Evaluate the integral (x^2-2)/(x^4+3) from 1 to infinity using a comparison test (evaluate if converging). I understand the basic idea is to find a function with...