Question

How do you use comparison test to determine is the integral is convergent or divergent given `int x / (8x^2 + 2x^2 - 1) dx` ?

Answer 1

First of all a think there is a mistake: maybe `8x^2` would be `8x^3`,

so the function is:

`x/(8x^3+2x^2-1)~1/(8x^2)` (`~ =`asymptotic)

that is a convergent function because it's a generalized armonic series, `1/x^alpha`, with `alpha>1`.