Improper Integrals: Divergence at x=0?

[aaaa202]

Homework Statement

Check if the following integrals diverge:
Int(1/(x^3-2x^2+x), from 0 to 1) and Int(1/(x^3+x^2-2x)

Homework Equations

Ratio-test(not sure if that's the name)

The Attempt at a Solution

I have solved the problem and found that both integrals diverge at x=0. I just want to check if you guys agree with me.

 

[MostlyHarmless]

Ratio test is for infinite series, not a improper integrals. It would be helpful to see your work.

 

[Mark44]

Homework Statement

Check if the following integrals diverge:
Int(1/(x^3-2x^2+x), from 0 to 1) and Int(1/(x^3+x^2-2x)

Homework Equations

Ratio-test(not sure if that's the name)

The Attempt at a Solution

I have solved the problem and found that both integrals diverge at x=0.

Both integrands are undefined at x = 0, which is why the integrals are improper. Both integrands are also undefined at the other endpoint, x = 1.

You need to use limits to evaluate these integrals - then you can decide whether either one diverges.

I just want to check if you guys agree with me.

 

[aaaa202]

Okay ratio test was then not the correct name. What I did was use the test that if limx->0[g/f>0] then g also diverges if f diverges. So I took f as 1/x^3. Isn't this correct, and don't you guys get that both integrals diverge?