# When will the following converge/diverge?

for what values of p, q will the following integral converge??

intergal from (0 - ∞ ) of

$$\int$$dx/(x^p +x^q)

i know that both $$\int$$dx/(x^p) and $$\int$$dx/(x^q) will converge when p,q>1 and i know that is smaller than either $$\int$$dx/(x^p) or $$\int$$dx/(x^q) alone since x>0, the denominator will be bigger so the fraction will be smaller.

so p,q>1 converge

but i dont think this is a proper answer, since as far as i see it is a possibility but not necessarily the only one,

how do i reach the correct answer?

Avodyne