Comparison test on second species integrals

[Rono]

Homework Statement

Determine if the following integrals are convergent or divergent. Explain why.

$\int^{1}_{0} \frac{1}{1-x^{4}} dx$

The Attempt at a Solution

I've tried using Comparison Test, using $f(x) = \frac{1}{1-x^{4}} and\; g(x) = \frac{1}{1-x}$, $0 \leq f(x)\leq g(x)$ $in ] 0,1 [$ and I know $g(x)$ is divergent. My question is if its plausible that, by using Comparison Test, if $g(x)$ is divergent, will $f(x)$ be divergent too?

 

[Dick]

No. Not plausible. You want a divergent integral that's less than f(x), not greater. Hint: factor 1-x out of (1-x^4).

 

[Rono]

It was my first thought, but I considered it too simple to be true, thanks!