# Homework Help: Comparison test on second species integrals

1. Dec 23, 2012

### Rono

1. The problem statement, all variables and given/known data
Determine if the following integrals are convergent or divergent. Explain why.

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

3. 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?

2. Dec 23, 2012

### 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).

3. Dec 23, 2012

### Rono

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