Comparison test on second species integrals

[Rono]

Homework Statement

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

[itex]\int^{1}_{0} \frac{1}{1-x^{4}} dx[/itex]

The Attempt at a Solution

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