Originally Posted by

**joatmon** $\displaystyle \int_1^\infty \frac{1}{(x^4+x+1)^{\frac{1}{3}}}dx$

I don't think that I can evaluate the integral easily, so I'm looking for a comparative function. If I say that:

$\displaystyle x^4 + x + 1 \geq x for [1,\infty)$

then I can also say that

$\displaystyle \frac{1}{x^4 + x + 1} \leq \frac{1}{x}$

$\displaystyle \frac{1}{(x^4+x+1)^{\frac{1}{3}}} \leq \frac{1}{x^{\frac{1}{3}}}$

The problem is that

$\displaystyle \int_1^\infty \frac{1}{x^{\frac{1}{3}}} = \infty$

which doesn't help me in determining the value of the original integral.

Can anybody see what I am doing wrong or recommend another function to use as a comparison?

Thanks.