I swear I've done something wrong with this one.

$\displaystyle \int_{-1}^1 x^{-2/3} dx$ (This is an improper integral, because the integrand is an unbounded function at x=0)

Here's what I got:

$\displaystyle \int x^{-2/3} dx = 3\sqrt[3]{x}+C$

$\displaystyle \Rightarrow \int_{-1}^1 x^{-2/3} dx = 3-3\sqrt[3]{-1}\approx 1.5-2.59808i$

I'm probably missing something really basic, but I've been tangled up with other stuff and, well, when you take in new material, the other stuff either gets jumbled or pushed out.

If anyone could see if I've made a mistake somewhere, it'd be appreciated.