1. Length of a curve

Find the length of the curve

$x=3y^{ \frac{4}{3} } - \frac{3}{32} y^{ \frac{2}{3} }$

$-216 \leq y \leq 125$

I got to the integral, which is $\int^{125}_{-216} (1+(4y^{ \frac {1}{3}} + \frac{1}{16} y^{ \frac{-1}{3} })^{2})^{\frac{1}{2}}$

But how do I solve this integral?

2. Are you sure you have it stated correctly?. It appears to have a complex result.