Determine the arc length of the curve $$y=\frac12(x^2+2)^{\frac32},\ 0\le x\le2$$
I have tried doing this and reached the point: $$L=\frac32 \int_0^2 \sqrt{(x^2+1)^2-\frac59}\ dx$$
Now I'm stuck, and I've tried using conjugates and substitution without success.