Actually i am finding the arc length of curve
$24xy = y^4 + 48$ from $y = 2$ to $y = 4$
i have found the derivative with respect to $y$ and that is $\frac{y^2}6 -\frac{x}y$ by putting this derivative in the arc length formula i get the following
$\int_2^4 \sqrt{1+ \left(\frac{y^2}6 -\frac{x}y\right)^2}$
I solve this definite integral by substitution but i am failed please help me, give me some hints. I will be thankful.