Find the length of the curve $x=0.5y\sqrt{y^2-1}-0.5\ln(y+\sqrt{y^2-1})$ from y=1 to y=2.
My attempt involves finding $\frac {dy}{dx}$ of that function first, which leaves me with a massive equation.
Next, I used this formula,
$\int_1^2\sqrt{1+(\frac{dy}{dx})^2}$
this attempt leaves me with such a messy long equation that eventually took up 2 pages, and still left me unsolved. I am convinced there must be an easier way.
Any hints please? thanks in advance.