Calculate the arclength of $$y=\frac{\sqrt{x}(x^2+2)}{3}, \hspace{0.5cm} 2\leq x\leq 4$$
My work: I have calculated
$$1+(\frac{dy}{dx})^2=\frac{25x^4+20x^2+36x+4}{36x}$$
I need your help to solve the integral
$$\int_2^4\sqrt{\frac{25x^4+20x^2+36x+4}{36x}}dx$$
Please help me to find its EXACT VALUE.