Length of curve!! Calculus

y = (x^3)/3 + 1/(4x) from x = 1 to x = 3

What is the length of the curve?

thanks!

y = x^3 / 3 + 1 / (4x)
dy/dx = 3x^2 / 3 - 1/(4x^2)
dy/dx = x^2 - 1/(4x^2)
dy/dx = (4x^4 - 1) / (4x^2)

sqrt(1 + (dy/dx)^2) * dx =>
sqrt(1 + ((4x^4 - 1)^2 / (4x^2)^2) * dx =>
sqrt((16x^4 + 16x^8 - 8x^4 + 1) / (16x^4)) * dx =>
sqrt((16x^8 + 8x^4 + 1) / (16x^4)) * dx =>
sqrt((4x^4 + 1)^2 / (4x^2)^2) * dx =>
(4x^4 + 1) * dx / (4x^2) =>
x^2 * dx + dx / (4x^2)

Integrate

(1/3) * x^3 - 1/(4x) + C

From 1 to 3

(1/3) * (3^3 - 1^3) - (1/(4 * 3) - 1 / (4 * 1)) =>
(1/3) * (27 - 1) - (1/12 - 1/4) =>
(1/3) * 26 - (-2/12) =>
26/3 + 2/12 =>
26/3 + 1/6 =>
52/6 + 1/6 =>
53/6

link
http://patrickjmt.com/arc-length/