Finding the length of a graph I am asked to find the length of the graph of the function: $\dfrac{x^2}{8} - \ln (x)$ , $x\in[1,4]$.
I am really struggling with this problem. As far as I know, we use the formula:
$L(c)= \sqrt{1 + [f'(x)]^2}$
Either I am deriving it wrong or I am missing steps because I am not getting the answer the book gives.

The length is
$$\int_1^4 \sqrt{1+\Bigl(\frac x4-\frac1x\Bigr)^2}\,dx
  =\int_1^4\sqrt{\Bigl(\frac x4+\frac1x\Bigr)^2}\,dx\ .$$
I'm sure you can finish it from here.
