I am learning about how to calculate the length of a path with integration. The equation is:
$$\sqrt{1+\Big (\frac{dy}{dx} \Big)^2} $$
So I have to integrate it between $a$ and $b$. In my book I have an example, I understand it but don't know how he solved this:
$$\sqrt{\frac{1}{4} \times (x^4 + 2 + \frac{1}{x^4})}$$
for which the result after eliminating the square root is:
$$1/2 \times (x^2 + \frac{1}{x^2})$$
I know that $\sqrt{1/4} = 1/2$ but I can't understand how the rest is solved.