Definite integral $\int_1^2 \sqrt{1+\left(-x^{-2}+x^2/4\right)^2}\,dx$ I'm having trouble solving this integral. It relates to an arc length question. I tried Wolfram|Alpha, but when it solves it doesn't give me the option to view step-by-step. 
Integral:
$$
\int_{1}^{2} \sqrt{1+\left(-x^{-2}+\frac{x^2}{4}\right)^2}\,dx
$$
Original question: 
$$
y=\frac{1}{x} + \frac{x^3}{12}
$$
Find the arc length of the function on [1,2]. 
I used the equation:
$$
L = \int_a^b \sqrt{1+(f'(x))^2}
 dx$$

Simplifying the integrand proceed as follows.$$1+\left( -x^{-2}+\frac14x^2\right)^2=1+\left(\frac{x^4-4}{4x^2}\right)^2=\frac{(x^4+4)^2}{16x^4}$$Then after taking a square root, the integrand simplifies to $$\frac{x^4+4}{4x^2}=x^{-2}+\frac14x^2$$which is trivial to integrate.
