Question

If I have sqrt((x^-1+2+x)/4) how does it "turn into a square" so I can then sqrt it and then finish my integration?

Answer 1

factor out a 1/x

Answer 2

\(\huge \dfrac{((x^{-1/2})^2+2\times x^{-1/2}x^{1/2}+(x^{1/2})^2)}{2^2} \\ = \huge (\dfrac{x^{-1/2}+x^{1/2}}{2})^2\)

Answer 3

so, \(\huge \sqrt{(x^{-1}+2+x)/4}=(x^{-1/2}+x^{1/2})/2\)
can you integrate now ?