By considering:
\displaystyle \int \left(\sqrt{\tan x} \pm \sqrt{\cot x}\right) \mathrm dx
evaluate the classic integral:
\displaystyle \int \sqrt{\tan x}\mathrm dx
Hence evaluate:
\displaystyle \int \frac {x^2} {x^4 + 1} \mathrm dx
By considering:
\displaystyle \int \left(\sqrt{\tan x} \pm \sqrt{\cot x}\right) \mathrm dx
evaluate the classic integral:
\displaystyle \int \sqrt{\tan x}\mathrm dx
Hence evaluate:
\displaystyle \int \frac {x^2} {x^4 + 1} \mathrm dx