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Let's join this 4U train :)

Re: HSC 2013 4U Marathon a) Find \int \sqrt{\tan x} \;\; dx b) Hence find \int \sqrt{\tan x}^{13} \;\; dx c) Finally, for those top notch students, prove that, if I_{k}=\int \sqrt{\tan x}^{k} \;\; dx then, for all positive integers n, I_{8n+5} = I_{8n-3} +\frac{2}{8n+3}{\sqrt{\tan...