Evaluate the integral
(tan x + cot x)^2

For this integration, we will be using the pythagorean identities:  tan^2 x + 1 = sec^2 x  cot^2 x + 1 = csc^2 x  tan x * cot x = 1

and the integration formulas:  int(sec^2 x dx) = tan x  int(csc^2 x dx) = -cot xintegral of (tan x + cot x) ^ 2 dx

Expanding the internal expression first.= int(tan^2 x + 2 * tan x * cot x + cot^2 x dx)= int(tan^2 x + cot^2 x + 2 dx)= int(tan^2 x + 1 + cot^2 x + 1 dx)= int(sec^2 x + csc^2 x dx)= int(sec^2 x dx) + int(csc^2 x dx)= tan x - cot x + C

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