Evaluate the following integrals:

Let


We know (a + b)2 = a2 + 2ab + b2


Therefore, we can write the integral as





We have sec2θ – tan2θ = cosec2θ – cot2θ = 1









Recall and


We also have


I = a2tan x + b2(–cot x) – (a - b)2 × x + c


I = a2tan x – b2cot x – (a – b)2x + c


Thus,


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