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,