∫ 1 + tan x tan x + a tan x tan x + a d x =

1. $\tan a\left(\log \left(\sec \left(x+a\right)\right)+\mathrm{logsec}x+C\right)$
2. $\cot a\left(\log \left|\sin x\right|-\log \left|\sin \left(x+a\right)\right|\right)+C$
3. $\tan a\left(\log \left(\frac{\cos x}{\sin \left(x+a\right)}\right)\right)+C$
4. $\cot a\left(\log \frac{\sin \left(x+a\right)}{\cos \left(x+a\right)}\right)+C$

Solution

Asked in: AP EAMCET 2022 (04 Jul Shift 2)

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