∫ dx/(cos x √sin^2 x - cos^2 x) . dx =

Question

\(\int \frac{dx}{cos\,x\sqrt{sin^2 x - cos^2 x}}.dx =\)

∫ dx/(cos x √sin²x - cos²x) . dx =

(a) log(tan x - \(\sqrt{tan^2 x - 1} \)) + c

(b) sin^-1(tan x) + c

(c) 1 + sin^-1(cot x) + c

(d) log(tan x + \(\sqrt{tan^2 x - 1} \)) + c

Answer 1

Correct answer is (d) log(tan x + \(\sqrt{tan^2 x - 1} \)) + c