Question

$2\log\left( {logtan}\frac{x}{2} \right) + c$

• A. $\frac{1}{2}\log\left( {logtan}\frac{x}{2} \right) + c$
• B. $\int_{}^{}{\frac{1}{\cos^{2}x(1 - \tan x)^{2}}dx =}$
• C. $\frac{1}{\tan x - 1} + c$
• D. None of these

Answer 1

Answer: (B)

$\int_{}^{}{\frac{1}{\cos^{2}x(1 - \tan x)^{2}}dx =}$

Answer 2

$\frac{1}{\sqrt{2}}{logtan}\left( \frac{\pi}{8} + \frac{x}{2} \right) + c$

Putting $\int_{}^{}{\frac{1}{x\sqrt{x^{2} - 1}}\mspace{6mu} dx =}$ we get

$\cos^{- 1}x + c$.