Question

$\int \frac{\tan x}{\log \sec x}dx.$

• A. $\log \left(\log \sin x\right).$
• B. $\log \left(\log \cos x\right).$
• C. $\log \left(\log \sec x\right).$
• D. $\left(\log \sec x\right).$

Answer 1

Answer: (C)

$\log \left(\log \sec x\right).$

Let $I=\int \frac{\tan x}{\log \sec x}dx$
Put $\log \sec x=t\Rightarrow \tan xdx=dt$
Therefore
$I=\int \frac{dt}{t}=\log t=\log \left(\log \sec x\right)$