Question

The value of $\int \frac{{\sec }^2(\log x)}{x}dx$ is :

• A. tan (log x) + c
• B. tan x + c
• C. log (tan x) + c
• D. none of these

Answer 1

Answer: (A)

Let $I=\int \frac{{\sec }^2(\log x)}{x}dx$
Put $\log x=t\Rightarrow \frac{1}{x}dx=dt$
$\therefore \int {\sec }^{2}tdt=\tan t+c=\tan (\log x)+c$