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Question
` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
Sum
Solution
` Note: Here , we are " considering " log x as log_e x` .
Let I = ` ∫ {sec x "cosec " x}/{log ( tan x) }` dx
` "Putting" "log" \ tan x = t `
\[ \Rightarrow \frac{\sec^2 x}{\tan x} = \frac{dt}{dx}\]
\[ \Rightarrow \text{sec x cosec x dx} = dt\]
\[ \therefore I = \int\frac{1}{t}dt\]
\[ = \text{log }\left| \text{t }\right| + C\]
\[ = \text{log} \left| \text{log} \left( \tan x \right) \right| + C\]
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