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∫ Sec X C O S E C X Log ( Tan X ) D X - Mathematics

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Sum

` ∫  {sec  x   "cosec " x}/{log  ( tan x) }`  dx

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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 `
\[ \Rightarrow \frac{\sec^2 x}{\tan x} = \frac{dt}{dx}\]
\[ \Rightarrow \text{sec x cosec x dx} = dt\]
\[ \therefore I = \int\frac{1}{t}dt\]
\[ = \text{log }\left| \text{t }\right| + C\]
\[ = \text{log} \left| \text{log} \left( \tan x \right) \right| + C\]

Concept: Indefinite Integral Problems
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APPEARS IN

RD Sharma Class 12 Maths
Chapter 19 Indefinite Integrals
Exercise 19.8 | Q 15 | Page 47

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