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Evaluate the Following Integrals: ∫ Sec X Sec 2 X D X - Mathematics

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Question

Evaluate the following integrals:

`int "sec x"/"sec 2x" "dx"`

Sum

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Solution

\[I = \int\frac{\sec x}{\sec 2x}dx\]

`"sec x"/("sec"(2"x")) = ("cos"(2"x"))/"cos x"`

`= (2 "cos"^2"x" - 1)/"cos x"`

`= ("2 cos"^"x")/"cos x" - 1/"cos x"`

= 2 cos x - sec x

`int ("sec"("x"))/("sec"(2"x")) "dx" = int[2 "cos x" - "sec x"] "dx"`

`= 2 int "cos x" "dx" - int "sec"("x") "dx"`

= 2 sin(x) - ln |sec (x) + tan (x)| + C

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Evaluation of Simple Integrals of the Following Types and Problems

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Chapter 19: Indefinite Integrals - Exercise 19.08 [Page 47]

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RD Sharma Mathematics [English] Class 12

Chapter 19 Indefinite Integrals
Exercise 19.08 | Q 5 | Page 47

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