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Evaluate: ∫ 2 Cos 2 X − Cos 2 X Cos 2 X D X

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Question

Evaluate:

\[\int\frac{2 \cos^2 x - \cos 2x}{\cos^2 x}dx\]

Sum

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Solution

\[\int\left( \frac{2 \cos^2 x - \cos 2x}{\cos^2 x} \right)dx\]
\[ = \int\left( \frac{2 \cos^2 x - \left( 2 \cos^2 x - 1 \right)}{\cos^2 x} \right)dx \left[ \because \cos 2x = 2 \cos^2 x - 1 \right]\]
\[ = \int \sec^2\text{ x dx}\]
\[ = \ \text{tan x} + C\]

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Evaluation of Definite Integrals by Substitution

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Q 5.2 Q 5.1 Q 6

Chapter 18: Indefinite Integrals - Exercise 19.01 [Page 4]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12

Chapter 18 Indefinite Integrals
Exercise 19.01 | Q 5.2 | Page 4

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