What is the integration of $\int {\frac{{dx}}{{1 + \cos x}}} $ ~~~~~[NCERT Exemp. Q. 6,Page 164 ]By admin / April 18, 2021 Let $I = \int {\frac{{dx}}{{1 + \cos x}}} = \int {\frac{{dx}}{{1 + 2{{\cos }^2}\frac{x}{2} – 1}}} $$ = \frac{1}{2}\int {\frac{1}{{{{\cos }^2}\frac{x}{2}}}} dx = \frac{1}{2}\int {{{\sec }^2}} \frac{x}{2}dx$ $ = \frac{1}{2} \cdot \tan \frac{x}{2} \cdot 2 + C = \tan \frac{x}{2} + C$ Buy Best Mathematics E-Books Visit : https://mathstudy.in/ Buy Mathematics Formula Book for Class XI,XII,JEE and other Engineering Competition Exam https://mathstudy.in/product/mathematics-formula-book/ Buy Mathematics Workbook for Class XII ( Fully Solved ) : https://mathstudy.in/product/work-book-class-xii-c-b-s-e-fully-solved/ Buy Mathematics Chapter Tests for Class XII ( Fully Solved) : https://mathstudy.in/product/mathematics-chapter-tests-class-xii-c-b-s-e/ Buy Objective Type Question Bank Class XII (Fully Solved ) : https://mathstudy.in/product/objective-type-question-bank-for-mathematics-class-xii-c-b-s-e/