What is the integration of \[ \int {\frac{{dx}}{{x\sqrt {{x^4} – 1} }}} \] ~~~~~[NCERT Exemp. Q. 26,Page 165 ]

Let \[ I = \int {\frac{{dx}}{{x\sqrt {{x^4} – 1} }}} \]


Let’s put \[ {x^2} = \sec \theta \Rightarrow \theta = {\sec ^{ – 1}}{x^2}\]

\[ \Rightarrow \] \[ 2xdx = \sec \theta \cdot \tan \theta d\theta \]

therefore,\[ I = \frac{1}{2}\int {\frac{{\sec \theta \cdot \tan \theta }}{{\sec \theta \tan \theta }}} d\theta = \frac{1}{2}\int d \theta = \frac{1}{2}\theta + C\]

\[ = \frac{1}{2}{\sec ^{ – 1}}\left( {{x^2}} \right) + C\]

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/