Let \[ I = \int {\frac{{{x^2}}}{{1 – {x^4}}}} dx\]

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

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

\[ = \frac{1}{2}\int {\frac{1}{{1 – {x^2}}}} dx – \frac{1}{2}\int {\frac{1}{{1 + {x^2}}}} dx = \frac{1}{2} \cdot \frac{1}{2}\log \left| {\frac{{1 + x}}{{1 – x}}} \right| + {C_1} – \frac{1}{2}{\tan ^{ – 1}}x + {C_2}\]

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/