Show that \[\int {\frac{{2x – 1}}{{2x + 3}}} dx = x – \log \left| {{{(2x + 3)}^2}} \right| + C\] ~~~~~[NCERT Exemp. Q. 1,Page 163 ]

Let $I = \int {\frac{{2x - 1}}{{2x + 3}}} dx = \int {\frac{{2x + 3 - 3 - 1}}{{2x + 3}}} dx$

$ = \int 1 dx - 4\int {\frac{1}{{2x + 3}}} dx = x - \int {\frac{4}{{2\left( {x + \frac{3}{2}} \right)}}} dx$

$ = x - 2\log + \left| {\left( {x + \frac{3}{2}} \right)} \right|{C^\prime } = x - 2\log \left| {\left( {\frac{{2x + 3}}{2}} \right)} \right| + {C^\prime }$

$ = x - 2\log |(2x + 3)| + 2\log 2 + {C^\prime }$

$ = x - \log \left| {{{(2x + 3)}^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/