What is the integration of \[ \int {\frac{{3x – 1}}{{\sqrt {{x^2} + 9} }}} dx\] ~~~~~[NCERT Exemp. Q. 16,Page 164 ] Post author:admin Post published:April 18, 2021 Post category:Uncategorized Let \[ I = \int {\frac{{3x – 1}}{{\sqrt {{x^2} + 9} }}} dx\] \[I = \int {\frac{{3x}}{{\sqrt {{x^2} + 9} }}} dx – \int {\frac{1}{{\sqrt {{x^2} + 9} }}} dx\] \[ I = {I_1} – {I_2}\] Now, \[ {I_1} = \int {\frac{{3x}}{{\sqrt {{x^2} + 9} }}} \] Let’s put \[ {x^2} + 9 = {t^2} \Rightarrow 2xdx = 2tdt \Rightarrow xdx = tdt\] therefore,\[{I_1} = 3\int_t^t d t\] \[ = 3\int d t = 3t + {C_1} = 3\sqrt {{x^2} + 9} + {C_1}\] and \[ {I_2} = \int {\frac{1}{{\sqrt {{x^2} + 9} }}} dx = \int {\frac{1}{{\sqrt {{x^2} + {{(3)}^2}} }}} dx\] \[ = \log \left| {x + \sqrt {{x^2} + 9} } \right| + {C_2}\] therefore,\[ I = 3\sqrt {{x^2} + 9} + {C_1} – \log \left| {x + \sqrt {{x^2} + 9} } \right| – {C_2}\] 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/ Please Share This Share this content Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window Opens in a new window You Might Also Like mental math – grade 1 math worksheets June 1, 2021 pdf worksheets mathematics June 15, 2021 maths online practice tests quizzes for grade 2 June 6, 2021