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Example 9 - Find integrals (i) dx / x2 - 6x + 13 - Class 12

Example 9 - Chapter 7 Class 12 Integrals - Part 2

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Example 9 Find the following integrals: (i) ∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 6π‘₯ + 13) ∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 6π‘₯ + 13) =∫1▒𝑑π‘₯/(π‘₯^2βˆ’ 2 Γ— 3 Γ— π‘₯ + 13) = ∫1▒𝑑π‘₯/((π‘₯^2 βˆ’ 2 . 3 π‘₯ + 3^2 ) + 13 βˆ’ 3^2 ) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 13 βˆ’ 9) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 4) = ∫1▒𝑑π‘₯/((π‘₯ βˆ’ 3)^2 + 2^2 ) ("Adding and subtracting " (3)^2 ) ("Using " π‘Ž^2βˆ’2π‘Žπ‘+𝑏^2=(π‘Žβˆ’π‘)^2 ) It is of form 𝑑π‘₯/(π‘₯^2 + π‘Ž^2 )=1/π‘Ž γ€–π‘‘π‘Žπ‘›γ€—^(βˆ’1)⁑〖π‘₯/π‘Žγ€—+𝐢 Replacing π‘₯ with (π‘₯βˆ’3) and π‘Ž with 2 =𝟏/𝟐 〖𝒕𝒂𝒏〗^(βˆ’πŸ)⁑〖(𝒙 βˆ’ πŸ‘)/πŸγ€— +π‘ͺ

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.