Chapter 7 Class 12 Integrals

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Important Questions for exams Class 12

Example 9 (i) - Chapter 7 Class 12 Integrals (Important Question)

Last updated at July 14, 2026 by

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

Example 9 - Chapter 7 Class 12 Integrals - Part 2

 

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Transcript

Example 9 Find the following integrals: (i) āˆ«1ā–’š‘‘š‘„/(š‘„^2āˆ’ 6š‘„ + 13) āˆ«1ā–’š‘‘š‘„/(š‘„^2āˆ’ 6š‘„ + 13) =āˆ«1ā–’š‘‘š‘„/(š‘„^2āˆ’ 2 Ɨ 3 Ɨ š‘„ + 13) = āˆ«1ā–’š‘‘š‘„/((š‘„^2 āˆ’ 2 . 3 š‘„ + 3^2 ) + 13 āˆ’ 3^2 ) = āˆ«1ā–’š‘‘š‘„/((š‘„ āˆ’ 3)^2 + 13 āˆ’ 9) = āˆ«1ā–’š‘‘š‘„/((š‘„ āˆ’ 3)^2 + 4) = āˆ«1ā–’š‘‘š‘„/((š‘„ āˆ’ 3)^2 + 2^2 ) ("Adding and subtracting " (3)^2 ) ("Using " š‘Ž^2āˆ’2š‘Žš‘+š‘^2=(š‘Žāˆ’š‘)^2 ) It is of form š‘‘š‘„/(š‘„^2 + š‘Ž^2 )=1/š‘Ž 怖š‘”š‘Žš‘›ć€—^(āˆ’1)ā”怖š‘„/š‘Žć€—+š¶ Replacing š‘„ with (š‘„āˆ’3) and š‘Ž with 2 =šŸ/šŸ 怖š’•š’‚š’ć€—^(āˆ’šŸ)ā”怖(š’™ āˆ’ šŸ‘)/šŸć€— +š‘Ŗ

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