Chapter 7 Class 12 Integrals
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Ex 7.6, 20 - Chapter 7 Class 12 Integrals

Last updated at July 26, 2026 by

Ex 7.6, 20 - Integrate (x - 3)ex / (x - 1)3 - Class 12 - Ex 7.6

Ex 7.6, 20 - Chapter 7 Class 12 Integrals - Part 2

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Ex 7.6, 20 Integrate the function (š‘„ āˆ’ 3)š‘’š‘„/(š‘„ āˆ’ 1)3 āˆ«1ā–’怖((š‘„ āˆ’ 3))/(š‘„ āˆ’1)3 .š‘’š‘„" " š‘‘š‘„怗 = āˆ«1ā–’怖(š‘„ āˆ’ 1 āˆ’ 2)/(š‘„ āˆ’1)^3 .š‘’š‘„" " š‘‘š‘„怗 = āˆ«1ā–’怖š‘’š‘„ ((š‘„ āˆ’ 1)/(š‘„ āˆ’1)^3 āˆ’ 2/(š‘„ āˆ’1)^3 )š‘‘š‘„怗 = āˆ«1ā–’怖š‘’š‘„ (1/(š‘„ āˆ’1)^2 āˆ’ 2/(š‘„ āˆ’1)^3 )š‘‘š‘„怗 It is of the form āˆ«1ā–’怖š‘’^š‘„ [š‘“(š‘„)+š‘“^ā€² (š‘„)] 怗 š‘‘š‘„=š‘’^š‘„ š‘“(š‘„)+š¶ Where š‘“(š‘„)=" " 1/(š‘„ āˆ’1)^2 āˆ“ š‘“^ā€² (š‘„)= (āˆ’ 2)/(š‘„ āˆ’ 1)^3 So, our equation becomes āˆ«1ā–’怖š‘’š‘„ (1/(š‘„ āˆ’ 1)^2 āˆ’ 2/(š‘„ āˆ’ 1)^3 )š‘‘š‘„怗 = š’†š’™/(š’™ āˆ’ šŸ)šŸ +š‘Ŗ

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