Misc 21 - Chapter 7 Class 12 Integrals

Last updated at July 20, 2026 by

Misc 21 - Integrate x^2 + x + 1 / (x + 1)^2 (x + 2) - Class 12 - Miscellaneous

part 2 - Misc 21 - Miscellaneous - Serial order wise - Chapter 7 Class 12 Integrals

Take a fresh quiz. Then take another.
Every attempt is a new AI-adaptive Teachoo quiz with 5 questions, selected from your answers, mistakes, and progress.
Remove Ads

Transcript

Misc 21 Integrate the function (š‘„^2 + š‘„ + 1)/((š‘„ + 1)^2 (š‘„ + 2) ) āˆ«1ā–’怖(š‘„^2 + š‘„ + 1)/((š‘„ + 1)^2 (š‘„ + 2) ) " " š‘‘š‘„怗 By partial fraction (š‘„^2 + š‘„ + 1)/((š‘„ + 1)^2 (š‘„ + 2) )=A/(š‘„ + 2)+B/(š‘„ + 1)+C/怖(š‘„ + 1)怗^2 (š‘„^2 + š‘„ + 1)/((š‘„ + 1)^2 (š‘„ + 2) )=(A怖(š‘„ + 1)怗^2 + B(š‘„ + 1)(š‘„ + 2) + C(š‘„ + 2))/(怖(š‘„ + 1)怗^2 (š‘„ + 2) ) Cancelling denominators š‘„^2+š‘„+1=A怖 (š‘„+1)怗^2+B(š‘„+2)(š‘„+1)+C(š‘„+2) Hence, (š‘„^2 + š‘„ + 1)/((š‘„ + 1)^2 (š‘„ + 2))=3/(š‘„ +2)āˆ’2/(š‘„ +1)+1/怖(š‘„ + 1)怗^2 āˆ«1ā–’(š‘„^2+ š‘„ +1)/(怖(š‘„ + 1)怗^2 (š‘„ + 2))=āˆ«1ā–’(3 š‘‘š‘„)/(š‘„ + 2)āˆ’āˆ«1ā–’(2 š‘‘š‘„)/(š‘„ + 1)+āˆ«1ā–’(1 š‘‘š‘„)/(š‘„ + 1)^2 = 3log |š‘„+2| "ā€“ 2log " |š‘„+1|āˆ’ 1/(š‘„ + 1)+š¶ = "ā€“ 2log " |š’™+šŸ|āˆ’ šŸ/(š’™ + šŸ)+"3log " |š’™+šŸ|+š‘Ŗ

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.