Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

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Chapter 7 Class 12 Integrals

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Last updated at June 13, 2023 by Teachoo

Misc 21 Integrate the function (š„^2 + š„ + 1)/((š„ + 1)^2 (š„ + 2) ) ā«1āć(š„^2 + š„ + 1)/((š„ + 1)^2 (š„ + 2) ) " " šš„ć By partial fraction (š„^2 + š„ + 1)/((š„ + 1)^2 (š„ + 2) )=A/(š„ + 2)+B/(š„ + 1)+C/ć(š„ + 1)ć^2 (š„^2 + š„ + 1)/((š„ + 1)^2 (š„ + 2) )=(Ać(š„ + 1)ć^2 + B(š„ + 1)(š„ + 2) + C(š„ + 2))/(ć(š„ + 1)ć^2 (š„ + 2) ) Cancelling denominators š„^2+š„+1=Ać (š„+1)ć^2+B(š„+2)(š„+1)+C(š„+2) Hence, (š„^2 + š„ + 1)/((š„ + 1)^2 (š„ + 2))=3/(š„ +2)ā2/(š„ +1)+1/ć(š„ + 1)ć^2 ā«1ā(š„^2+ š„ +1)/(ć(š„ + 1)ć^2 (š„ + 2))=ā«1ā(3 šš„)/(š„ + 2)āā«1ā(2 šš„)/(š„ + 1)+ā«1ā(1 šš„)/(š„ + 1)^2 = 3log |š„+2| "ā 2log " |š„+1|ā 1/(š„ + 1)+š¶ = "ā 2log " |š+š|ā š/(š + š)+"3log " |š+š|+šŖ