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CBSE Class 12-science Answered

integral of x^2+x+1/(x+1)^2(x+2) 
Asked by lekhakarthikeyan | 20 Dec, 2018, 03:16: PM
answered-by-expert Expert Answer
begin mathsize 12px style I space equals space integral fraction numerator x squared plus x plus 1 over denominator open parentheses x plus 1 close parentheses squared open parentheses x plus 2 close parentheses end fraction d x L e t space u s space g e t space p a r t i a l space f r a c t i o n space f o r space fraction numerator begin display style x squared plus x plus 1 end style over denominator begin display style open parentheses x plus 1 close parentheses squared open parentheses x plus 2 close parentheses end style end fraction fraction numerator begin display style x squared plus x plus 1 end style over denominator begin display style open parentheses x plus 1 close parentheses squared open parentheses x plus 2 close parentheses end style end fraction space equals space fraction numerator A x plus B over denominator begin display style open parentheses x plus 1 close parentheses squared end style end fraction plus fraction numerator C over denominator open parentheses x plus 2 close parentheses end fraction space equals space fraction numerator open parentheses A x plus B close parentheses begin display style open parentheses x plus 2 close parentheses end style begin display style space end style begin display style plus end style begin display style C end style begin display style begin display style open parentheses x plus 1 close parentheses end style squared end style over denominator open parentheses x plus 1 close parentheses squared open parentheses x plus 2 close parentheses end fraction H e n c e space x squared plus x plus 1 space equals space open parentheses A x plus B close parentheses open parentheses x plus 2 close parentheses space plus C open parentheses x plus 1 close parentheses squared space B y space e q u a t i n g space c o e f f i c i e n t s space o f space s a m e space p o w e r s space o f space x comma space w e space g e t space A space equals negative 2 comma space B space equals space minus 1 space a n d space C space equals 3 H e n c e space I space equals space integral fraction numerator begin display style x squared plus x plus 1 end style over denominator begin display style open parentheses x plus 1 close parentheses squared open parentheses x plus 2 close parentheses end style end fraction d x space equals space integral fraction numerator 3 d x over denominator open parentheses x plus 2 close parentheses end fraction space minus space integral fraction numerator 2 x over denominator begin display style open parentheses x plus 1 close parentheses squared end style end fraction d x space plus integral fraction numerator d x over denominator begin display style open parentheses x plus 1 close parentheses squared end style end fraction I space equals space 3 space log open parentheses x plus 2 close parentheses space minus space log left parenthesis x plus 1 right parenthesis squared space minus space fraction numerator 1 over denominator open parentheses x plus 1 close parentheses end fraction space equals space log fraction numerator begin display style open parentheses x plus 2 close parentheses cubed end style over denominator begin display style open parentheses x plus 1 close parentheses squared end style end fraction space minus space fraction numerator 1 over denominator x plus 1 end fraction space plus C space end style
Answered by Thiyagarajan K | 20 Dec, 2018, 07:23: PM

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CBSE 12-science - Maths
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