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CBSE Class 12-science Answered

Find the integral of x+2/sqrt ((x-2)(x-3))  
Asked by lekhakarthikeyan | 27 Dec, 2018, 12:31: AM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator straight x plus 2 over denominator square root of open parentheses straight x minus 2 close parentheses open parentheses straight x minus 3 close parentheses end root end fraction dx straight I equals integral fraction numerator straight x plus 2 over denominator square root of straight x squared minus 5 straight x plus 6 end root end fraction dx Consider comma straight x plus 2 equals straight A straight d over dx straight x squared minus 5 straight x plus 6 plus straight B straight x plus 2 equals straight A left parenthesis 2 straight x minus 5 right parenthesis plus straight B...... left parenthesis straight i right parenthesis straight x plus 2 equals 2 Ax minus 5 straight A plus straight B 2 straight A equals 1 rightwards double arrow straight A equals 1 half minus 5 straight A plus straight B equals 2 minus 5 cross times 1 half plus straight B equals 2 rightwards double arrow straight B equals 9 over 2 Put space it space in space left parenthesis straight i right parenthesis straight I equals integral fraction numerator 1 half left parenthesis 2 straight x minus 5 right parenthesis plus 9 over 2 over denominator square root of straight x squared minus 5 straight x plus 6 end root end fraction dx straight I equals integral open parentheses fraction numerator 1 half left parenthesis 2 straight x minus 5 right parenthesis over denominator square root of straight x squared minus 5 straight x plus 6 end root end fraction plus 9 over 2 fraction numerator 1 over denominator square root of straight x squared minus 5 straight x plus 6 end root end fraction close parentheses dx Solve space it space further. end style
Answered by Sneha shidid | 27 Dec, 2018, 12:25: PM

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