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CBSE Class 12-science Answered

Integrate  x2 dx ( x2 + 6x -3)
Asked by haroonrashidgkp | 02 Nov, 2018, 09:46: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator straight x squared over denominator straight x squared plus 6 straight x minus 3 end fraction dx
straight I equals integral fraction numerator straight x squared plus 6 straight x minus 3 minus 6 straight x plus 3 over denominator straight x squared plus 6 straight x minus 3 end fraction dx
straight I equals integral open parentheses 1 plus fraction numerator 3 minus 6 straight x over denominator straight x squared plus 6 straight x minus 3 end fraction close parentheses dx
Consider comma
3 minus 6 straight x equals straight A fraction numerator straight d left parenthesis straight x squared plus 6 straight x minus 3 right parenthesis over denominator dx end fraction plus straight B
3 minus 6 straight x equals straight A left parenthesis 2 straight x plus 6 right parenthesis plus straight B
3 minus 6 straight x equals 2 Ax plus 6 straight A plus straight B
2 straight A equals negative 6
straight A equals negative 3
6 straight A plus straight B equals 3
6 cross times left parenthesis negative 3 right parenthesis plus straight B equals 3
straight B equals 21
straight I equals integral open parentheses 1 plus fraction numerator negative 3 left parenthesis 2 straight x plus 6 right parenthesis plus 21 over denominator straight x squared plus 6 straight x minus 3 end fraction close parentheses dx
straight I equals integral open parentheses 1 minus fraction numerator 3 left parenthesis 2 straight x plus 6 right parenthesis over denominator straight x squared plus 6 straight x minus 3 end fraction plus fraction numerator 21 over denominator straight x squared plus 6 straight x minus 3 end fraction close parentheses dx
Integrate space it space further.
end style
Answered by Sneha shidid | 06 Nov, 2018, 11:01: AM
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