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Integration of 1/(x+2)(x^2+6x+7)^1/2

Asked by Balbir 5th October 2017, 4:31 PM
Answered by Expert
Answer:
begin mathsize 16px style NOTE colon
The space question space you space sent space which space should space be space like space this space integral fraction numerator open parentheses straight x plus 2 close parentheses dx over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction space instead space of space integral fraction numerator dx over denominator open parentheses straight x plus 2 close parentheses square root of straight x squared plus 6 straight x plus 7 end root end fraction.
integral fraction numerator open parentheses straight x plus 2 close parentheses dx over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction
Put space straight x squared plus 6 straight x plus 7 space equals space straight t
rightwards double arrow open parentheses 2 straight x plus 6 close parentheses dx space equals space dt
1 half integral fraction numerator 2 straight x space plus space 4 over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction space dx
fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction integral fraction numerator begin display style 2 straight x space plus space 6 minus 2 end style over denominator begin display style square root of straight x squared plus 6 straight x plus 7 end root end style end fraction space dx
1 half integral fraction numerator 2 straight x space plus space 6 over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction dx minus 1 half integral fraction numerator begin display style 2 end style over denominator begin display style square root of straight x squared plus 6 straight x plus 7 end root end style end fraction space dx
1 half integral fraction numerator dt over denominator square root of straight t end fraction minus fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction integral fraction numerator begin display style 2 end style over denominator begin display style square root of straight x squared plus 6 straight x plus 7 end root end style end fraction space dx
For space the space first space term space you space can space solve space using space integration space directly.
For space the space second space term space use space completing space square space method space then space integrate.



end style
Answered by Expert 27th December 2017, 5:29 PM
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