Please solve the following

Asked by Balbir | 6th Oct, 2017, 11:37: AM

Expert Answer:

begin mathsize 16px style 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
Put space log space open parentheses straight x plus 2 close parentheses equals straight t space rightwards double arrow fraction numerator 1 over denominator straight x plus 2 end fraction dx equals dt
rightwards double arrow straight x plus 2 equals straight e to the power of straight t
rightwards double arrow straight x equals straight e to the power of straight t space minus space 2
integral fraction numerator begin display style fraction numerator dx over denominator straight x plus 2 end fraction end style over denominator square root of straight x squared plus 6 straight x plus 7 end root end fraction
integral fraction numerator dt over denominator square root of begin display style open parentheses straight e to the power of straight t space bold minus bold space 2 close parentheses squared plus 6 open parentheses straight e to the power of straight t space minus space 2 close parentheses plus 7 end style end root end fraction
integral fraction numerator dt over denominator square root of straight e to the power of 2 straight t end exponent minus 4 straight e to the power of straight t plus 4 plus 6 straight e to the power of straight t minus 12 plus 7 end root end fraction
integral fraction numerator dt over denominator square root of straight e to the power of 2 straight t end exponent plus 2 straight e to the power of straight t minus 1 end root end fraction
integral fraction numerator begin display style dt end style over denominator begin display style square root of straight e to the power of 2 straight t end exponent plus 2 straight e to the power of straight t plus 1 minus 2 end root end style end fraction
integral fraction numerator dt over denominator square root of begin display style open parentheses straight e to the power of straight t plus 1 close parentheses squared minus open parentheses square root of 2 close parentheses squared end style end root end fraction
Use space formula space for space the space integration space and space solve space it space further.


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Answered by Sneha shidid | 22nd Dec, 2017, 09:39: AM