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CBSE Class 12-science Answered

Integration x/(1 + x)1/2 dx explain in great detail
Asked by haroonrashidgkp | 03 Oct, 2018, 08:57: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator straight x over denominator square root of 1 plus straight x end root end fraction dx
1 plus straight x equals straight t
straight x equals straight t minus 1
dx equals dt
straight I equals integral fraction numerator straight t minus 1 over denominator square root of straight t end fraction dt
straight I equals integral open parentheses straight t to the power of 1 half end exponent minus straight t to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent close parentheses dt
straight I equals fraction numerator straight t to the power of begin display style 3 over 2 end style end exponent over denominator begin display style 3 over 2 end style end fraction minus fraction numerator straight t to the power of begin display style 1 half end style end exponent over denominator begin display style 1 half end style end fraction plus straight c
straight I equals 2 open parentheses open parentheses 1 plus straight x close parentheses to the power of begin display style 3 over 2 end style end exponent over 3 minus open parentheses 1 plus straight x close parentheses to the power of 1 half end exponent close parentheses plus straight c end style
Answered by Sneha shidid | 04 Oct, 2018, 04:14: PM
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