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Home / Doubts and Solutions/JEE/Mathematics

Integration of dx÷x(1-x^3)^1÷2

Asked by khedejalaj7 28th August 2018, 7:21 PM
Answered by Expert
Answer:
begin mathsize 18px style straight I equals integral fraction numerator 1 over denominator straight x square root of 1 minus straight x cubed end root end fraction dx put space 1 minus straight x cubed equals straight u straight I equals 1 third integral fraction numerator begin display style 1 end style over denominator begin display style open parentheses straight u minus 1 close parentheses square root of straight u end style end fraction du sub space straight v equals square root of straight u straight I equals 2 integral fraction numerator 1 over denominator straight v squared minus 1 end fraction dv straight I equals space integral fraction numerator begin display style 2 end style over denominator begin display style open parentheses straight v minus 1 close parentheses open parentheses straight v plus 1 close parentheses end style end fraction dv equals integral fraction numerator begin display style straight v plus 1 minus open parentheses straight v minus 1 close parentheses end style over denominator begin display style open parentheses straight v minus 1 close parentheses open parentheses straight v plus 1 close parentheses end style end fraction dv straight I space equals integral fraction numerator 1 over denominator open parentheses straight v minus 1 close parentheses end fraction dv minus integral fraction numerator begin display style 1 end style over denominator begin display style open parentheses straight v plus 1 close parentheses end style end fraction dv.... integrate space and space re space substitute end style
Answered by Expert 29th August 2018, 11:38 AM
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