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CBSE Class 12-science Answered

Integration x5/(1+ x3)1/2 dx explain in great detail
Asked by haroonrashidgkp | 03 Oct, 2018, 08:56: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator straight x to the power of 5 over denominator square root of open parentheses 1 plus straight x cubed close parentheses end root end fraction dx straight I equals integral fraction numerator straight x squared straight x cubed dx over denominator square root of 1 plus straight x cubed end root end fraction 1 plus straight x cubed equals straight t rightwards double arrow straight x cubed equals straight t minus 1 3 straight x squared dx equals dt straight x squared dx equals dt over 3 straight I equals integral fraction numerator left parenthesis straight t minus 1 right parenthesis begin display style dt over 3 end style over denominator square root of straight t end fraction straight I equals 1 third integral open parentheses square root of straight t minus straight t to the power of fraction numerator negative 1 over denominator 2 end fraction end exponent close parentheses dt straight I equals 1 third open parentheses 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 close parentheses plus straight c straight I equals 2 over 3 open parentheses open parentheses 1 plus straight x cubed close parentheses to the power of begin display style 3 over 2 end style end exponent over 3 minus square root of 1 plus straight x cubed end root close parentheses plus straight c end style
Answered by Sneha shidid | 04 Oct, 2018, 10:09: AM

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