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CBSE Class 12-science Answered

Integration dx/(x1/2 + x1/3) explain in great detail
Asked by haroonrashidgkp | 05 Oct, 2018, 12:14: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral fraction numerator 1 over denominator straight x to the power of begin display style 1 half end style end exponent plus straight x to the power of begin display style 1 third end style end exponent end fraction dx straight x equals straight t to the power of 6 rightwards double arrow straight t equals straight x to the power of 1 over 6 end exponent dx equals 6 straight t to the power of 5 dt straight I equals integral fraction numerator 6 straight t to the power of 5 dt over denominator open parentheses straight t to the power of 6 close parentheses to the power of begin display style 1 half end style end exponent plus open parentheses straight t to the power of 6 close parentheses to the power of begin display style 1 third end style end exponent end fraction straight I equals integral fraction numerator 6 straight t to the power of 5 dt over denominator straight t cubed plus straight t squared end fraction straight I equals integral fraction numerator 6 straight t to the power of 5 dt over denominator straight t squared open parentheses straight t plus 1 close parentheses end fraction straight I equals integral fraction numerator 6 straight t cubed over denominator straight t plus 1 end fraction dt straight I equals 6 integral fraction numerator straight t cubed plus 1 minus 1 over denominator straight t plus 1 end fraction dt straight I equals 6 integral open parentheses fraction numerator open parentheses straight t plus 1 close parentheses open parentheses straight t squared minus straight t plus 1 close parentheses over denominator straight t plus 1 end fraction minus fraction numerator 1 over denominator straight t plus 1 end fraction close parentheses dt straight I equals 6 integral open parentheses straight t squared minus straight t plus 1 minus fraction numerator 1 over denominator straight t plus 1 end fraction close parentheses dt straight I equals 6 open parentheses straight t cubed over 3 minus straight t squared over 2 plus straight t minus log open vertical bar straight t plus 1 close vertical bar close parentheses plus straight c straight I equals 6 open parentheses straight x to the power of 1 half end exponent over 3 minus straight x to the power of 1 third end exponent over 2 plus straight x to the power of 1 over 6 end exponent minus log open vertical bar straight x to the power of 1 over 6 end exponent plus 1 close vertical bar close parentheses plus straight c space space space space space space space space space space space space space space space space space space space space space because space space straight t equals straight x to the power of 1 over 6 end exponent end style
Answered by Sneha shidid | 06 Oct, 2018, 07:19: PM

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