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CBSE Class 12-science Answered

  Integration e2x ( 1 + sin 2x /1 + cos 2x) dx  explain in great detail
Asked by haroonrashidgkp | 28 Oct, 2018, 01:20: PM
answered-by-expert Expert Answer
begin mathsize 16px style straight I equals integral straight e to the power of 2 straight x end exponent open parentheses fraction numerator 1 plus sin 2 straight x over denominator 1 plus cos 2 straight x end fraction close parentheses dx Put space 2 straight x equals straight t straight x equals straight t over 2 dx equals dt over 2 straight I equals integral straight e to the power of straight t open parentheses fraction numerator 1 plus sint over denominator 1 plus cost end fraction close parentheses dt over 2 straight I equals 1 half integral straight e to the power of straight t open parentheses fraction numerator 1 plus sint over denominator 2 cos squared begin display style straight t over 2 end style end fraction close parentheses dt straight I equals 1 half integral straight e to the power of straight t open parentheses 1 half sec squared straight t over 2 plus fraction numerator 2 sin straight t over 2 space cos straight t over 2 over denominator 2 cos squared straight t over 2 end fraction close parentheses dt straight I equals 1 half integral straight e to the power of straight t open parentheses 1 half sec squared straight t over 2 plus tan straight t over 2 close parentheses dt Consider comma space straight f left parenthesis straight t right parenthesis equals tan straight t over 2 space then space straight f apostrophe left parenthesis straight t right parenthesis equals 1 half sec squared straight t over 2 straight I equals 1 half straight e to the power of straight t tan straight t over 2 plus straight c straight I equals 1 half straight e to the power of 2 straight x end exponent tanx plus straight c end style
Answered by Sneha shidid | 29 Oct, 2018, 09:31: AM

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