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CBSE Class 12-science Answered

Integration e2x ( 2x – 1/4x2) dx explain in great detail
Asked by haroonrashidgkp | 27 Oct, 2018, 05:41: 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 2 straight x minus 1 over denominator 4 straight x squared end fraction close parentheses dx Put space 2 straight x equals straight t rightwards double arrow straight x equals straight t over 2 rightwards double arrow dx equals dt over 2 straight I equals integral straight e to the power of straight t open parentheses fraction numerator straight t minus 1 over denominator 4 cross times open parentheses begin display style straight t over 2 end style close parentheses squared 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 straight t minus 1 over denominator straight t squared end fraction close parentheses dt straight I equals 1 half integral straight e to the power of straight t open parentheses 1 over straight t minus 1 over straight t squared close parentheses dt Consider space straight f left parenthesis straight t right parenthesis equals 1 over straight t space then space straight f apostrophe left parenthesis straight t right parenthesis equals fraction numerator negative 1 over denominator straight t squared end fraction straight I equals 1 half straight e to the power of straight t cross times 1 over straight t plus straight c straight I equals 1 half straight e to the power of 2 straight x end exponent cross times fraction numerator 1 over denominator 2 straight x end fraction plus straight c straight I equals fraction numerator straight e to the power of 2 straight x end exponent over denominator 4 straight x end fraction plus straight c end style
Answered by Sneha shidid | 29 Oct, 2018, 09:22: AM

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CBSE 12-science - Maths
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