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CBSE Class 12-science Answered

Integration e2x sin x dx explain in great detail
Asked by haroonrashidgkp | 23 Oct, 2018, 02:16: 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 sinxdx straight I equals integral sinxe to the power of 2 straight x end exponent dx straight I equals sinx integral straight e to the power of 2 straight x end exponent dx minus integral open parentheses straight d over dx sinx integral straight e to the power of 2 straight x end exponent dx close parentheses dx straight I equals straight e to the power of 2 straight x end exponent over 2 sinx minus integral cosx straight e to the power of 2 straight x end exponent over 2 dx straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half integral cosxe to the power of 2 straight x end exponent dx straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half open square brackets cosx integral straight e to the power of 2 straight x end exponent dx minus integral open parentheses straight d over dx cosx integral straight e to the power of 2 straight x end exponent dx close parentheses dx close square brackets straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half open square brackets straight e to the power of 2 straight x end exponent over 2 cosx minus integral open parentheses negative sinx straight e to the power of 2 straight x end exponent over 2 dx close parentheses dx close square brackets straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half open square brackets straight e to the power of 2 straight x end exponent over 2 cosx plus 1 half integral open parentheses sinxe to the power of 2 straight x end exponent dx close parentheses dx close square brackets straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half straight e to the power of 2 straight x end exponent over 2 cosx minus 1 fourth straight I straight I plus 1 fourth straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half straight e to the power of 2 straight x end exponent over 2 cosx plus straight c 5 over 4 straight I equals fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus 1 half straight e to the power of 2 straight x end exponent over 2 cosx plus straight c straight I equals 4 over 5 open parentheses fraction numerator straight e to the power of 2 straight x end exponent sinx over denominator 2 end fraction minus straight e to the power of 2 straight x end exponent over 4 cosx close parentheses plus straight c end style
Answered by Sneha shidid | 23 Oct, 2018, 05:26: PM

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