Find begin mathsize 20px style integral e to the power of x open square brackets fraction numerator x squared minus x plus 1 over denominator open parentheses x squared plus 1 close parentheses to the power of begin display style bevelled 3 over 2 end style end exponent end fraction close square brackets end style (please I need the answer today before 9pm)

Asked by sunil2791 | 2nd Jul, 2017, 11:46: AM

Expert Answer:

begin mathsize 16px style straight I equals integral straight e to the power of straight x open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses dx
In space this space case space we space have space to space separate space the space terms space like space one space should space be space straight f left parenthesis straight x right parenthesis
and space otehr space term space should space be space straight f apostrophe left parenthesis straight x right parenthesis
open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses equals fraction numerator straight x squared plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction minus straight x over open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent
open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses equals 1 over open parentheses straight x squared plus 1 close parentheses to the power of 1 divided by 2 end exponent minus straight x over open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent
If space you space see space it space clearly space first space term space is space straight f left parenthesis straight x right parenthesis space and space its space derivative space is space second space term
straight I equals straight e to the power of straight x space 1 over open parentheses straight x squared plus 1 close parentheses to the power of 1 divided by 2 end exponent plus straight c end stylebegin mathsize 16px style straight I equals integral straight e to the power of straight x open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses dx
In space this space case space we space have space to space separate space the space terms space like space one space should space be space straight f left parenthesis straight x right parenthesis
and space otehr space term space should space be space straight f apostrophe left parenthesis straight x right parenthesis
open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses equals fraction numerator straight x squared plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction minus straight x over open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent
open parentheses fraction numerator straight x squared minus straight x plus 1 over denominator open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent end fraction close parentheses equals 1 over open parentheses straight x squared plus 1 close parentheses to the power of 1 divided by 2 end exponent minus straight x over open parentheses straight x squared plus 1 close parentheses to the power of 3 divided by 2 end exponent
If space you space see space it space clearly space first space term space is space straight f left parenthesis straight x right parenthesis space and space its space derivative space is space second space term
straight I equals straight e to the power of straight x space 1 over open parentheses straight x squared plus 1 close parentheses to the power of 1 divided by 2 end exponent plus straight c end style

Answered by Sneha shidid | 2nd Jul, 2017, 06:56: PM