integral subscript 2 superscript 3 fraction numerator x minus 1 over denominator open parentheses x plus 1 close parentheses cubed end fraction e to the power of x d x

Asked by Eng.surinder.singh | 27th Jan, 2019, 07:45: PM

Expert Answer:

begin mathsize 16px style straight I equals integral subscript 2 superscript 3 space fraction numerator straight x minus 1 over denominator open parentheses straight x plus 1 close parentheses cubed end fraction straight e to the power of straight x dx
straight I equals integral subscript 2 superscript 3 space fraction numerator straight x plus 1 minus 2 over denominator open parentheses straight x plus 1 close parentheses cubed end fraction straight e to the power of straight x dx
straight I equals integral subscript 2 superscript 3 space open parentheses 1 over open parentheses straight x plus 1 close parentheses squared minus 2 over open parentheses straight x plus 1 close parentheses cubed close parentheses dx
Consider comma space straight f left parenthesis straight x right parenthesis equals 1 over open parentheses straight x plus 1 close parentheses squared space then space straight f apostrophe left parenthesis straight x right parenthesis equals negative 2 over open parentheses straight x plus 1 close parentheses cubed
straight I equals open square brackets straight e to the power of straight x cross times 1 over open parentheses straight x plus 1 close parentheses squared close square brackets subscript 2 superscript 3
straight I equals straight e cubed cross times 1 over open parentheses 3 plus 1 close parentheses squared minus straight e squared cross times 1 over open parentheses 2 plus 1 close parentheses squared
straight I equals straight e cubed over 16 minus straight e squared over 9
straight I equals straight e squared open parentheses straight e over 16 minus 1 over 9 close parentheses equals straight e squared over 144 open parentheses 9 straight e minus 16 close parentheses
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Answered by Sneha shidid | 28th Jan, 2019, 10:14: AM