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Integrals

Question
CBSEENMA12036052
Wired Faculty App

The integral integral open parentheses 1 plus straight x space minus 1 over straight x close parentheses straight e to the power of straight x plus 1 over straight x end exponent dx is equal to 

  • left parenthesis straight x minus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • xe to the power of straight x plus 1 over straight x end exponent plus straight C
  • left parenthesis straight x plus 1 right parenthesis straight e to the power of straight x plus 1 over straight x space plus straight C end exponent
  • negative xe to the power of straight x plus 1 over straight x end exponent plus straight C

Solution

B.

xe to the power of straight x plus 1 over straight x end exponent plus straight C integral open parentheses 1 plus straight x minus 1 over straight x close parentheses straight e to the power of straight x plus 1 over straight x dx end exponent space equals space integral straight e to the power of straight x plus 1 half end exponent dx space plus integral straight x open parentheses 1 minus 1 over straight x squared close parentheses straight e to the power of straight x space plus 1 over straight x end exponent dx equals space integral straight e to the power of straight x plus 1 over straight x end exponent dx space plus xe to the power of straight x plus 1 over straight x end exponent minus integral straight e to the power of straight x plus 1 over straight x end exponent dx space equals space straight e to the power of straight x plus 1 over straight x dx end exponent space plus xe to the power of straight x plus 1 over straight x end exponent minus integral straight e to the power of straight x plus 1 over straight x end exponent dx open square brackets because space integral straight e to the power of straight x plus 1 over straight x end exponent dx space plus xe to the power of straight x plus 1 over straight x end exponent minus integral straight e to the power of straight x plus 1 over straight x end exponent dx space equals space straight e to the power of straight x plus 1 over straight x end exponent close square brackets equals space straight e to the power of straight x plus 1 over straight x end exponent dx space plus xe to the power of straight x plus 1 over straight x end exponent minus integral ex to the power of straight x plus 1 over straight x end exponent dx space equals space xe to the power of straight x plus 1 over straight x end exponent space plus straight C

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