anonymous
  • anonymous
int e^-x/(9-e^-x) dx shouldn't be the -ln(9-e^-x) ? whereas both text & maple shows ln(9-e^-x), why?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
no, because if you did u-sub with u=9-e^-x, du=e^-x dx
anonymous
  • anonymous
i got the second answer you posted.
anonymous
  • anonymous
int e^-x/(9-e^-x) dx =int 1/(9-e^-x) d(9-e^-x) <---- note that d(-e^-x) = -(-e^-x) dx=e^-x dx =ln (9-e^-x) +

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anonymous
  • anonymous
u = 9 - e^-x => du = e^-x dx => Int ( du/ u ) = ln ( 9 - e^-x) + C
anonymous
  • anonymous
ohh gosh I was doing the wrong substitution instead of u=denominator i was doing u=numerator
anonymous
  • anonymous
thanks @ all

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