Question

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?

Answer 1

no, because if you did u-sub with u=9-e^-x, du=e^-x dx

Answer 2

i got the second answer you posted.

Answer 3

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) +

Answer 4

u = 9 - e^-x => du = e^-x dx
=> Int ( du/ u ) = ln ( 9 - e^-x) + C

Answer 5

ohh gosh I was doing the wrong substitution instead of u=denominator i was doing u=numerator

Answer 6

thanks @ all