Question

the integral of e^6x/e^6x+9

Answer 1

put z=denominator of d integrand

Answer 2

then dz=6 e^(6x) dx

Answer 3

does it make sense?

Answer 4

yeah but then what?

Answer 5

I think I read it wrong not sure you can do long division.. but you can use u substitution twice

Answer 6

\[\int\limits_{?}^{?}\frac{ e^{6x}}{ e^{6x} +9}\]

Answer 7

first let u = 6x... then do substitution again and use v=e^u+9

Answer 8

\[\int\limits_{}^{} \frac{ e ^{6x} }{ e ^{6x}+9 }\] Let: \[u=e ^{6x}+9\] Therefore: \[du = 6e ^{6x} dx\] Just divide the 6 out and put it outside the integral. The integral is now: \[\frac{ 1 }{ 6 } \int\limits_{}^{} \frac{ 1 }{ u } du = \frac{ 1 }{ 6 }\ln(u) + c\] Simply replace u with the function we originally substituted out: \[=\frac{ 1 }{ 6 }\ln(e ^{6x}+9)+c\]

Answer 9

nj that was perfect. thanks for the help!

Answer 10

Not a problem :D

Answer 11

NJ could you help me with another please?

Answer 12

Certainly :) Just post it for me to see!