Question

Can someone please help me integrate

Answer 1

\[\int\limits_{?}^{?}\frac{ e ^{3x}+3}{ e ^{3x}+9x } dx\]

Answer 2

have you thought of using the substitution ?

Answer 3

would \[\frac{ f'(x) }{ f(x) } = \ln | f(x)|+c \] come in handy?

Answer 4

yes! thats what will help

Answer 5

do you see the derivative of denominator in the numerator?

Answer 6

am i allowed to introduce 3 to the numerator?

Answer 7

since it is a constant, yes.

Answer 8

if you're a beginner in integration,
i suggest you use the substitution method and not that formula

Answer 9

make u=e^3x?

Answer 10

wouldn't
\(u = e^{3x} + 9 \)
be a better one?

Answer 11

\(\Large ** u = e^{3x}+9x\)

Answer 12

ah yes much better

Answer 13

its much easier to do

Answer 14

thanks so much!

Answer 15

\[\frac{ 1 }{ 3 } \ln |e ^{3x}+9x| \]

Answer 16

ah i wish i never let that formula distract me :(

Answer 17

that formula is useful once you get comfortable with it, until then, substitution all the way! :)

Answer 18

could u please show me the formula way if you can?