Question

integrate

Answer 1

\[\huge \int\limits_{}^{} \frac {9}{xln(3x)} dx\]

Answer 2

did you try the substution

u = ln 3x ??

Answer 3

du= ...

Answer 4

\[du = \frac{ 1 }{ x } dx\]

Answer 5

yes!
so your new integral becomes
\(\Large \int \dfrac{9}{u}du\)
can you integrate this ? :)

Answer 6

do i move the u to the numerator or something ?

Answer 7

use this standard integral
\(\Large \int \dfrac{1}{x}dx = \ln |x| +c\)

Answer 8

so \[\int\limits_{}^{} \frac{9}{u} = \ln|9u|+c = \ln|9(\ln(3x))| +C\]
correct?

Answer 9

nopes,
9 is constant, it can be thrown out of integral

Answer 10

\(\Large 9\int (1/u)du = 9 \ln |u|+c = 9 \ln |\ln(3x) |+c\)
thats it!

Answer 11

ooh okay Thanks a lot
i got a question
is it possible to integrate by part that problem ? cuz that's what i did at first

Answer 12

not actually....i mean it could be possible but very difficult....and not even worth thinking about :P