Question

indefinite integral of 1/xln(x^3) dx

Answer 1

I have work so far but as usual it is probably wrong...

Answer 2

kind of....

Answer 3

here's a hint.. let \[u = \ln (x^3)\]
so \[ du = \frac 3xdx\]
agree?

Answer 4

Yeah.. so one gets integral 1/u*(3/xdx)

Answer 5

and then do you move the 3/x to the outside?

Answer 6

hmm wait.. im getting confused with these x and u's combined

Answer 7

\[du = \frac 3x dx\]
so \[\frac{du}{3} = \frac{dx}{x}\]
\[\int \frac{dx}{x \ln x^3} \implies \int \frac{du}{3u}\]
right?

Answer 8

Oh, okay... yeah

Answer 9

so take out 1/3 out of the integral \[\implies \frac 13\int \frac{du}{u}\]
now this is basic integration right?

Answer 10

right because integral u/du is the same as integral 1/u du which is log u

Answer 11

sub for u and multiply by 1/3?

Answer 12

right.

Answer 13

meant du/u* okay thanks

Answer 14

welcome