int x^5 ln(3x) dx Find the indefinite integral

Given to solve
int x^5 ln(3x) dx
let u= ln(3x) ,u' = (ln(3x))'
=(1/(3x))*(3) = 1/x
so u' = 1/x
and v'= x^5 => v= x^6/6
by applying the integration by parts we get,
int uv' dx= uv - int u'v dx
so,
int x^5 ln(3x) dx
=(ln(3x))(x^6/6) - int (1/x)(x^6 /6) dx
= (ln(3x))(x^6/6) - (1/6) int (1/x)(x^6 ) dx
= (ln(3x))(x^6/6) - (1/6) int (x^5 ) dx
= (ln(3x))(x^6/6) - (1/6) int (x^5 ) dx
= (ln(3x))(x^6/6) - (1/6) [x^6 /6]+c
= ln(3x)x^6/6 - 1/36 x^6 +c
= x^6/6(ln(3x)-x^6/6) + c