Answer
\[ 2(3u-5)^{1/2}+C \]
Work Step by Step
In order to integrate this function, we have to use an «z» substitution.
But first let's rewrite the function:
\[ \int 3(3u-5)^{-1/2} \]
Choose a z, derivate it:
$ z = 3u-5$
$ dz = 3du$
Then substitute:
\[ =\int z^{-1/2}dz \]
Then integrate
\[ =2z^{1/2} + C \]
And undo the substitution:
\[ =\boxed{2(3u-5)^{1/2}+C} \]
