Answer
$\ln |\csc (3x)+\cot (3x) | +C$
Work Step by Step
Our aim is to solve the integral $ \int 3 \csc (3x) \ dx$
Let us consider that $a =3 x$ and $\dfrac{da}{dx}=3 \implies dx=\dfrac{1}{3} \ da$
Now, $ \int 3 \csc (3x) \ dx = \int 3 \csc a \times (\dfrac{1}{3}) \ da$
or, $= \int \csc a \ da$
or, $=\ln |\csc a+\cot a | +C$
or, $= \ln |\csc (3x)+\cot (3x) | +C$
