Question

using the substitution rule for integration, integrate (sec^2x)(tan3x)dx.

Answer 1

put
\[
u= \tan (3 x)\\
du = 3 \sec^2( 3x) dx
\]
Are you sure that your numerator is
\[ \sec^2(x)
\]

Answer 2

yes its all multiplied together and that's what I got for du too but I don't understand how to get dx by itself

Answer 3

I think it should be
\[ \sec^2(3x)
\]
otherwise, you cannot od this problem.