Answer
$\dfrac{1}{3}\tan(3x)(\sec^23x+2)+C$
Work Step by Step
Use the Reduction Formula:
$\int\sec^naxdx=\frac{\sec^{n-2}ax\tan ax}{a(n-1)}+\dfrac{n-2}{n-1}\int\sec^{n-2}(a\space x)dx$
Let $I=\int3\sec^43xdx\\=3[\dfrac{\sec^23 x\tan 3 x}{3\times3}+\dfrac{2}{3}\int\sec^23xdx] \\\dfrac{\sec^23 x\tan 3 x}{3}+2\int\sec^23\space xdx\\=\dfrac{\sec^23 x\tan 3 x}{3}+2(\dfrac{\sec^03x\tan (3x) }{3}+\dfrac{0}{1}\int\sec^03(x)dx) \\=\dfrac{1}{3}\tan(3x)(\sec^23x+2)+C$
