Let $f(x)=(6 \sin x+3 \cos x) \tan ^{-1} x$

Step 1 ：Let's consider the function \(f(x)=(6 \sin x+3 \cos x) \tan ^{-1} x\).

Step 2 ：We will plot this function to observe its behavior.

Step 3 ：The function is plotted over the range of x from -10 to 10.

Step 4 ：The plot shows that the function has a complex behavior, with multiple peaks and valleys.

Step 5 ：The function seems to be oscillating around the x-axis, with the amplitude of the oscillations decreasing as x increases.

Step 6 ：The function also seems to be symmetric around the y-axis.

Step 7 ：\(\boxed{\text{The plot of the function } f(x) = (6\sin(x) + 3\cos(x))\arctan(x) \text{ is as shown above.}}\)