DO2

Evaluate $(D^2+5D-1) (\tan 2x - 3/x),\,\,\,D=\frac{d}{dx}\,$

$= D^2(\tan 2x) - D^2(-3/x) + 5D(\tan 2x) + 5D(-3/x) - \tan 2x + 3/x\,$

Use this Maple code to evaluate this:

simplify(diff(tan(2*x),x,x) - diff(-3/x,x,x) + 5*diff(-3/x,x) - tan(2*x) + 3/x);

The answer is:

$7 \tan(2x) + 8 \tan(2x)^3 + 6x^{-3} + 15x^{-2} + 3x^{-1}\,$