Find an anti-derivative (or integral) of the following functions by the method of inspection.

sin 2x – 4 e^3x

We know that

Therefore, the anti-derivative of sin2x is …(1)

Also,

Therefore, the anti-derivative of is …(2)

From (1) and (2), we get,

= sin 2x – 4 e^3x

Therefore, the anti-derivative of sin 2x – 4 e^3x is .