Question

Find an anti derivative (or integral) of the following functions by the method of inspection: sin2x - 4e3x

Answer 1

The anti derivative of (sin2x - 4e3x) is the function of x whose derivative is (sin2x - 4e3x) .
It is known that,
$\frac{d}{dX}\bigg(-\frac{1}{2}cos2x-\frac{4}{3}e^{3x}\bigg) = \sin2x-4e^{3x}$

Therefore, the anti derivative of (sin2x - 4e3x) is$\bigg(-\frac{1}{2}cos2x-\frac{4}{3}e^{3x}\bigg)$ .