# Q5  Find an anti derivative (or integral) of the following functions by the method of inspection. $\sin 2x - 4 e ^{3x}$

GIven $\sin 2x - 4 e ^{3x}$;
So, the anti derivative of $\sin 2x - 4 e ^{3x}$ is a function of x whose derivative is $\sin 2x - 4 e ^{3x}$.
$\frac{d}{dx} (-\frac{1}{2}\cos 2x - \frac{4}{3}e^{3x}) = \sin 2x -4e^{3x}$
Therefore, we have the anti derivative of $\sin 2x - 4 e ^{3x}$ is  $\left ( -\frac{1}{2}\cos 2x - \frac{4}{3}e^{3x} \right )$.