Prove
Question:

$\sin 2 x-4 e^{3 x}$

Solution:

The anti derivative of $\left(\sin 2 x-4 e^{3 x}\right)$ is the function of $x$ whose derivative is $\left(\sin 2 x-4 e^{3 x}\right)$.

It is known that,

$\frac{d}{d x}\left(-\frac{1}{2} \cos 2 x-\frac{4}{3} e^{3 x}\right)=\sin 2 x-4 e^{3 x}$

Therefore, the anti derivative of $\left(\sin 2 x-4 e^{3 x}\right)$ is $\left(-\frac{1}{2} \cos 2 x-\frac{4}{3} e^{3 x}\right)$.