Question 98
Let the function $f:\left[\pi ; \frac{3 \pi}{2}\right] \rightarrow \mathbb{R}$, $f(x)=\frac{3 \cos (2 x)-4 \sin (2 x)+\cos x-3 \sin x}{(\sin x+3 \cos x)^{2022}}$. Determine the antiderivative $F:\left[\pi ; \frac{3 \pi}{2}\right] \rightarrow \mathbb{R}$ of the function $f$ for which $F\left(\frac{3 \pi}{2}\right)=\frac{1}{2021}$.