$6 \cdot 79$ Find the minimum value of $f(x)=\frac{9 x^{2} \sin ^{2} x+4}{x \sin x}(0<x<\pi)$.
[Solution] Let $t=x \sin x$. By $00$. Then
$$
f(x)=\frac{9 t^{2}+4}{t} \geqslant \frac{2 \times 3 t \times 2}{t}=12 \text {. }
$$

Therefore, the minimum value of $f(x)$ is 12.