$$\int \frac{1}{\sin (x-a) \sin x} d x=$$

If $$f(x)=\sqrt{\tan x}$$ and $$g(x)=\sin x \cdot \cos x$$ then $$\int \frac{f(x)}{g(x)} \mathrm{d} x$$ is equal to (where $$C$$ is a constant of integration)

$$\int \frac{3 x-2}{(x+1)(x-2)^2} \mathrm{~d} x=$$

(where $$C$$ is a constant of integration)

$$\int \frac{\sin \frac{5 x}{2}}{\sin \frac{x}{2}} d x=$$

(where $$C$$ is a constant of integration.)