$$\int \sec ^{-1} x d x=$$

If $$\int \frac{\sqrt{x}}{x(x+1)} d x=k \tan ^{-1} m+c$$, (where c is constant of integration), then

$$\int \frac{d x}{\cos x \sqrt{\cos 2 x}}=$$

If $$\int \frac{\sin x}{\sin (x-\alpha)} d x=A x+B \log \sin (x-\alpha)+c$$, then the value of A and B are respectively (where $$\mathrm{c}$$ is a constant of integration)