If $\int \frac{1}{1-\cot x} d x=A x+B \log |\sin x-\cos x|+c$ then $A+B=\ldots \ldots$

$$\int \frac{d x}{(\sin x+\cos x)(2 \cos x+\sin x)}=$$

If $$\int \frac{\cos x-\sin x}{8-\sin 2 x} d x=\frac{1}{p} \log \left[\frac{3+\sin x+\cos x}{3-\sin x-\cos x}\right]+c,$$ then $p=$ .............

$$\begin{aligned} & \text { If } \int \tan (x-\alpha) \tan (x+\alpha) \cdot \tan 2 x d x \\ & =p \log |\sec 2 x|+q \log |\sec (x+\alpha)| \\ & +r \log |\sec (x-\alpha)|+c \text { then } p+q+r=\ldots \ldots \ldots \end{aligned}$$