$$\int \mathrm{e}^x\left(1-\cot x+\cot ^2 x\right) \mathrm{d} x=$$

If $$\int \sqrt{\frac{x-7}{x-9}} d x=A \sqrt{x^2-16 x+63}+\log \left|(x-8)+\sqrt{x^2-16 x+63}\right|+c,$$

(where $$\mathrm{c}$$ is a constant of integration) then $$\mathrm{A}$$ is

$$\int \frac{1}{7-6 x-x^2} d x=$$

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