If $\int \frac{1 - (\cot x)^{2021}}{\tan x + (\cot x)^{2022}} dx = \frac{1}{A} \log |(\sin x)^{2023} + (\cos x)^{2023}| + c$,then $A = . . . . . .$

If $\int (e^{2x} + 2e^{x} - e^{-x} - 1) e^{(e^{x} + e^{-x})} dx = g(x) e^{(e^{x} + e^{-x})} + c$,where $c$ is a constant of integration,then $g(0)$ is equal to

If $I_n = \int \frac{\sin nx}{\cos x} dx$,then $I_n =$

If $I_n = \int \cos^n x \, dx$, then $6 I_6 - 5 I_4 = $

If $\int {\frac{{dx}}{{{x^3}{{\left( {1 + {x^6}} \right)}^{2/3}}}} = xf\left( x \right){{\left( {1 + {x^6}} \right)}^{\frac{1}{3}}} + C} $ where $C$ is a constant of integration,then the function $f(x)$ is equal to

If $\int \frac{\sin ^8 x-\cos ^8 x}{1-2 \sin ^2 x \cos ^2 x} d x=A \sin 2 x+B$,then $A$ is equal to