$\int(x-a)(x^{n-1}+x^{n-2}a+\ldots+a^{n-1})dx=$ (where $C$ is a constant of integration)

$\int \frac{\sin x + \cos x}{\sqrt{1 + \sin 2x}} \, dx = $

If $f(x)=x$ and $g(x)=\sin x$,then $\int f(g(x)) \, dx$ is equal to

Find the following integral: $\int \sec x(\sec x+\tan x) \, dx$

If $f\left( \frac{3x - 4}{3x + 4} \right) = x + 2, x \ne -\frac{4}{3}$,and $\int f(x) dx = A \log |1 - x| + Bx + C$,then the ordered pair $(A, B)$ is equal to: (where $C$ is a constant of integration)

$\int \sec^2 x \csc^2 x \, dx = $ . . . . . . $+ C$