$\int \frac{1}{x} \sec^2(\log x) \, dx = $

The value of $\int \frac{x^{2} d x}{\sqrt{x^{6}+a^{6}}}$ is equal to

The value of $\int \frac{d x}{x^2(x^4+1)^{\frac{3}{4}}}$ is

If $\int \frac{\cos x-\sin x}{\sqrt{8-\sin 2 x}} \,d x=\operatorname{a} \sin^{-1}\left(\frac{\sin x+\cos x}{b}\right)+c$,where $c$ is a constant of integration,then the ordered pair $(a, b)$ is equal to

$\int \frac{\cos^3 x + \cos^5 x}{\sin^2 x + \sin^4 x} \, dx$

If $\int \frac{\sin x}{\cos x(1+\cos x)} d x=f(x)+c$, then $f(x)$ is equal to