$\int \frac{1}{x} \log x \, dx$ is equal to

$\int x^2 (3)^{x^3 + 1} dx = $

$\int \frac{3^x}{\sqrt{9^x-1}} dx =$

$\int \sqrt{\frac{\cos x - \cos^3 x}{1 - \cos^3 x}} \, dx = $ . . . . . . $+ C$.

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$,then $g(x)$ is equal to

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