Integrate the function $\sec ^{2}(7-4 x)$.

$\int \frac{\sqrt{\tan x}}{\sin x \cdot \cos x} \,d x=$

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

If $\int(7x-2)\sqrt{3x+2} \, dx = A(3x+2)^{\frac{5}{2}} + B(3x+2)^{\frac{3}{2}} + c$ (where $c$ is a constant of integration),then the values of $A$ and $B$ are respectively:

Integrate the function $x \sqrt{1+2 x^{2}}$.

The integral $\int {\frac{{dx}}{{{{(x + 1)}^{\frac{3}{4}}}{{(x - 2)}^{\frac{5}{4}}}}}} $ is equal to