For each of the following integrals find an appropriate trigonometric substitution of the form $x = f(t)$ to simplify the integral.

1. $\displaystyle{ \int (4 x^2 - 6)^{3/2}\, dx }$
   $x =$
2. $\displaystyle{ \int \frac{x^2}{\sqrt{4 x^2 + 7}}\, dx }$
   $x =$
3. $\displaystyle{ \int x\sqrt{8 x^2 - 64 x + 123}\, dx }$
   $x =$
4. $\displaystyle{ \int \frac{x}{\sqrt{-74 - 5 x^2 + 40 x}}\, dx }$
   $x =$