Integrating this indefinite integral $$\int\dfrac{t-2}{t+2-3\sqrt{2t-4}}dt$$
I'm not sure whether to use substitution or what.

Hint
With the change of variable $x=\sqrt{2t-4}$ the integral becomes
$$\int\frac{x^3}{x^2-6x+8}dx$$
then use the partial fraction decomposition (notice that $x^2-6x+8=(x-2)(x-4)$).
