Question

integrate f(q)= (q -4)² - 12

Answer 1

why not expand the brackets first then differentiate?

Answer 2

expand the brackets first then integrate

Answer 3

(a-b)^2 = a^2-2ab + b^2

Answer 4

Nope no need to expand.
\[\int\limits [(q-4)^2-12] dq\]
\[\frac{1}{3}(q-4)^3-12q+C\]

Answer 5

Anti-differentiate.

Answer 6

Anti-differentiating is one of the fastest ways to integration unless there comes a time when anti-differentiation starts to not work, then you go to other methods (eg. Using
partial fractions" to integrate).