Question

Find the anti-derivative (or integral) of the following by the method of inspection.
$(ax+b{)}^2.$

Answer 1

$\int (ax+b{)}^{2}dx=\frac{1}{3a}(ax+b{)}^3+C(\begin{array}{c}\because \frac{d}{dx}\left(\frac{1}{3a}\right(ax+b{)}^3=\frac{1}{3a}.3(ax+b{)}^{2}a)\\ =(ax+b{)}^2\end{array})$