Question

Age at BBM 2019 Question Group 'A Brief answer questions; 1. Integrate the following: S(ax? + 2bx + c)3/2(2xa + 2b) dx 2.

Answer 1

If the integral is

$\displaystyle \int (ax^2+2bx+c)^{3/2}(2ax+2b)\,\mathrm dx$

substitute $u = ax^2+2bx+c$ and $\mathrm du=(2ax+2b)\,\mathrm dx$. Then you end up with

$\displaystyle \int u^{3/2}\,\mathrm du = \frac25u^{5/2} + C$

which in terms of x is

$\boxed{\dfrac25(ax^2+2bx+c)^{5/2} + C}$