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.

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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{\frac25(ax^2+2bx+c)^(5/2) + C}`