Edexcel A-Level Mathematics A2 P4.6.3 Simple Cases of Integration Questions

Practise algebraic integration of rational functions after division or partial fractions, giving exact values with logs simplified.

Exam points

decompose rational functions into partial fractions before integrating to ln forms
use algebraic division to rewrite fractions before finding exact areas or integrals

[Maximum number: 3]

f(x)=\frac{2 x^{4}+15 x^{3}+35 x^{2}+21 x-4}{(x+3)^{2}} \quad x \in \mathbb{R} \quad x>-3

Hence find,

\int \mathrm{f}(x) \mathrm{d} x

$\int f(x)\,dx=\int\left(2x^2+3x-1+\frac{5}{(x+3)^2}\right)\,dx$ $=\frac{2x^3}{3}+\frac{3x^2}{2}-x-\frac{5}{x+3}+c$
(3)

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