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

Practise Edexcel IAL P4.6.3 algebraic integration: divide or decompose rational expressions, integrate each term, and simplify exact results.

Exam points

Rewrite rational expressions by division or partial fractions before integrating
Integrate each rational term to powers or logarithms with correct constants
Evaluate the definite integral exactly and simplify the resulting logarithms or fractions

[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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