Integration using partial fractionsEdexcel A-Level Further Maths: Mind map

Exam questions on Integration using partial fractions

1. Let $f(x)=\frac{5}{(x+1)(x^2+4)}$, which is to be written in the form $\frac{A}{x+1}+\frac{Bx+C}{x^2+4}$.
   Given that $A=1$, find the values of $B$ and $C$.2 marks
2. Let $g(x)=\frac{1-x}{x^2+4}$.
   Hence find the exact value of $\int_0^2 g(x)\,dx$.2 marks
3. Let $f(x)=\frac{2x^2+17}{(x+2)(4x^2+9)}$.
   Express $f(x)$ in the form $\frac{A}{x+2}+\frac{Bx+C}{4x^2+9}$, where $A$, $B$ and $C$ are constants to be found.3 marks