Partial fractionsEdexcel International A Level Maths: Mind map

Exam questions on Partial fractions

1. The function $f(x)=\frac{10x-1}{(x-1)(2x+1)}$ can be written in the form $\frac{A}{x-1}+\frac{B}{2x+1}$.
   Hence find $\int f(x)\,\mathrm{d}x$.2 marks
2. The function $g(x)=\frac{3x^2+6}{(x+2)(x-1)^2}$ can be written in the form $\frac{A}{x+2}+\frac{B}{x-1}+\frac{C}{(x-1)^2}$.
   Find the value of $B$.2 marks
3. The function $h(x)=\frac{3x^2+6x-3}{(x-1)(x+2)}$ is defined for $x>1$.
   Express $h(x)$ in the form $P+\frac{Q}{x-1}+\frac{R}{x+2}$, where $P$, $Q$ and $R$ are constants.3 marks