Integration using partial fractionsAQA A-Level Maths: Mind map

Exam questions on Integration using partial fractions

1. Let $\frac{5x+1}{(x-1)(x+2)}\equiv\frac{A}{x-1}+\frac{B}{x+2}$, where $A$ and $B$ are constants.
   Hence find the exact value of $\int_2^4\frac{5x+1}{(x-1)(x+2)}\,dx$, giving your answer in the form $a\ln3+b\ln2$.2 marks
2. It is given that $\frac{4}{(2x-1)(2x+1)}\equiv\frac{2}{2x-1}-\frac{2}{2x+1}$, and $x>\frac12$.
   Hence find the exact value of $\int_1^2\frac{4}{(2x-1)(2x+1)}\,dx$.2 marks
3. Let $f(x)=\frac{11x-1}{(x-2)(3x+1)}$ for $x>2$.
   Express $f(x)$ in the form $\frac{A}{x-2}+\frac{B}{3x+1}$, where $A$ and $B$ are constants to be found.3 marks