Partial fractions and reduction formulaeAQA A-Level Further Maths: Mind map

Exam questions on Partial fractions and reduction formulae

1. Let $\mathrm{f}(x)=\dfrac{5x+1}{(x-1)(x+2)}$.
   Find the exact value of $\int_2^3\mathrm{f}(x)\,dx$, giving your answer as a single logarithm.2 marks
2. Let $\mathrm{g}(x)=\dfrac{5x^2+4x+9}{(x+1)(x^2+4)}$, and let $\mathrm{g}(x)\equiv\dfrac{A}{x+1}+\dfrac{Bx+C}{x^2+4}$.
   Find the exact value of $\displaystyle\int_0^2\frac{3x}{x^2+4}\,dx$, giving your answer in the form $p\ln q$.2 marks
3. For integer $n\ge0$, let $I_n=\int_0^1x^n\mathrm{e}^x\,dx$.
   Show that $I_n=\mathrm{e}-nI_{n-1}$ for $n\ge1$.3 marks