Integration using partial fractionsEdexcel International A Level Maths: Mind map

Exam questions on Integration using partial fractions

1. Let $f(x)=\frac{4x+5}{(x+1)(x+2)}$ for $x>-1$.
   Hence find $\int_0^2f(x)\,dx$, giving your answer in the form $\ln k$.2 marks
2. A curve $C$ has gradient $\frac{dy}{dx}=\frac{2}{3x+5}+\frac{3}{(x-1)^2}$ for $x>1$.
   The curve $C$ passes through the point $(2,1)$. Find the equation of $C$.2 marks
3. Let $f(x)=\frac{5x+7}{(x-1)(x+3)}$ for $x>1$.
   Express $f(x)$ in partial fractions.3 marks