Integration using partial fractions and reverse chain ruleEdexcel A-Level Maths: Mind map

Exam questions on Integration using partial fractions and reverse chain rule

1. Two rational functions are defined for $x\ge0$ by $h(x)=\frac{2}{3x+5}$ and $k(x)=\frac{x}{x^2+5}$.
   Find the exact value of $\int_0^2 3k(x)\,\mathrm{d}x$.2 marks
2. Let $f(x)=\frac{4x+11}{(x-1)(2x+3)}$ for $x>1$.
   Find the exact value of $\int_2^5 f(x)\,\mathrm{d}x$, giving your answer as a single logarithm.2 marks
3. A curve $C$ has gradient $\frac{\mathrm{d}y}{\mathrm{d}x}=\frac{2}{(2x-1)^4}$ for $x>\frac12$, and passes through the point $(1,\,1)$.
   Find the equation of $C$.3 marks