Rewrite $\frac{2}{(x + 1)(x + 3)}$ as partial fractions.
(ii)[2]
Using the answer from part (i), show that $\left( \frac{2}{(x + 1)(x + 3)} \right)^2 = \frac{1}{(x + 1)^2} - \frac{1}{x + 1} + \frac{1}{x + 3} + \frac{1}{(x + 3)^2}$.
(iii)[5]
Hence show that $\int_0^1 \frac{4}{(x + 1)^2 (x + 3)^2} \, dx = \frac{7}{12} - \ln \frac{3}{2}$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “State or show the form $\frac{A}{x+1}+\frac{B}{x+3}$ and use a suitable method to determine $A$ or $B$” …