Find $\int (2\cos\theta - 3)(\cos\theta + 1)\, d\theta$ by integrating the expanded product.
(b(i))[2]
Find $\int \left( \frac{4}{2x + 1} + \frac{1}{2x} \right) dx$ by direct integration.
(b(ii))[3]
Hence find $\int_{1}^{4} \left( \frac{4}{2x + 1} + \frac{1}{2x} \right) dx$, and give your answer in the form $\ln k$.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Obtain $\int(2\cos^2\theta-\cos\theta-3)\,d\theta$ from the expansion.” …