(i)[5]
Show that $(2\sin x + \cos x)^2$ may be expressed in the form $\dfrac{5}{2} + 2\sin 2x - \dfrac{3}{2}\cos 2x$.
(ii)[4]
Hence find the exact value of the integral $\int_0^{\frac{\pi}{4}} (2\sin x + \cos x)^2\,dx$.
Mathematics 9709 · AS & A Level · Integration