Apply double-angle and product-to-sum identities before integrating

Find the following integrals:

(a) $\displaystyle\int\dfrac1{1+\cos4\theta}\,d\theta$,2 marks

(b) $\displaystyle\int\cos2x\sin3x\,dx$, given $2\sin A\cos B=\sin(A+B)+\sin(A-B)$.3 marks