1. (i) Integrate

$\intsin(2x+1)dx.$

(ii) Use calculus to find the exact value of

${\int}_{\frac{ \pi }{6}}^{\frac{ \pi }{4}}{sec}^{2}(2 \theta -\frac{ \pi }{6})d \theta .$

(iii) Find an expression for $y$ given that

$\frac{dy}{dx}=4cos(5x+2).$