Please Help integrating $P(t) = 3 + 2 \cos((1+t)/26)\pi$ I am given the equation:
$$P(t) = 3 + 2 \cos \left(\frac{1+t}{26}\right)\pi$$  
Where $t$ = time in weeks and $P$ = pollutant released into the atmosphere
I am told to integrate:
$$\int_0^4 3 + 2 \cos \left(\frac{1+t}{26} \right)\pi  dt$$
in stages:
(i) $$\int_0^4 3 dt$$
(ii) $$\int_0^4 2 \cos \left(\frac{1+t}{26}\right)\pi dt$$ Where, for (ii), I am told to use the substitution $u = \left(\frac{1+t}{26}\right)\pi$
I know that after integrating, (i) $= 12$.
For (ii), I have tried differentiating $u$ with respect to $t$ using the quotient rule with varying results. I'm not sure what I'm doing wrong, so any help would be appreciated. Thanks. 

To evaluate 
$$\int_{0}^{4} 2 \cos \left( \frac{\pi(1+t)}{26} \right)  \mathrm{d}t$$
substitute $\frac{\pi(1+t)}{26} = u$ and apply $\sin A - \sin B$ identity to simplify your answer. 
