Answer
$$\int\cos(1+5t)dt=\frac{\sin(1+5t)}{5}+C$$
Work Step by Step
$$A=\int\cos(1+5t)dt$$
Let $u=1+5t$
Then we have $du=5dt$. That means $dt=\frac{1}{5}du$
Substitute into $A$: $$A=\frac{1}{5}\int\cos udu$$ $$A=\frac{1}{5}\sin u+C$$ $$A=\frac{\sin(1+5t)}{5}+C$$
