Answer
$$\int e^{\cos t}\sin tdt=-e^{\cos t}+C$$
Work Step by Step
$$A=\int e^{\cos t}\sin tdt$$
Let $u=\cos t$.
We would have $du=-\sin tdt$. Therefore, $\sin tdt=-du$
Substitute into $A$, we have $$A=-\int e^udu$$ $$A=-e^u+C$$ $$A=-e^{\cos t}+C$$
