Answer
$$\int\cos^3\theta\sin\theta d\theta=-\frac{\cos^4\theta}{4}+C$$
Work Step by Step
$$A=\int\cos^3\theta\sin\theta d\theta$$
Let $u=\cos\theta$.
Then $du=-\sin\theta d\theta$, so $\sin\theta d\theta=-du$
Substitute into $A$, we have $$A=-\int u^3du$$ $$A=-\frac{u^4}{4}+C$$ $$A=-\frac{\cos^4\theta}{4}+C$$
