Find $\int \cos ^{3} \beta d \beta$ .
A) $\sin \beta-\frac{1}{3} \sin ^{3} \beta+C$
B) $\frac{1}{3} \sin \beta+\frac{2}{3} \sin ^{3} \beta+C$
C) $\sin \beta-\frac{2}{3} \sin ^{3} \beta+C$
D) $\frac{1}{3} \sin \beta+\sin ^{3} \beta+C$

Question

Quizplus · Accepted Answer

To solve $\int \cos ^{3} \beta d \beta$, use the identity $\cos^2\beta = 1 - \sin^2\beta$ to rewrite $\cos^3\beta$ as $\cos\beta(1 - \sin^2\beta)$. Then, set $u = \sin\beta$, so $du = \cos\beta d\beta$, and integrate $u - u^3$, which gives $\sin\beta - \frac{1}{3}\sin^3\beta + C$.

Find ∫cos⁡3βdβ\int \cos ^{3} \beta d \beta∫cos3βdβ A) sin⁡β−13sin⁡3β+C\sin \beta-\frac{1}{3} \sin ^{3} \beta+Csinβ−31​sin3β+C

Find $\int \cos ^{3} \beta d \beta$
A) $\sin \beta-\frac{1}{3} \sin ^{3} \beta+C$