Find $\int 3 y\left(y^{2}+2\right)^{3} d y$
A) $\frac{3}{8 y}\left(y^{2}+2\right)^{4}+C$
B) $\frac{3 y^{2}}{8}\left(y^{2}+2\right)^{4}+C$
C) $\frac{3}{8}\left(y^{2}+2\right)^{4}+C$
D) $\frac{3}{4}\left(y^{2}+2\right)^{4}+C$

Question

Quizplus · Accepted Answer

The integral can be solved by a simple substitution. Let $u = y^2 + 2$, then $du = 2y dy$. The integral becomes $\frac{3}{2} \int u^3 du$, which evaluates to $\frac{3}{2} \cdot \frac{1}{4} u^4 + C = \frac{3}{8}(y^2 + 2)^4 + C$.

Find ∫3y(y2+2)3dy\int 3 y\left(y^{2}+2\right)^{3} d y∫3y(y2+2)3dy A) 38y(y2+2)4+C\frac{3}{8 y}\left(y^{2}+2\right)^{4}+C8y3​(y2+2)4+C B) 3y28(y2+2)4+C\frac{3 y^{2}}{8}\left(y^{2}+2\right)^{4}+C83y2​(y2+2)4+C C) 38(y2+2)4+C\frac{3}{8}\left(y^{2}+2\right)^{4}+C83​(y2+2)4+C

Find $\int 3 y\left(y^{2}+2\right)^{3} d y$ A) $\frac{3}{8 y}\left(y^{2}+2\right)^{4}+C$ B) $\frac{3 y^{2}}{8}\left(y^{2}+2\right)^{4}+C$ C) $\frac{3}{8}\left(y^{2}+2\right)^{4}+C$