Integration simple question

Question

I want to integrate $$\int\left(\frac{y}{2}\right)^\frac{2}{3}dy$$

Doing this I get $$\cfrac{3}{5}\left(\cfrac{y}{2}\right)^\cfrac{5}{3}$$

But the answer is $$\cfrac{6}{5}\left(\cfrac{y}{2}\right)^\cfrac{5}{3}$$

What step am I missing

Answer 1

Substitute $u=\dfrac y2$.

Then $du=\dfrac {dy}2$, so $$\int\left(\frac{y}{2}\right)^{2/3}dy=\int u^{2/3}2du=2\left(\dfrac35u^{5/3}\right)+C=\dfrac65\left(\dfrac y2\right)^{5/3}+C$$