Answer
The formula is correct.
Work Step by Step
Verifying by differentiation:
$\frac{d}{dx}(\frac{2}{15b^2}(3bx-2a)(a+bx)^{\frac{3}{2}})
=\frac{2}{5b}(\sqrt{a+bx}^3)+\frac{3}{5}(\sqrt{a+bx})-\frac{2a}{5b}(\sqrt{a+bx})=\frac{2}{5b}(a+bx)(\sqrt{a+bx})+\frac{3x}{5}(\sqrt{a+bx})-\frac{2a}{5b}\sqrt{a+bx}=(\frac{2a}{5b}+\frac{2x}{5}+\frac{3x}{5}-\frac{2a}{5b})(\sqrt{a+bx})=x\sqrt{a+bx}$.
