Answer
$-\frac{\sqrt{4-5x^2}}{5}+C$
Work Step by Step
Use the substitution $u=4-5x^2$. Then $du=-10xdx$, so $xdx=-\frac{1}{10}du$.
$\int\frac{x}{\sqrt{4-5x^2}}dx$
$=\int\frac{1}{\sqrt{u}}*(-\frac{1}{10})du$
$=\int-\frac{1}{10}u^{-\frac{1}{2}}du$
$=-\frac{1}{10}*\frac{u^\frac{1}{2}}{\frac{1}{2}}+C$
$=-\frac{\sqrt{u}}{5}+C$
$=-\frac{\sqrt{4-5x^2}}{5}+C$