Example $3$

Video Example

Find ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x}{\sqrt[\phantom{2}]{2-3x^2}}dx$

Solution

Let $u=2-3x^2.$ Then $du={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}dx,$ and $xdx={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}du$ and