About an integration technique My professor wrote this : 
$\displaystyle \int  x^2\log(\sqrt{1-x^2}) \,\mathrm{d}x = \frac{1}{3}\int \log(\sqrt{1-x^2})   \, \mathrm dx^3$
Can someone explain me what is going on with the integration variable ? 

$
\int x^2 \log \sqrt{1 - x^2} \ dx \\
= \int x^2 \log \sqrt{1 - x^2} \ \frac{dx}{dx^3} \ dx^3 \\
= \int x^2 \log \sqrt{1 - x^2} \ \frac{1}{3x^2} \ dx^3 \\
= \frac13 \int \log \sqrt{1 - x^2} \ dx^3
$
