please help me to solve this math problem =
Are you required to use integration by parts? The obvious way to integrate this is to let $\displaystyle y= 1- x^2$ so that $\displaystyle dy= -2x dx$ or $\displaystyle -\frac{1}{2}dy= x dx$, $\displaystyle x^2= 1- y$ and the integral becomes $\displaystyle \int \frac{(x^2)(x dx)}{\sqrt{1- x^2}}= -\frac{1}{2}\int\frac{(1- y)dy}{\sqrt{y}}$$\displaystyle = -\frac{1}{2}\int\frac{(1- y)dy}{y^{\frac{1}{2}}}$$\displaystyle = -\frac{1}{2}\int \left(y^{-\frac{1}{2}}- y^{\frac{1}{2}}\right)dy$.