Is Substitution Effective for Integrating \(\frac{x^2}{(4-x^2)^{3/2}} \, dx\)?

[shamieh]

Evaluate the Integral.

Please help! I am so lost on this one!

$$\frac{x^2}{(4 - x^2)^\frac{3}{2}} \, dx$$

 

[Prove It]

Evaluate the Integral.

Please help! I am so lost on this one!

$$\frac{x^2}{(4 - x^2)^\frac{3}{2}} \, dx$$

The substitution $$\displaystyle \begin{align*} x = 2\sin{(\theta)} \implies dx = 2\cos{(\theta)}\,d\theta \end{align*}$$ will probably work...