The integral \(\frac{x^2}{(4 - x^2)^{3/2}} \, dx\) can be effectively evaluated using the substitution \(x = 2\sin{(\theta)}\), which leads to \(dx = 2\cos{(\theta)}\,d\theta\). This substitution simplifies the integral significantly, allowing for easier integration. The discussion confirms that this method is a valid approach to solve the integral.
PREREQUISITESStudents and educators in calculus, mathematicians focusing on integral evaluation, and anyone seeking to enhance their skills in solving complex integrals using substitution methods.
shamieh said:Evaluate the Integral.
Please help! I am so lost on this one!
$$\frac{x^2}{(4 - x^2)^\frac{3}{2}} \, dx$$