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#### skatenerd

##### Active member

- Oct 3, 2012

- 114

$$\int \frac{x^2}{\sqrt{1-x^2}}\,dx$$

I begin by substituting

$$x={sin{\theta}}$$

I am fine with doing everything up to the point where I have an answer for the integral in terms of \(\theta\). This answer is

$$\frac{\theta}{2}-\frac{sin{2\theta}}{4}$$

I know the first term is just

$$\frac{sin^{-1}x}{2}$$

However the second term is always the part that throws me off. How do you find what to plug back in for \(\theta\) when the \(\theta\) is inside of a sine? Any help is appreciated!