Question:

Put $\sqrt{x-\alpha} = t \Rightarrow x-\alpha = t^2 \Rightarrow dx = 2t dt$<br>$\int \frac{2t dt}{t \sqrt{\beta - (t^2 + \alpha)}} \Rightarrow 2 \int \frac{dt}{\sqrt{(\beta - \alpha) - t^2}}$<br>$\Rightarrow 2 \sin^{-1}\left(\frac{t}{\sqrt{\beta - \alpha}}\right) \Rightarrow \left[ 2 \sin^{-1}\left(\frac{\sqrt{x-\alpha}}{\sqrt{\beta - \alpha}}\right) \right]_{\alpha}^{\beta}$<br>$\Rightarrow 2\left(\frac{\pi}{2} - 0\right) \Rightarrow \pi$