\(\displaystyle \int \sqrt{\dfrac{1 + x}{1 - x}}\,dx\)

\(-\cos^{-1} x - \sqrt{1 - x^2} + C\)

\(\displaystyle \int \dfrac{\sqrt{16 - x^2}}{x^2}\,dx\)

\(\dfrac{-\sqrt{16 - x^2}}{x} - \sin^{-1} \dfrac{x}{4} + C\)

\(\displaystyle \int \sqrt{\dfrac{1}{1 - x}}\,dx\)

\(\sin^{-1} \sqrt{x} - \sqrt{x(1 - x)} + C\)

\(\displaystyle \int_{1 / \sqrt{3}}^1\ \,\dfrac{1}{x^2\sqrt{1 + x^2}}\,dx\)

\(\pi - 2\)