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\sin(2 \arccos (d/R)) = \frac{\sqrt{R^2 - d^2}{R}}
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\displaystyle = \frac{\sqrt{4}}{(x+3)\sqrt{2+2x}}}}
\displaystyle = \frac{2}{\sqrt{2}}\frac{1}{{(x+3)\sqrt{1+x}}}}}
\displaystyle \Rightarrow \int \frac{1}{{(x+3)\sqrt{x+1}}}}} \ dx = \frac{\sqrt{2}}{2}\arcsin \left(\frac{x-1}{x+3}\right) + C
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