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$${\displaystyle \int \frac{-3}{\sqrt{- 5 x^{2}+ 2 x+ 1}}\ dx}$$
\({\frac{6}{\sqrt{5}} \ tan^{-1}(\frac{\sqrt{- 5 x^{2}+ 2 x+ 1} - 1}{\sqrt{5} x}) + \ \small{C}}\)
\({-4 \ tan^{-1}(\frac{\sqrt{- x^{2}- 4 x+ 4} - 2}{ x}) + \ \small{C}}\)
\({\frac{8}{\sqrt{5}} \ tanh^{-1}(\frac{\sqrt{ 5 x^{2}- 2 x+ 1} - 1}{\sqrt{5} x}) + \ \small{C}}\)
\({\frac{6}{\sqrt{2}} \ tan^{-1}(\frac{\sqrt{- 2 x^{2}- 5 x+ 3} - \sqrt{3}}{\sqrt{2} x}) + \ \small{C}}\)