$\int\frac{\sqrt{y^2-25}}{y^9}dy$

$\frac{\frac{1}{50000}\sqrt{y^2-25}}{y^2}+\frac{1}{250000}\mathrm{arcsec}\left(\frac{y}{5}\right)+\frac{\frac{1}{3000}\sqrt{y^2-25}}{y^{4}}+\frac{\sqrt{y^2-25}}{150y^{6}}+\frac{-\frac{7}{1200000}\sqrt{y^2-25}\left(1+\frac{-2\left(y^2-25\right)}{y^2}\right)}{y^2}-\frac{7}{6000000}\mathrm{arcsec}\left(\frac{y}{5}\right)+\frac{-\frac{7}{300000}\sqrt{y^2-25}}{y^2}-\frac{7}{3000000}\mathrm{arcsec}\left(\frac{y}{5}\right)+\frac{-\frac{7}{1200}\sqrt{y^2-25}}{y^{6}}+\frac{-\sqrt{y^2-25}}{8y^{8}}+C_0$