Ayuda con esta integralk?

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%5C%5CI%3D%5Cint%5Cdfrac%7Bdx%7D%7B%28x%5E2-2x%2B5%29%5E2%7D%5C%5C%20%5C%5C%20%5C%5C%5Ctext%7BMetodo%20de%20Hermite%7D%5C%5C%20%5C%5C%20%5C%5CI%3D%5Cdfrac%7BAx%2BB%7D%7Bx%5E2-2x%2B5%7D%2B%5Cint%5Cdfrac%7BCx%2BD%7D%7Bx%5E2-2x%2B5%7Ddx%5C%5C%20%5C%5C%5Ctext%7BDerivamos%20ambos%20miembros%7D%5C%5C%20%5C%5C%20%5C%5C%5Cdfrac%7B1%7D%7B%28x%5E2-2x%2B5%29%5E2%7D%5Cequiv%20%5Cdfrac%7BA%28x%5E2-2x%2B5%29-%28Ax%2BB%29%282x-2%29%7D%7B%28x%5E2-2x%2B5%29%5E2%7D%2B%5Cdfrac%7BCx%2BD%7D%7Bx%5E2-2x%2B5%7D%5C%5C" /><img src="https://tex.z-dn.net/?f=%5Cdfrac%7B1%7D%7B%28x%5E2-2x%2B5%29%5E2%7D%5Cequiv%5Cdfrac%7BCx%5E3%20-%20x%5E2%28A%20%2B%202C%20-%20D%29%20-%20x%282B%20-%205C%20%2B%202D%29%20%2B%205A%20%2B%202B%20%2B%205D%7D%7B%28x%5E2-2x%2B5%29%5E2%7D%5C%5C%20%5C%5C%5Ctext%7BComparamos%20numeradores%20y%20tenemos%20el%20siguiente%20sistema%7D%5C%5C%5C%5C%5Cbegin%7Bcases%7DC%3D0%5C%5CA%20%2B%202C%20-%20D%3D0%5C%5C2B%20-%205C%20%2B%202D%3D0%5C%5C5A%20%2B%202B%20%2B%205D%3D1%5Cend%7Bcases%7D%5C%5C%20%5C%5C%5C%5CA%3D%5Cdfrac%7B1%7D%7B8%7D~~%5Cwedge%20~~B%3D%5Cdfrac%7B1%7D%7B8%7D~~%5Cwedge%20~~C%3D0~~%5Cwedge%20~~D%3D%5Cdfrac%7B1%7D%7B8%7D%5C%5C%20%5C%5C%20%5C%5C" /><img src="https://tex.z-dn.net/?f=%5Ctext%7BHasta%20aqu%5C%27i%20tenemos%20la%20integral%7D%5C%5C%20%5Cdisplaystyle%5C%5CI%3D%5Cdfrac%7Bx-1%7D%7B8%28x%5E2-2x%2B5%29%7D%2B%5Cdfrac%7B1%7D%7B8%7D%5Cint%5Cdfrac%7B1%7D%7Bx%5E2-2x%2B5%7Ddx%5C%5C%20%5C%5C%5C%5C%5Ctext%7BSea%20%7DI_1%3D%20%5Cint%5Cdfrac%7B1%7D%7Bx%5E2-2x%2B5%7Ddx%5C%5C%20%5C%5C%20%5C%5CI_1%3D%5Cint%20%5Cdfrac%7B1%7D%7B%28x-1%29%5E2%2B2%5E2%7Ddx%3D%5Cdfrac%7B1%7D%7B2%7D%5Carctan%20%5Cdfrac%7Bx-1%7D%7B2%7D%5C%5C%20%5C%5C%20%5C%5C%5Cboxed%7BI%3D%5Cdfrac%7Bx-1%7D%7B8%28x%5E2-2x%2B5%29%7D%2B%5Cdfrac%7B1%7D%7B16%7D%5Carctan%20%5Cdfrac%7Bx-1%7D%7B2%7D%2BC%7D" />.