Ayuda con esta integral de fracciones parciales por favor?

Vemos que es una fracción propia entonces

<img src="https://tex.z-dn.net/?f=%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%3D%5Cdfrac%7BA%7D%7Bx%2B3%7D%2B%5Cdfrac%7BBx%2BC%7D%7Bx%5E2%2B1%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%3D%5Cdfrac%7B%28A%2BB%29x%5E2%2B%283B%2BC%29x%2B%28A%2B3C%29%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Cbegin%7Bcases%7D%0AA%2BB%3D1%5C%5C%0A3B%2BC%3D-3%5C%5C%0AA%2B3C%3D2%0A%5Cend%7Bcases%7D%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BResolviendo%3A%20%7D%0AA%3D2%5C%3B%2C%5C%3BB%3D-1%5C%3B%2C%5C%3BC%3D0%5C%5C%20%5C%5C%20%5C%5C%0A%5Ctexttt%7BEntonces%3A%7D%5C%5C%20%5C%5C%0A%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%3D%5Cdfrac%7B2%7D%7Bx%2B3%7D-%5Cdfrac%7Bx%7D%7Bx%5E2%2B1%7D" />

Ahora integremos.

<img src="https://tex.z-dn.net/?f=%5Cdisplaystyle%0A%5Cint%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%5C%2C%20dx%3D%5Cint%5Cdfrac%7B2%7D%7Bx%2B3%7D-%5Cdfrac%7Bx%7D%7Bx%5E2%2B1%7D%5C%2Cdx%5C%5C%20%5C%5C%20%5C%5C%0A%5Cint%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%5C%2C%20dx%3D%5Cint%5Cdfrac%7B2%7D%7Bx%2B3%7D%5C%2Cdx-%5Cint%5Cdfrac%7Bx%7D%7Bx%5E2%2B1%7D%5C%2Cdx%5C%5C%20%5C%5C%20%5C%5C%20%5C%5C%0A%5Cboxed%7B%5Cint%5Cdfrac%7Bx%5E2-3x%2B2%7D%7B%28x%2B3%29%28x%5E2%2B1%29%7D%5C%2C%20dx%3D2%5Cln%7Cx%2B3%7C%2B%5Cdfrac%7B1%7D%7B2%7D%5Cln%20%28x%5E2%2B1%29%2BK%7D" />.