Q1 \int \frac{x^2+2}{(x^2+2x+2)(\sqrt {x-1})}
Add and subtract 2x in Nr
=>\int \frac{x^2+2+2x-2x}{(x^2+2x+2)(\sqrt {x-1})}
=>\int \frac{x^2+2+2x}{(x^2+2x+2)(\sqrt {x-1})}-\int\frac{2x}{(x^2+2x+2)(\sqrt {x-1})}
=> \int \frac {1}{\sqrt {x-1}}-\int\frac{2x}{(x^2+2x+2)(\sqrt {x-1})}
The situation is better now..