Question

integration of 2-x2/x2-x

Answer 1

Integration ... use partial fractions.

$I=\int {\frac{2-x^2}{x^2-x}} \: dx= -\int {(1+\frac{2}{x}-\frac{1}{x-1})} \, dx\\\\=-x-2Ln\: |x| + Ln|x-1|+K\\\\=Ln \: \frac{|x-1|} {e^x \: x^2} + K$