By consdering partial fractions find the integral of (1-x)/(5x-6-x^2) between x = 1 and x = 0, give your answer in an exact form.

The answer is Ln8/9, by first converting (1-x)/(5x-6-x^2) into partial fractions you get 1/(2-x) + 2/(x-3), the next step is a simple integration by inspection followed by log manipulations to get the final answer.