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.
OA
Related Maths A Level answers
All answers ▸integrate x^2 + ln(x)
How do I integrate ln(x)?
The velocity of a car at time, ts^-1, during the first 20 s of its journey, is given by v = kt + 0.03t^2, where k is a constant. When t = 20 the acceleration of the car is 1.3ms^-2, what is the value of k?
Core 3: Find all the solutions of 2cos(2x) = 1-2sin(x) in the interval 0<x<360