How do you integrate #int (1-x^2)/((x-9)(x+6)(x-2)) # using partial fractions?
Conveniently, the denominator in this problem is already factored.
To apply partial fraction decomposition, we want to express
in the form
So we can equate
Multiplying both sides by the denominator of the left, we get:
Now let's expand the parentheses and group similar terms:
Now we can compare the coefficients on both sides, and write a system of three equations:
Solving this system (whichever way you choose) gives:
So now we can rewrite the integral as:
Integrating, we get: