How do you integrate #int (x-x^2)/((x+3)(x-6)(x+4)) # using partial fractions?
First split the expression up into three elements, one for each of the bracketed terms in the denominator.
Restoring the denominator gives us
Each of the coefficients in the numerator must equal the coefficients in the original equation. Therefore
We can now solve these three equations to find A, B, and C.
Doubling the first equation and adding it to the second gives
Multiplying the second equation by 12 and subtracting it from the third gives
Substituting for C give
We can therefore write the original equation as