You will integrate the following rational function:
∫ 2-3x / (x-2)² dx
To do this, start by writing = 2-3x / (x-2)² = A / (x-2)² + C / x-2 (a) Put the right-hand side over a common denominator. Enter the numerator of the result. _____
Expand the numerator. It is a linear function of x, which must equal the numerator of the original function. By comparing coefficients you should get linear equations in A and C. Enter them with the constant on the right hand side, such as A+2*C=3. What equation can you deduce from: (b) the coefficients of x:
_____
(c) the constants (coefficients of 1): ______
(d) Solve these two equations, and enter the solution in the form A, C.
A, C = (e) Use these values, and the partial fraction form, to find the integral. Use a constant of integration k. Don't forget that the integral of 1/x is In |x| which has syntax In(abs(x))