You will integrate the following rational function: -3x+231-34 (x-7)(x-6x+13) To do this, start by writing -3x+232-34 (x-7)(x-6x+13) (a) Put the right-hand side over a common denominator. Enter the numerator of the result. x: da constants: (b) Expand the numerator. It is a quadratic in , which must equal the numerator of the original function. By equating the coefficients you should be able to formulate linear equation in A, B and C. In each case give an equation with the constant part on the right, for example A+ 2 * B = 3. What equation can you deduce from the coefficients of : 22: (d) The last term is in the form = x- L,r,s (c) Solve these three equations, and enter the solution in the form A,B,C Bx+C x-6x+13 + Bx+C 2-6x+13 . Find constants K and J such that B x + C = K (2x-6) + J, enter in the form K, J (e) Separating out the K and J terms, you now have a term of the form top and bottom by a constant you should be able to express this in the form A (f) Your rational function is now in the form + x-7 K (2x-6) 22-62+13 Don't forget that the integral of 1/x is In (x), not just In (x). J x2-6x+13 L (x-r) L (x-r) 82 +1 By completing the square in the denominator and possibly dividing for some constants L, r, s, with s> 0. Enter these in the form +1 now evaluate the integral. Use a constant of integration F.