Since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form†8x2 + 9x − 1x(2x − 1)(x + 2) =

perform the partial fraction decomposition of Integrate (2x ^ 2 + 3)/(x * (x - 1) ^ 2) dx

perform the partial fraction decomposition of integrate (2x ^ 2 - 1)/((4x - 1)(x ^ 2 + 1)) dx

Expressx(1 − 2x)2(1 − 3x)in partial fractions.

One of the factors of (1 +3x)2 + (9x2 -1) is :(a) 1-3x (b) 3-x(c) 3x+1 (d) x-3

lving, we get A = 12, B = , and C = , and so we have the following. (Remember to use absolute values where appropriate.)8x2 + 9x − 12x3 + 3x2 − 2x dx= 12 1x +  12x − 1 +  1x + 2 dx= + KIn integrating the middle term we have made the mental substitution u = 2x − 1, which gives du = 2 dx and dx = 12 du.