MATH128 Lecture Notes - Lecture 4: Horse Length
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Math 128 dr. smith lecture 4: integration by partial fractions (7. 4) Given rational function p(x)/q(x: if deg(p) > deg(q), divide q into p and separate out polynomial from rational remainder. = aix+bi: if q is a product of distinct linear factors, i. e. , q(x) = l1(x) l2(x) ln(x), where li(x, set xr xq. A n xl n: solve for ai xr, solve xq dx. A n xl n dx xr xq: if q is a product with some repeated linear factors q(x) = l1(x)p1 l2(x) p2 ln(x) pn, set. A pn xl n n p n dx xr xq. 1: if q contains quadratic factors, i. e. , q(x) = l1(x) l2(x) lm(x)q1(x)q2(x) qn(x), where qi(x) = aix2 + bix + ci. 1 xr xq: solve n, solve for ai, bi, ci. Cxb n xq n n dx: if q contains repeated quadratic factors, q(x) = l1(x) p1 lm(x) pmq1(x) r1q2(x) r2 qn(x) rn, set xr xq.
