(a) Express 3x- 32' + 20 +2 – 1 (* - 1)(2² +1) as a sum of rational functions of the form A, and B,r +C, (a,r + b,)" where A, B,, C3, a;, bi, c d, and e, are appropriate real numbers. Note: Factorise the rational function first. Do not calculate the constants Ai, B; and

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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te: Factorise the rational function first. Do mot calculate the constants Ai, Bj
3. (a) Express
3x - 32 + 20² +2 – 1
(*- 1)(22 + 1)
as a sum of rational functions of the form
A,
(a,a + b,)
B,» + C,
and
(c,a² +d;r + e;)"
where A, B, C, a;, bi, cj d; and e, are appropriate real numbers.
Note: Factorise the rational function first. Do not calculate the constants Ai,
and
(b) Let
2x
5x+9
(* – 1)(r+ 1).
Evaluate the
indefinite integralS(r)dr.
Hint: Do long division first.
(c) Use
evaluate
2.
dr.
Transcribed Image Text:te: Factorise the rational function first. Do mot calculate the constants Ai, Bj 3. (a) Express 3x - 32 + 20² +2 – 1 (*- 1)(22 + 1) as a sum of rational functions of the form A, (a,a + b,) B,» + C, and (c,a² +d;r + e;)" where A, B, C, a;, bi, cj d; and e, are appropriate real numbers. Note: Factorise the rational function first. Do not calculate the constants Ai, and (b) Let 2x 5x+9 (* – 1)(r+ 1). Evaluate the indefinite integralS(r)dr. Hint: Do long division first. (c) Use evaluate 2. dr.
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