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Why can partial fractions make a rational function easier to integrate?
A
Polynomial division gives P(x)Q(x)=S(x)+R(x)Q(x)\frac{P(x)}{Q(x)}=S(x)+\frac{R(x)}{Q(x)}Q(x)P(x)=S(x)+Q(x)R(x), where R(x)R(x)R(x) has lower degree than Q(x)Q(x)Q(x).
B
x+3ln∣x∣−2ln∣x+1∣+Cx+3\ln|x|-2\ln|x+1|+Cx+3ln∣x∣−2ln∣x+1∣+C
C
Ax−a+B(x−a)2+Cx−b\frac{A}{x-a}+\frac{B}{(x-a)^2}+\frac{C}{x-b}x−aA+(x−a)2B+x−bC
D
They split it into standard logarithmic or power-rule terms.
Card 1 of 23
1.9.30 Integration using partial fractions (A-level only) Flashcards
23 flashcards on OCR (MEI) A Level Maths 1.9.30 Integration using partial fractions (A-level only): the key formulae, methods and definitions you need to recall for Component 01, Component 02 and Component 03.