Why can partial fractions make a rational function easier to integrate?
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).
x+3ln∣x∣−2ln∣x+1∣+Cx+3\ln|x|-2\ln|x+1|+Cx+3ln∣x∣−2ln∣x+1∣+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
They split it into standard logarithmic or power-rule terms.
1.9.30 Integration using partial fractions (A-level only) Flashcards
Flashcards for OCR (MEI) A Level Maths 1.9.30 Integration using partial fractions (A-level only), covering the key formulae, methods and definitions you need to recall for Component 01, Component 02 and Component 03. 23 cards, matched to the OCR (MEI) A Level Maths (H640) specification. Recall questions account for roughly 50% of marks at A Level Maths, so these target the marks you can secure before the paper starts.