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1.8.10 Use of partial fractions in integration (A-level only)

The standard linear-factor integral is

∫1ax+b dx=<strong>[...]</strong>ln⁡∣ax+b∣+<strong>C</strong>. \int \frac{1}{ax+b}\,dx=<strong>\text{[...]}</strong>\ln|ax+b|+<strong>C</strong>. ∫ax+b1​dx=<strong>[...]</strong>ln∣ax+b∣+<strong>C</strong>.
A

The standard linear-factor integral is

∫1ax+b dx=<strong>1a</strong>ln⁡∣ax+b∣+<strong>C</strong>. \int \frac{1}{ax+b}\,dx=<strong>\boxed{\frac{1}{a}}</strong>\ln|ax+b|+<strong>C</strong>. ∫ax+b1​dx=<strong>a1​​</strong>ln∣ax+b∣+<strong>C</strong>.
B

They split the integrand into standard integrals.

C

Because the derivative of ax+bax+bax+b is aaa.

D

Differentiate it and recover the original integrand.

1.8.10 Use of partial fractions in integration (A-level only) Flashcards

  1. A Level
  2. /Maths
  3. /1.8.10 Use of partial fractions in integration (A-level only)

Flashcards for OCR A Level Maths 1.8.10 Use of partial fractions in integration (A-level only), covering the key formulae, methods and definitions you need to recall for Paper 1, Paper 2 and Paper 3. 23 cards, matched to the OCR A Level Maths (H240) 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.