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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+b1dx=<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+b1dx=<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.
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1.8.10 Use of partial fractions in integration (A-level only) Flashcards
23 flashcards on OCR A Level Maths 1.8.10 Use of partial fractions in integration (A-level only): the key formulae, methods and definitions you need to recall for Paper 1, Paper 2 and Paper 3.