A-level · Integration

Integrating with partial fractionsExam-style questions

Integrating a rational function by splitting it into partial fractions, so each piece integrates to a logarithm. When a fraction needs splitting; finding the numerators; integrating each piece, with the 1/a for a factor ax + b; definite integrals tidied with the laws of logs; dividing first when the fraction is improper; and repeated factors, which give a power rather than a log.

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18 questions · A-level level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 3 Level 4 Level 5

1
Find $\displaystyle\int \frac{3x + 5}{(x + 1)(x + 3)}\,dx$ .
Level 3 · 3 marksTry it
2
Find $\displaystyle\int \frac{4}{(x - 1)(x + 1)}\,dx$ .
Level 3 · 3 marksTry it
3
Find $\displaystyle\int \frac{x + 7}{(x + 2)(x - 3)}\,dx$ .
Level 3 · 3 marksTry it
4
Find $\displaystyle\int \frac{5}{(2x + 1)(x - 2)}\,dx$ .
Level 3 · 3 marksTry it
5
Evaluate $\displaystyle\int_2^4 \frac{4}{(x - 1)(x + 1)}\,dx$ , giving your answer as a single logarithm.
Level 3 · 4 marksTry it

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