A-level · Integration

Integrating standard functionsExam-style questions

The integrals you get by reading the derivative table backwards — e^x, sin, cos, sec² and 1/x. Why a linear inside, such as e^(3x) or cos 2x, means dividing by its coefficient; the signs on sine and cosine; why 1/x integrates to ln|x|, modulus included; reciprocals of linear functions; and exact values when these appear in definite integrals.

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

DifficultyAll Level 2 Level 3

1
Find $\displaystyle\int \left(e^{2x} + \cos 3x - \frac{4}{x}\right) dx$ .
Level 2 · 3 marksTry it
2
Find $\displaystyle\int \frac{1}{2x - 1}\,dx$ .
Level 2 · 2 marksTry it
3
Find $\displaystyle\int (4x + 3)^7\,dx$ .
Level 2 · 2 marksTry it
4
Find $\displaystyle\int \left(6\mathrm{e}^{3x} - \sin x\right) dx$ . (3 marks)
Level 2 · 3 marksTry it
5
Find $\displaystyle\int \dfrac{3}{2x + 5}\,dx$ . (3 marks)
Level 2 · 3 marksTry it