plumiIntegration by substitution: AQA A‑Level Maths questions
AQA A-Level Maths past-paper questions on H.6 Integration by substitution, 2018–2025, with mark schemes and examiner’s reports where available. Add MadAsMaths questions to your practice, or browse them separately by topic and difficulty.
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All 6 questions on Integration by substitution, as a list
- June 2025, Paper 1, Q17 (10 marks): (a) Use the substitution u = ex + 1 to show that ∫ e2x ex + 1 dx = ex – ln(ex + 1) + k [5 marks] 17 (b) Solve the differential equation ( ex + 1 e2x ) dy dx = c
- June 2024, Paper 1, Q18 (11 marks): (a) Use a suitable substitution to show that ∫ 4 0 (4x + 1)(2x + 1) 1 2 dx can be written as 1 2 ∫ 9 a (2u 3 2 – u 1 2)du where a is a constant to be found. [5
- June 2023, Paper 3, Q8 (7 marks): Use the substitution u = x5 + 2 to show that (1 0 x9 (x5 + 2)3 dx = 1 180 [7 marks]
- June 2022, Paper 1, Q15 (16 marks): (a) Given that y = cosecy 15 (a) (i) Express y in terms of siny. [1 mark] 15 (a) (ii) Hence, prove that dy dy = × cosecy cot y [3 marks] 15 (a) (iii) Show that
- November 2020, Paper 2, Q5 (6 marks): Use integration by substitution to show that (6 −1 4 x 4x + 1 p dx = 875 12 Fully justify your answer. [6 marks]
- June 2018, Paper 3, Q8 (9 marks): (a) Prove the identity sin 2x 1 + tan2 x × 2 sin x cos3 x [3 marks] 8 (b) Hence find ( 4 sin 4y 1 + tan2 2y dy [6 marks]
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