Integration by Parts | 40 Worked Examples | Edexcel A-Level Maths

40 progressive Edexcel A-Level (9MA0) integration by parts questions with full mark-scheme style worked solutions.

What’s inside:
Easy: single-application classics such as the integrals of x e^x, x sin x, ln x, x cos 2x and x sec^2 x.
Medium: repeated application (x^2 e^x, x^2 sin x), x ln x and x^2 ln x, the cyclic integrals of e^x sin x and e^x cos x, and definite integrals evaluated between limits.
Hard: triple application (x^3 e^x), inverse-trig integrals (arctan x, x arctan x), cyclic integrals with coefficients (e^2x sin 3x), (ln x)^2 and x(ln x)^2, an area application, the integral of sin(ln x), and a reduction formula proof.

Every solution applies LIATE selection explicitly, breaks the working into one atomic step per line with an annotation on each, and places B1, M1 and A1 marks exactly where the mark scheme awards them. The cyclic and reduction questions carry extra explanation of the underlying trick.

Ideal for: Year 13 students sitting Edexcel A-Level Mathematics (9MA0) Paper 1 / Paper 2 Pure, plus tutors and teachers building targeted practice. Print-friendly, hand straight to students.