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

A complete, fully worked set of 40 integration by parts questions for AQA A-Level Mathematics (7357), covering specification section H5 in full. Every solution is broken down one atomic step at a time, with a plain-English note on every working line and mark-scheme codes (M1, A1) placed exactly where the real AQA scheme rewards them, so students see not just the answer but precisely how marks are earned. The pack runs from gentle entry-level integrals up to genuinely demanding synoptic problems, split into 12 Easy, 16 Standard and 12 Challenging questions with continuous numbering. It teaches the LIATE rule for choosing u, the hidden product-with-one trick for integrating ln x, arctan x and arcsin x, repeated application of parts to grind powers of x down, definite integrals with careful limit substitution, and the cyclic boomerang method for integrals such as e^x sin x, e^2x cos 3x and sin(ln x) that reappear and must be solved algebraically. Reduction formulae are deliberately excluded, matching the AQA specification boundary. Extra-verbose explanations are woven into the harder questions to build genuine understanding of why each method works and to flag the classic sign-flip and interval traps that lose marks. Ideal for Year 13 revision, homework, cover lessons or targeted intervention. Answers are given in exact form throughout and have been hand-verified for accuracy.