H2 Maths Notes (JC 1-2): 5.3) Integration Techniques

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07 Oct 2025, 00:00 Z

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Q: What does H2 Maths Notes (JC 1-2): 5.3) Integration Techniques cover?
A: Substitution, parts, partial fractions, and special integrals for H2 Maths Topic 5.3.

Before you revise
Build a flowchart for integration: recognise the pattern (substitution, parts, partial fractions, trigonometric identities) before diving in. Always write differential substitutions explicitly.

Status: SEAB H2 Mathematics (9758, first exam 2026) syllabus last checked 2025-11-29 (PDF last modified 2024-10-16). Topic 5.3 scope unchanged; Section A still contributes 70 marks per paper (Pure Mathematics).

Core Formulae

Reverse of differentiation rules (power, exponential, trigonometric, logarithmic).
Integration by substitution: choose $u = g(x)$ to simplify integrand, rewrite $\mathrm{d}x = \dfrac{\mathrm{d}u}{g'(x)}$

Order	Pick this first when
I	an Inverse trigonometric term (e.g. $\operatorname{arctan} x$ ) appears
L	a Logarithmic term (e.g. $\ln x$ ) is present
A	an Algebraic factor (polynomial or rational) remains
T	Trigonometric or hyperbolic functions turn up
E	finally, the Exponential factor $e^{g(x)}$

H2 Maths Notes (JC 1-2): 5.3) Integration Techniques

Core Formulae

Substitution Examples

Integration by Parts

Partial Fractions

Trigonometric Identities

Improper Integrals and Convergence

Calculator Workflow

Exam Watch Points

Sources

Practice Quiz

Quick Revision Checklist

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