📚 PDF Joiner (4) Q52: Advanced Integration by Substitution | PDF合并(4) 第52题：高级换元积分法
This article provides a detailed walkthrough of a challenging integration problem from the Edexcel A-Level Mathematics syllabus, inspired by questions in the PDF Joiner compilation (page 4, Q52). Mastering integration by substitution is essential for tackling complex integrals involving radicals, rational functions, and trigonometric expressions.
本文深入讲解一个来自 Edexcel A-Level 数学大纲的高难度积分问题，题目灵感来自 PDF 合并文件（第4页第52题）。掌握换元积分法对于处理含有根号、有理函数和三角表达式的复杂积分至关重要。
1. Problem Statement | 题目陈述
The specific integral we will solve is ∫ x³ / √4 - x² dx. This is an indefinite integral where the integrand contains a polynomial numerator and a square root in the denominator. The goal is to find an antiderivative expressed in terms of x.
我们要解决的积分是 ∫ x³ / √4 - x² dx。这是一个不定积分，被积函数的分子是多项式，分母带有平方根。目标是求出用 x 表示的原函数。
2. Selecting the Appropriate Substitution | 选择恰当的换元
When facing an integral
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