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AP CALCULUS · MODULE 03B

Techniques of Integration
Advanced Methods for BC Calculus

Master the integration techniques required for AP Calculus BC: u‑substitution, integration by parts, polynomial long division, partial fractions, trigonometric substitution, improper integrals, and more.

📘 BUders Learning System
This module covers the most important integration techniques. Topics with 🔷 are BC Calculus only.
🔄 01
Substitution Rule
$\int f(g(x)) g'(x) dx = \int f(u) du$ — the "reverse chain rule" for both indefinite and definite integrals.
u‑substitution → start
✖️ 02
Integration by Parts
$\int u \, dv = uv - \int v \, du$ — derived from the product rule. Essential for products of functions.
integration by parts → start
➗ 03
Polynomial Long Division
When the degree of the numerator is greater than or equal to the degree of the denominator — simplify before integrating.
preparation → start
🧩 04
Partial Fractions (BC)
Decomposing rational functions $\frac{P(x)}{Q(x)}$ into simpler fractions — a BC Calculus topic.
🔷 BC only → start
🔷 05
Trigonometric Substitution (BC)
For $\sqrt{a^2 - x^2}$, $\sqrt{a^2 + x^2}$, $\sqrt{x^2 - a^2}$ — $x = a\sin\theta$, $x = a\tan\theta$, $x = a\sec\theta$.
🔷 BC only → start
♾️ 06
Improper Integrals (BC)
Integrals with infinite limits or unbounded integrands — limits of definite integrals.
🔷 BC only → start
📝 07
Practice Problems
20 solved problems covering all techniques of integration.
practice → start
🧪 08
Test Yourself
20-question interactive quiz with instant feedback.
assessment → start