We focus on integrating using substitution, from Topic 6.9 of AP Calculus, which is useful when direct integration isn't possible. The key to successful substitution is recognizing a function and its derivative within the integrand.

When an integral contains a function alongside its derivative, we can apply substitution effectively. We do this by setting u equal to the function we've identified, simplifying the integral, and then integrating with respect to u.

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Unit 6 of AP Calculus is all about Integration and Accumulation of Change:
6.1 Exploring Accumulations of Change
6.2 Approximating Areas with Riemann Sums
6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
6.4 The Fundamental Theorem of Calculus and Accumulation Functions
6.5 Interpreting the Behavior of Accumulation Functions Involving Area
6.6 Applying Properties of Definite Integrals
6.7 The Fundamental Theorem of Calculus and Definite Integrals
6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
6.9 Integrating Using Substitution
6.10 Integrating Functions Using Long Division and Completing the Square
6.11 Integrating Using Integration by Parts (BC only)
6.12 Using Linear Partial Fractions (BC only)
6.13 Evaluating Improper Integrals (BC only)
6.14 Selecting Techniques for Antidifferentiation

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