The indefinite integral, or antiderivative, reverses differentiation. Master the fundamental techniques: substitution, integration by parts, and special methods for rational and irrational functions.
Reverse of differentiation
Chain rule in reverse
Product rule in reverse
Euler & partial fractions
Derivatives, chain rule, product rule
Continuity, intermediate value theorem
Identities, inverse trig functions
Polynomial division, partial fractions
Definition of antiderivative (primitive function), indefinite integral notation, and fundamental properties.
Fundamental integration formulas for power, exponential, logarithmic, and trigonometric functions.
First and second substitution methods (u-substitution and inverse substitution) with trigonometric and algebraic techniques.
The integration by parts formula, LIATE rule, reduction formulas, and tabular integration.
Integration of rational functions, trigonometric rational functions, and irrational functions with Euler substitutions.