Calculus

5.

Antiderivatives and Indefinite Integration

5.1.

Introduction to Antiderivatives

5.1.1.

Definition of Antiderivative

5.1.2.

The Most General Antiderivative

5.1.3.

Notation for Indefinite Integrals

5.1.4.

Relationship Between Differentiation and Integration

5.2.

Basic Integration Formulas

5.2.1.

Power Rule for Integration

5.2.2.

Integrals of Exponential Functions

5.2.3.

Integrals of Trigonometric Functions

5.2.3.1.

Sine and Cosine

5.2.3.2.

Secant Squared and Cosecant Squared

5.2.3.3.

Secant Tangent and Cosecant Cotangent

5.2.4.

Integrals Involving Logarithms

5.2.5.

Integrals of Inverse Trigonometric Functions

5.3.

Basic Integration Techniques

5.3.1.

Integration by Substitution

5.3.1.1.

u-Substitution Method

5.3.1.2.

Choosing Appropriate Substitutions

5.3.1.3.

Definite Integrals with Substitution

5.3.2.

Integration by Parts

5.3.2.1.

Formula and Strategy

5.3.2.2.

Choosing u and dv

5.3.2.3.

Repeated Integration by Parts

5.3.2.4.

5.4.

Initial Value Problems

5.4.1.

Setting Up Initial Value Problems

5.4.2.

Solving for Particular Solutions

5.4.3.

Applications to Motion Problems

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6. The Definite Integral