# Antiderivatives From Derivatives of Basic Functions

## Antidifferentiation

Antiderivatives and indefinite integrals are defined. Constants of integration and integrands are also defined.

Course Material Related to This Topic:

## Antidifferentiation: Guess-and-Check

Guess-and-check method for finding antiderivatives. Includes an example and some helpful rules.

Course Material Related to This Topic:

## Introduction to Anti-Derivatives

Definition of the indefinite integral or anti-derivative and its use in finding information about a function when its derivative is known.

Course Material Related to This Topic:

## Non-Uniqueness of Anti-Derivatives

Discussion of the fact that any constant can be added to an antiderivative without changing the validity of that antiderivative.

Course Material Related to This Topic:

## Anti-Derivatives by Inspection

Applying differentiation rules backwards to find anti-derivatives. A list of types of functions that can or cannot be anti-differentiated. Linearity of the operation of anti-differentiation.

Course Material Related to This Topic:

## Basic Techniques for Integrals

Rules for integrating polynomials and other simple integrals by inspection, as well as techniques for integrating by substitution, parts, and partial fractions.

Course Material Related to This Topic:

## Evaluating Definite Integrals

Five-part problem evaluating integrals involving the substitution method, logarithmic functions, and trigonometric functions.

Course Material Related to This Topic:

## Antiderivatives Using Polynomial Division

Computing the antiderivative of a fraction of two polynomials.

Course Material Related to This Topic:

## Indefinite Integrals

Course Material Related to This Topic:

Three integrals to be evaluated.

Two integrals to be evaluated.

## Trigonometric and Logarithmic Integrals

Deriving a trigonometric formula and differentiating a logarithmic expression, then using those results to evaluate two integrals.

Course Material Related to This Topic:

## Definite Integrals

Two integrals to be evaluated.

Course Material Related to This Topic:

## Trigonometric Formulas and Identities

A list of trigonometric and inverse trigonometric identities and formulas involving integrals and derivatives.

Course Material Related to This Topic:

## Differentiation Formulas: Polynomials, Products, Quotients

Five questions which involve taking derivatives and antiderivatives of polynomials, finding the points on a graph which have horizontal tangent lines, and finding derivatives of rational functions.

Course Material Related to This Topic:

## Differentials and Indefinite Integration

Three questions which involve evaluating five differentials and twenty indefinite integrals using a range of techniques.

Course Material Related to This Topic:

## Inverse Trigonometric and Hyperbolic Functions

Six questions which involve evaluating integrals and derivatives of these functions, as well as graphing them and finding tangent lines or average values.

Course Material Related to This Topic: