6.2 - Antidifferentiation by Subsitution

Indefinite Integral

The indefinite integral is the family of all antiderivatives of a function $f(x)$, denoted by $\int (x)dx$. If $F(x)$ is an antiderivative of $f$, then $\int (x)dx=F(x)+C$ where $C$ is the constant of integration.

• A definite integral (what we have seen up to this point) is bounded, and so it’s a number.
• An indefinite integral is a family of functions that all have the same derivative.

Properties of Indefinite Integrals

U-Substitution for Integration