The list

The big list

Basics

Integrals using only the definition and linearity. Let F^\prime(x) = f(x) and G^\prime(x) = g(x)

• \int f(x) \, dx
• \int f(x) + g(x) \, dx
• \int k f(x) \, dx
• \int -f(x) \, dx
• \int af(x) + bg(x) \, dx

Inverse power rule

For this section apply the following

Definition (Inverse power rule)

For all n \in \mathbb{R} \backslash \{-1\} \int x^{n} dx = \frac{x^{n+1}}{n+1} + C.

• \int x \, dx
• \int x^2 \, dx
• \int \, dx
• \int 2x^2 - 3x - 1 \, dx
• \int \sqrt{x} \, dx
• \int x^\pi \, dx
• \int \frac{1}{\sqrt{x}} \, dx