Indefinite Integrals

Abstract

There are a lot of integration rules. Look through them all. Some of them will seem trivial if you've seen the differentiation rules.

Trig identities are useful
Guessing and fixing: usually, in the case of composition, we may try to integrate the first function. Then, differentiating it, we find extra coefficients moved out, so we have to include the inverse of those.
Always a good idea to verify by differentiation

Definition

The indefinite integral of is the collection of all possible antiderivatives. We denote if by:

Integration Rules

Power rule
- "Increase the exponent by 1, then divide by the new exponent"
- For
Special case for power rule when
Exponent Rule
Trigonometric Rules

Example

Example - Guess and Fix Up

Evaluate

We guess that this involves . But , so all we need to do it account for the 2

Check your answer

Example

Evaluate .
We need the half angle identity

Example

Evaluate