https://www.eeweb.com/tools/calculus-integrals-sheet

#### Integrals

#### Definition of an Integral

The integral is a mathematical analysis applied to a function that results in the area bounded by the graph of the function, x axis, and limits of the integral. Integrals can be referred to as anti-derivatives, because the derivative of the integral of a function is equal to the function.

#### Properties

#### Common Integrals

#### Integration by Substitution

where and

#### Integration by Parts

where

#### Integration by Trigonometric Substitution

Trigonometric identities can be use with integration substitution to simplify integrals. There are three common substitutions.

##### First Trigonometric Substitution

To take advantage of the property

Substitute

After substitution

##### Second Trigonometric Substitution

To take advantage of the property

Substitute

After substitute

##### Third Trigonometric Substitution

To take advantage of the property

Substitute

After substitute