Integration is one of the basic and key calculations in the field of analysis. Below is a collection of integral formulas, generalized, extended, trigonometric, basic, partial, antiderivative integral formulas... for your reference.
Table of Contents

Basic integral
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Integration by parts
According to the rule of taking the derivative of a product:
d(uv) = udv + vdu
Integrating both sides we get:
uv = ∫udv + ∫vdu
From here we have the following formula:
∫udv = uv − ∫vdu
Trigonometric integral
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Definite integral
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Extended integral
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Indefinite integral
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Integration of rational functions
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example of integral calculation
Calculate the following integrals:
Example 1:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example 2:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example 3:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example 4:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example 5:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
Example 6:
![Basic integral formulas, by parts, trigonometry, identification and expansion Basic integral formulas, by parts, trigonometry, identification and expansion]()
In addition to the above integral formulas, you can refer to the most complete derivative and trigonometric derivative formulas .