Integration - rules

The integration rules are the differentiation rules in reverse.
 

multiply by the index reduce the index by 1	increase the index by 1 divide by the new index

The last result requires explanation. Consider the direction field for .

Solutions are given by:

• if 
• if 

This is abbreviated to .

The chain rule in reverse works easily for power and exponential functions of linear expressions.
 

Guess and check is always an option for the chain rule in reverse, especially when the function does not involve a linear expression.

The chain rule in reverse leading to a log result requires that the numerator is the derivative of the denominator.