Calculus - Integration - Summary of the steps for integrating.
There are many formats for functions which we need to integrate.
The most common formats for the functions we encounter - especially at first - can be integrated with the following steps:
| Step 1: | Copy any constant in front of the term. |
| Step 2: | Rewrite the x (or whatever pronumeral is being used - the other common pronumeral is t). |
| Step 3: | Add 1 to the index (except if it is -1 - see later under logs). |
| Step 4: | Divide the x term by the new index. |
| For a term in brackets raised to a power. | Follow the steps above but then divide by the new index for the brackets. NOTE: the terms in the brackets can only have a power of 0 or 1 (i.e. be terms in x or constants). |
Other strategies:
1. Negative indices and fractional indices are treated in the same way as integer indices - EXCEPT when the index value is -1. Then you check the Integration page for Logarithms.
2. If a function is in brackets, has terms raised to powers or are roots) and the brackets are raised to a power of say 2 (or maybe 3) expand the brackets and then integrate each term separately.
3. If you have to integrate two functions in x (or a pronumeral) multiplied together or divided one into the other, check the approach for the Reverse Chain Rule.