Integration+Techniques-+Power,+Chain,+Log+or+Exp,+u-substitution

=__Rules for Integration__= Integration, like Differentiation, has many rules and techniques that make finding the integral much simpler.

//Power Rule for Integrals//
Find the anti-derivative of x 2 +2x+1.
 * Example One **

Solution: By the power rule and the addition property above, we will add one to each exponent and then divide each term by the new exponent: This yields: **(1/3)x 3 +x 2 +x+C**.

//Chain Rule for Integrals: u-Substitution//
The opposite of the chain rule we learned earlier is Integration by substitution. We will set the variable "u" equal to the inner function, and then take the derivative of this equation in order to get all of the integral's terms in terms of "u" and "du" Please see the following example.


 * Example Two **