Integration by Parts

Integration by parts the easiest and probably the most popular method for integration components and finding the area under the curve. This can get very complex, very fast. 

It is important when looking at an equation to try and work out what you want to be your u and v. The best way for this is to use LogAlgTrigExp. You may see the connection, you may not. When initially looking at the equation if the equation contains a logarithm then make that your u, if not use an algebraic expression, if this again doesn't exist use a trigonometric expression and finally use an exponential function. 

Shown below is the integration by parts equation as well as a quick example