3 Integration by Parts dv is easy to integrate. u differentiates to zero (usually).The Integration by Parts formula is a “product rule” for integration.Choose u in this order: LIPETLogs, Inverse trig, Polynomial, Exponential, Trig
8 A Shortcut: Tabular Integration Tabular integration works for integrals of the form:where:Differentiates to 0 in several steps.Integrates repeatedly.Example:
9 Example This is the expression we started with! This is called “solvingfor the unknown integral.”It works when both factors integrate and differentiate forever.
10 How to choose u and dvTry to choose u so that du (its derivative) becomes easier to integrate than u.If ln is present, then u must be ln.Oftentimes, let u be the powers of x.Also, choose dv so that it is easy to integrate dv.If ex is present, let dv = ex dxOftentimes, let dv be the sin or cos.After integrating by parts, you should wind up with the integral that is “easier” to integrate.