# Modified Tabular Integration

Several weeks ago Dr. Qibo Jing an AP teachers at Rancho Solano Preparatory School in Scottsdale, Arizona, posted a new way to approach tabular integration to the AP Calculus Community discussion group.  He calls this the Modified Tabular Method. The algorithm makes repeated integration by parts quicker and more streamlined than the usual method. The…

# Integration by Parts 2

Sometimes when doing an Antidifferentiation by Parts, the resulting integral is simpler than the one you started with but requires another, perhaps several more, antidifferentiations. You can do this but it can get a little complicated keeping track of everything especially with all the minus signs. There is an easier way. Let’s consider an example:…

# Integration by Parts 1

The antidifferentiation technique known as Integration by Parts or Antidifferentiation by Parts is based on the formula for the Product Rule: . Solve this equation for the second term on the right: . Integrating this gives the formula . By the FTC the first term on the right can be simplified giving the formula for…