In this lecture you will learn how to Integrate by Parts. Professor Murray will explain how Integration by Parts originates from the Product Rule and why you should use it. You will also learn how to speed up the process by using Tabular Integration and the mnemonic 'LIATE' (Logarithmic, Inverse Trigonometric, Algebraic, Trigonometric, and Exponential).
Integration by parts never solves the integral completely for you. The point is
to reduce a difficult integral to an easier one.
If you have a polynomial multiplied by an exponential or trigonometric
function, you can use the tabular integration shortcut.
You may have to use parts more than once in the same problem.
Sometimes, after using parts one or more times, you get the original integral
reappearing. Then you can set up an equation for the original
integral and find the solution algebraically without doing any more
Use the mnemonic LIATE (Logarithmic, Inverse, Algebraic, Trigonometric,
Exponential) to know which part of the expression to make the u.
Sometimes you have to make one or more substitution before you get a form that
works well for integration by parts.
Integration by Parts
Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.