We have all seen various questions of integral around us wherein we were given “two varieties” of functions multiplied together. It looks like
![\[ \int\of\ udv=uv-\int\of\ vdu \]](https://i0.wp.com/tutortonight.com/wp-content/ql-cache/quicklatex.com-6905a8ad45a4e1cd61c23ca28effa404_l3.png?resize=175%2C40&ssl=1 "Rendered by QuickLaTeX.com")
We often ponder about which one is u and which one is v? That’s where ILATE, LIATE or DETAIL (just to remember we added “D”) comes in. We will stick with ILATE in our discussion.
Every letter corresponds to a function type:
I – Inverse
L – Logarithm
A – Algebraic
T – Trigonometry
E – Exponent
Here is a short video explaining how to use ILATE: