Question
Sat November 12, 2011 By: Raunak Jain

ILATE: I HAVE SEEN IN SOME BOOK... THAT ITS WRITTEN ILAET ... I WISH TO KNOW... WHETHER WE CAN CHANGE ITS ORDER ANYWAY WE LIKE... WHATS THE BASIC LOGIC BEHIND IT??

Expert Reply
Sat November 12, 2011
ILATE means Inverse Logarithmic Algebraic Trigonometric and Exponential
 
and 
 
ILAET would mean 
Inverse Logarithmic Algebraic Exponential and Trigonometric
 
This is for assigning the priority while using integration by parts
 
It is not a hard and fast rule, sometimes it can be more easy
to integrate the trigonometric function and in other cases
the exponential function. That is why few books prefer the first and few
the later. 
 
The logic is the idea that whatever function is easy to integrate becomes
the first choice, and so it can vary between trigonometric and exponential
function depending upon the question involved.
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