How to know if an antiderivative exists before I try to find it?

A

Al-Layth

Junior Member
Joined
Dec 28, 2021
Messages
83
I have seen people deduce at a glance that an integrand's antiderivative does not exist in terms of elementary functions. How do they do this?
 
Al-Layth said:
I have seen people deduce at a glance that an integrand's antiderivative does not exist in terms of elementary functions. How do they do this?
Click to expand...
All integrals exist, of course. But the bulk of them can only be done numerically. The answer to your question is lots and lots of practice. You learn to recognize specific forms over time, those that can be done and those that can't. Certain fields of study usually have typical types of integrals and you can specialize from those. For example, in Mechanics, common undoable integrals are those of the form of elliptic integrals. Similar comments also apply to Differential Equations, which can be seen as a kind of integration.

Remember those integral tables you thought I was being facetious about? If you learn how to do them you will have a good grasp of which integrals can be done.

-Dan
 
You must log in or register to reply here.
Top