choosing u in integrate by parts, i know there is formula call LIATE, but what if there is hyperbolic function?

Question

hero · Answer

In that case, just memorize this: https://en.wikipedia.org/wiki/List_of_integrals_of_hyperbolic_functions

anonymous · Answer

thanks for the link but what i meant is if we have this kind of question
$$\int\limits e ^{-3x}  coshx dx$$

anonymous · Answer

which one is u and which one is dv?

hero · Answer

The one that is easiest to take the derivative of should be u. That way you can easily find du.

hero · Answer

Also you might find this helpful. If I were you, I'd avoid using LIATE. It doesn't work for all integration by parts. The table method is better.

hero · Answer

http://pages.pacificcoast.net/~cazelais/187/tabular.pdf

hero · Answer

So yeah, between the two functions, the one easiest to derivate should be u. The one easiest to integrate should be dv. This is a general guideline. Between these two rules, you should be able to figure out which function is convenient to label u and which is convenient to label dv.

ganeshie8 · Answer

IBP works just fine. As an alternative, you could also replace $\cosh x$ by  $\dfrac{e^x+e^{-x}}{2}$

anonymous · Answer

sor for the tabular method, which one is suppose to differentiate and which one should be integrate

anonymous · Answer

it is the same as choosing u and dv??

ganeshie8 · Answer

that is a definition of hyperbolic cosine function

anonymous · Answer

thanks for the notes guys.