Question

Integration by parts: ILATE
Does e fall under the category of logarithms or algebraic?

Answer 1

please post your full question.

Answer 2

e is just a number, not an operation, so it doesn't fall under any category.
If you mean stuff like e^x, the exponential operation,
then it falls under E, exponentials... :D

Answer 3

e is just a number just like i^2

Answer 4

The LIATE rule

L log. functions
I inverse trig. functions
A algebraic functions
T trig functions
E exponential functions

Answer 5

functions like e^x
are exponential functions

Answer 6

\[\int\limits_{}^{}e^{2x}x^2\]

Answer 7

which would I choose to be my u? Sorry for the delay computer died while I was at the coffeeshop

Answer 8

u is the one that you want to "destroy" so to speak.

If you let e^{2x} be your u,\[\large\rm e^{2x}\qquad\to\qquad 2e^{2x}\qquad\to\qquad 4e^{2x}\]The derivatives don't "break it down", do they?



If you instead let x^2 be your u,\[\large\rm x^2\qquad\to\qquad 2x\qquad\to\qquad 2\qquad\to\qquad 0\]It breaks down much nicer, yes?
Giving you much simpler stuff in your "new integrals" that show up from IBP.

Answer 9

I don't really like the ILATE thing or whatever...
You just have to use logic and remember some of the "tricks" they teach you.
For the most part its just about breaking down your u.

But yes,
be aware of some of the tricks required for integrals like this, \(\int e^x\sin x~dx\)

Answer 10

This is another one that requires a little tricky thinking instead of immediately trying to break down the x: \(\int 2x\arctan x~dx\)