Why I don't teach LIATE (integration by parts trick)

0:00 why I don't use LIATE (also called LIPTE) for integration by parts
0:17 integral of x^2*ln(x)
2:11 integral of x*sin(x)
3:55 check out Brilliant
4:49 integral of sec^3(x)
9:05 *hard* integral of ln(x)/(1+ln(x))^2
14:43 bonus example

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[blackpenredpen]

It doesn’t matter if it’s ILATE or LIATE. Since if you have an integral with both log and inverse function, then it’s most likely not doable in the first place 😆

[gcewing]

I prefer the LATTE method. If the integral looks hard, go and make yourself a coffee.

[shehnazsalahuddin]

I believe that by inspection we can easily see which one is easier to differentiate and which one to integrate. This idea or sense helps students in the long run. Tricks might help for short term, but not for the long run. This also helps students to recognise different patterns and get familiar with mathematics.

[turtledruid]

My calc 2 teacher taught us the LIATE method but didn't make us use it if we didn't want to. Same with the DI method. I personally never used it but for some people it did help. IMO it's just about teaching the tools, not telling the students which ones to use.

[japotillor]

I agree in not using LIATE, it's not about memorising a mechanic, I like having the openness of realising a mechanic doesn't always work. When I teach integration by parts, I always teach find the function to integrate first

[reidpattis]

I feel like most Mathematicians do this anyways subconsciously. And it is a good first instinct to have to quickly solve problems. But there are cases that don't quite work, and I think it's up to the student to discern for themselves.

[shubhankurkumar]

My first class of calculus was in 11th grade in India, that's Junior Year in America. We were always taught ILATE, explanation was "Choose whichever is the harder to integrate" and like you said, it works in almost all scenarios.

Wherever there was an exception we were given the solution and were told the specifics.

It's the first time I'm hearing of DI method. Pretty amazing!!

[richardryan]

Excellent video. Before I retired, I told my students that LIATE is a nice "rule of thumb" but, when integration by parts is applicable, LIATE does not work 100% of the time. The example I used to demonstrate this fact is the integral of (xe^x)/(x+1)^2. in this case, the factor to be differentiated is xe^x and the factor to be integrated is 1/(x+1)^2.

[alessiodaniotti]

Another way to deal with sec^3 is:
sec^3(x)= 1/cos^3(x)= cos(x)/cos^4(x)=
and with a substitution: sin(x)=u ; cos(x)dx=du
we have the integral of 1/(1-u^2)^2 wich is a rational funcion, so quite easy to integrate.

Is a method that works for 1/cos^n(x)and 1/sin^n(x) for every odd n.

[seanbastian]

The way I learned the LIATE method was that you should use it when first attempting the question. They said it won't always work, but it can help you start working out the problem.

[abdelkaderzeramdini]

For the integral of xsin(x^2) there is no need of integration by parts. Just U-substitution let u=x^2 so du=2xdx
It becomes integral of-1/2cos(u) and the final answer is-1/2cos(x^2)+C

[tortillajoe]

My teacher didn’t like the idea of restricting us to LIATE so we instead subscribed to a some rules of thumb. These are the ones I remember, still use, and are almost always enough to make the right choice.
A) If one of the functions has cyclic (sines, cosines, exponentials, etc.) or terminal derivatives (polynomials), let that one be the one you differentiate. Unless the other function’s integral is unknown or unsolvable by you, in which case…
B) Let the most difficult of the functions that you CAN use integrate be the one you integrate.

[davcaslop]

In spanish we say ALPES:
A=arcsin, arccos, arctan, etc.
L=logs
P=polynomios
E=exponential
S=sin, cos, tan, etc.

It's said that not always work but it has always work for me with this set.

[easyfundbles]

for guys lived in morocco 🇲🇦, they have been using a technic called "ALPES" istead of laatte
A -Arctan, arcsin,arcos
L - ln
P - polynomial
E - Exponential
S -Sin, cos, tan

[aggman]

I just discovered your videos last week but have only seen ones from about 5 years ago. Having seen them and just coming across this one and the change from no beard to beard is the best thing I've seen in a while

[lutherlessor]

This video is great. There's always that tension between "tools that are very helpful most of the time" and "concepts that work nearly all the time, " and you balanced this excellently in this video with examples to both sides. 💪

[Samir-zbxk]

For integral of xsin(x^2)dx in the end card: its easier to do u-sub then by parts

u=x^2, dx=du/2x

integral of xsin(x^2)dx
=1/2 * integral of sin(u)du
=1/2 * -cos(u)
=-1/2 * cos(x^2)+c

[tholod]

It's fun, in France we have ALPES, for arccos/arcsin ; log ; polynomial ; exponential ; sinusoidal. At the time I learnt integration, my teacher said like you that it is better to search which part is better to integrate than use this tip.

[Kiwinov]

I completely agree, you can't exactly impose strict rules for calculus. It always matters the type of problems you are solving and thinking a few steps ahead is the key. I always hated that rule

[TkK]

I haven't finished the video, but I'm so much satisfied by the way you change markers (so Smooth dude) 😂❤️