Integral

[olive spoke]

It needs to be solved using euler sub.

[rough canyon]

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[old trellis]

Well, do you remember the three Euler substitutions and when to use them?

[olive spoke]

yes i know the sub

but idk why im lagging so much

i believe its the third sub

when both a and c are negatives

a and x in the the

sqrt(ax^2 +bx +c)

[old trellis]

Both negative? Maybe our classification is a bit different.

Can you show what you did?

[olive spoke]

its in my note book arghh

wait

1 sec

cus i dont have my phone on me

[old trellis]

Don't worry, take your time!

[olive spoke]

ty ty

i think im just probably doing some stupid mistake when differentiating

or even worse when multiplying or some algebra like that

[old trellis]

Ah, alright, it's also the third according to my classification.

Let me check whether you found x correctly...

[olive spoke]

okay ty

i did not

i just looked at it

damn

[old trellis]

Ah, I see the mistake, yeah.

[olive spoke]

what mistake

i put -t^2

hahahahah

shit

[old trellis]

Yeah, this should be a plus.

[olive spoke]

damn it

wait imma retry

then ill get back to u if im struggling

should i make a new post?

or

how does it work

do i just come back here

[old trellis]

Nah, let's continue here.

Same question, after all.

[olive spoke]

ok bet gimme a few

i think i did it

[old trellis]

Alright, nice!

[old trellis]

Yeah, something like that.
Note that due to the domain of our function we can also do √((2 - x)(x - 1))/(x - 1) = √((2 - x)/(x - 1)).

[olive spoke]

yeah

i wanted to do it like that

js didnt wanna

fiddle with it

too much

[old trellis]

Well, yeah, it's not required, of course.

[olive spoke]

if u can see

in top right

i wrote that

but js didnt use it

[old trellis]

Ah, yeah!

[olive spoke]

but yeah thank u kindly fr!

[old trellis]

You're welcome!

[olive spoke]

i need to have more water near me and get good sleep

[old trellis]

Been a while since I've used Euler substitutions.

I usually go for trigonometric or Abel.

[olive spoke]

its not required per se here

but its the only one we learn

for these types of integrals

we are allowed to use different ones

[old trellis]

Yeah, I get that. I did the same in my previous uni.

We learned Euler, Abel and Chebyshev.

[olive spoke]

i just always mess up in these small things like forgetting to change a minus or smth minor like that

[old trellis]

The first two are cool, but trigonometric is usually enough. The latter is quite nice, since it also tells you when the antiderivative is non-elementary.

[olive spoke]

euler did work out pretty nicely here though i must say

things cancelled out pretty good

[old trellis]

Yeah.

Really, when you have a root of a quadratic in the denominator, that tends to happen.

[olive spoke]

its a shame we dont utilise trig subs to their full capacity her

its justthat we dont rly learn trig identities with sec and csc here (in highschool)

so they just dont teach the subs using them in uni either

[old trellis]

Huh, really? That's a shame.

[olive spoke]

yeah

like i mean we learn what sec and csc are

like i mean 1/cos and 1/sin

but nothing else

[old trellis]

Interesting. Kinda the reverse in Russia: identities are given in school, but sec and csc are rarely used in writing.

[olive spoke]

and maybe just the derivatives on the derivative table

but never in like half angle, double angle

etc etc

[old trellis]

Odd.

Well, I certainly recommend learning them.

[olive spoke]

yeah ive written down all the stuff to remember and am just practicing them and reading them throughout the day or whenever im free rly

but yea i should get to studying

tysm man!

[old trellis]

You're welcome, good luck!

[olive spoke]

do i close this or just leave it as is

[old trellis]

Better to close it if you're done.

[olive spoke]

ah alrighty