Trig Sub, I do not know how to start this problem. | Mathematics | Page 1

fair hinge Sep 27, 2022, 2:09 PM

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I am not sure how to start this problem.

hollow timber Sep 27, 2022, 2:11 PM

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fair hinge I am not sure how to start this problem.

Firstly, put the constant outside the integral, you probably know this

fair hinge Sep 27, 2022, 2:12 PM

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right

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put the 2 outside the integral

hollow timber Sep 27, 2022, 2:12 PM

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ignore the dx

fair hinge Sep 27, 2022, 2:13 PM

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We have a sheet with a bunch of different trig identities and trig sub forms

hollow timber Sep 27, 2022, 2:13 PM

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it will look like this

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$2\int \frac{1}{(x^2-1)^{\frac{3}{2}}}$

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huh

heavy wedgeBOT Sep 27, 2022, 2:15 PM

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PooPoo, not CEO of comedy

fair hinge Sep 27, 2022, 2:15 PM

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gotcha

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from here idk what to do

hollow timber Sep 27, 2022, 2:17 PM

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wait

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uhhh

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let me calculate a bit

fair hinge Sep 27, 2022, 2:17 PM

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kk

silent frigate Sep 27, 2022, 2:17 PM

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Theres actually a really cool method flr these kinda questions

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Other than the obvious trig substitution

fair hinge Sep 27, 2022, 2:17 PM

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really?

silent frigate Sep 27, 2022, 2:18 PM

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The idea is, take out a power of x which has power equal to the denominator of the power of the radical

fair hinge Sep 27, 2022, 2:18 PM

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hm

silent frigate Sep 27, 2022, 2:19 PM

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So what i mean is, for this example, the power is 3/2 right

fair hinge Sep 27, 2022, 2:19 PM

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right

silent frigate Sep 27, 2022, 2:19 PM

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The denominator is 2

fair hinge Sep 27, 2022, 2:19 PM

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yes

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the denominator of the power

silent frigate Sep 27, 2022, 2:19 PM

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So we try to take x^2 out of the x^2-1 part

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Well idk latex so i gotta write that down one sec

hollow timber Sep 27, 2022, 2:20 PM

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hmm

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i was about to use trig sub but blab way seems interesting

hollow timber Sep 27, 2022, 2:20 PM

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silent frigate Well idk latex so i gotta write that down one sec

what do you need to write

fair hinge Sep 27, 2022, 2:20 PM

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If you don't mind

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after we do this way could be do trig sub also

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just so I could see

silent frigate Sep 27, 2022, 2:21 PM

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rn_image_picker_lib_temp_84778c81-2d6e-4985-aa25-830d69eccae8.jpg

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So thats the denomiator of the fraction

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See what happens when u put 1- 1/x^2 as u

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Substituion i mean

fair hinge Sep 27, 2022, 2:22 PM

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right

silent frigate Sep 27, 2022, 2:22 PM

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Did u get it?

fair hinge Sep 27, 2022, 2:22 PM

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wait

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why did it just go from x^2 to x^3

silent frigate Sep 27, 2022, 2:23 PM

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Cuz i took it out of the bracket

fair hinge Sep 27, 2022, 2:23 PM

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ohohho

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I see

silent frigate Sep 27, 2022, 2:23 PM

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So( x^2)^3/2

fair hinge Sep 27, 2022, 2:24 PM

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so now I would make u = 1 - 1/x^2 and do u sub?

silent frigate Sep 27, 2022, 2:24 PM

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Yea

fair hinge Sep 27, 2022, 2:25 PM

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silent frigate Sep 27, 2022, 2:25 PM

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Correct

fair hinge Sep 27, 2022, 2:25 PM

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and just do usub from here?

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interesting

silent frigate Sep 27, 2022, 2:25 PM

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Oh wait have u learnt integration by substitution?

fair hinge Sep 27, 2022, 2:25 PM

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wym

silent frigate Sep 27, 2022, 2:25 PM

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Oh

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Eeeee

fair hinge Sep 27, 2022, 2:25 PM

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we've learned u-sub, integration by parts, and trig sub

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I think that's all?

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maybe

silent frigate Sep 27, 2022, 2:26 PM

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Yea that

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Ah then its fine

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So whats du?

fair hinge Sep 27, 2022, 2:27 PM

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du= 2x^-1

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no?

silent frigate Sep 27, 2022, 2:27 PM

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Nope

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Whats -2-1?

fair hinge Sep 27, 2022, 2:27 PM

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-3

silent frigate Sep 27, 2022, 2:27 PM

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Yep

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Derivarive of x^n = nx^n-1

fair hinge Sep 27, 2022, 2:28 PM

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ahhh

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I went the other way

silent frigate Sep 27, 2022, 2:28 PM

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Yea happens a lot lol

fair hinge Sep 27, 2022, 2:28 PM

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so it would be
0 - -2x^-3

silent frigate Sep 27, 2022, 2:28 PM

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Right

fair hinge Sep 27, 2022, 2:28 PM

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2x^3

silent frigate Sep 27, 2022, 2:28 PM

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Mhm

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Wait

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Raised to minus 3

fair hinge Sep 27, 2022, 2:29 PM

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-3

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i meant

silent frigate Sep 27, 2022, 2:29 PM

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Yea

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Do u see it now?

fair hinge Sep 27, 2022, 2:29 PM

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yes

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I can figure the rest out from here I think

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just regular stuff

silent frigate Sep 27, 2022, 2:29 PM

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Mhm

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Gl

fair hinge Sep 27, 2022, 2:29 PM

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thanks

silent frigate Sep 27, 2022, 2:29 PM

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Np

fair hinge Sep 27, 2022, 2:29 PM

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is the regular trig sub way super long

silent frigate Sep 27, 2022, 2:30 PM

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Nah not really, i think

fair hinge Sep 27, 2022, 2:30 PM

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do you know how to do it?

silent frigate Sep 27, 2022, 2:30 PM

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But the thing about this is u can use it for any power

silent frigate Sep 27, 2022, 2:30 PM

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fair hinge do you know how to do it?

Ah yea

fair hinge Sep 27, 2022, 2:30 PM

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right

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If you have time, could you show me how?

silent frigate Sep 27, 2022, 2:30 PM

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Sure

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I gotta write it down again, one sec

fair hinge Sep 27, 2022, 2:31 PM

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yea no rush

silent frigate Sep 27, 2022, 2:36 PM

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rn_image_picker_lib_temp_356f82eb-d8ea-4d54-ad90-5830fe6daa81.jpg

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Oh wait uhm, wrong pic

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One sec

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rn_image_picker_lib_temp_60ca7c0c-b2de-453f-8a87-94e28d8bacda.jpg

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This is just a standard integral form

fair hinge Sep 27, 2022, 2:38 PM

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hm

silent frigate Sep 27, 2022, 2:38 PM

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If im not being dumb

fair hinge Sep 27, 2022, 2:38 PM

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x = secO

silent frigate Sep 27, 2022, 2:38 PM

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Mhm, do u understand why i did that?

fair hinge Sep 27, 2022, 2:39 PM

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on my paper it says
x^2 - a^2

x=asecO
dx=asecOtanOdO

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the one isn't squared tho

silent frigate Sep 27, 2022, 2:39 PM

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Here a is one so

fair hinge Sep 27, 2022, 2:40 PM

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right

silent frigate Sep 27, 2022, 2:40 PM

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1^2 is 1

fair hinge Sep 27, 2022, 2:40 PM

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ahahhahahah

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makes sense

silent frigate Sep 27, 2022, 2:40 PM

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Mm

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Well honestly i find trig substitution to be a pain in the butt

fair hinge Sep 27, 2022, 2:40 PM

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same

silent frigate Sep 27, 2022, 2:40 PM

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Wooo, u sub gang

fair hinge Sep 27, 2022, 2:40 PM

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however, we just started learning about it friday so

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lmao

silent frigate Sep 27, 2022, 2:41 PM

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Friday huh, this feels pretty tough for someone who just started, idk

fair hinge Sep 27, 2022, 2:41 PM

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maybe it was thursday

silent frigate Sep 27, 2022, 2:42 PM

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Oh yes, one day makes a big difference

fair hinge Sep 27, 2022, 2:42 PM

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yesterday my prof gave all of us an intergral that we had one week to solve. Would you like to see it? (I don't need help on it rn, its a later me problem)

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everyone got a different intergral

silent frigate Sep 27, 2022, 2:42 PM

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Sure ig

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I suck at integration but, ill try

fair hinge Sep 27, 2022, 2:42 PM

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nah you don't have to

silent frigate Sep 27, 2022, 2:42 PM

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I havent even learnt integrarion by parts

fair hinge Sep 27, 2022, 2:42 PM

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wait what

silent frigate Sep 27, 2022, 2:42 PM

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No its fine, i like a challenge every now and then

fair hinge Sep 27, 2022, 2:42 PM

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really

silent frigate Sep 27, 2022, 2:43 PM

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Yea really

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Im self studying

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I dropped off at integrain by parts cuz lazy

fair hinge Sep 27, 2022, 2:43 PM

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so are you not in a calc class?

silent frigate Sep 27, 2022, 2:44 PM

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Nope

fair hinge Sep 27, 2022, 2:44 PM

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damnnn

silent frigate Sep 27, 2022, 2:44 PM

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Heh

fair hinge Sep 27, 2022, 2:44 PM

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nice

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calc 2 kinda tough but

silent frigate Sep 27, 2022, 2:44 PM

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Thanks

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Oof, dont scare me man

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I gotta do sum hw rn

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So ill check thqt question later

fair hinge Sep 27, 2022, 2:45 PM

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I mean if you already know all this clac 2 will be ezpz for you

silent frigate Sep 27, 2022, 2:45 PM

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It was cool meetingu

silent frigate Sep 27, 2022, 2:45 PM

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fair hinge I mean if you already know all this clac 2 will be ezpz for you

Oh phew

fair hinge Sep 27, 2022, 2:45 PM

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yea no worries, like I said, that a later me problem

silent frigate Sep 27, 2022, 2:45 PM

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Hope we meet again huh

fair hinge Sep 27, 2022, 2:45 PM

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yea it was a good meeting, cya

silent frigate Sep 27, 2022, 2:45 PM

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Ciao

silent frigate Sep 27, 2022, 3:30 PM

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fair hinge

Oop, this is quite ez

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Im quite interested in how ur gonna do it tho

fair hinge Sep 27, 2022, 4:20 PM

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silent frigate Im quite interested in how ur gonna do it tho

Planning on starting it tomorrow

#Trig Sub, I do not know how to start this problem.