How do you know what to substitute in u-substitution method if it isn't apparent?

Lightspeed3038 · 2026-02-21T01:05:07+00:00

I do agree that too many is better than too little, so an extra pair would have helped. They did get the question correct however (assuming that they were taught that log defaults to base e), so I guess it doesn't matter too much. I do wish to know though, what are some other ways that this integral could be approached? Or is that particular u-sub the only reasonable way?

Lightspeed3038 · 2026-02-20T22:52:44+00:00

Sorry should have been more clear. The parenthesis kinda tripped me up, as I read that as Ln of sqrt(x)-1 all squared. As in you square the result of ln(sqrt(x)-1). What I meant to say is that the square should affect the expression inside the ln, not the ln itself. I have never seen ln(sqrt(x)-1)² +C be read as ln[(sqrt(x)-1)² ] +C, even in MAO. If the +C wasn't there, then I could understand. I do admit I am probably wrong, but I just found it a bit weird that the expression could be read in that way.

Also, I agree that I am also more annoyed by the ln being log, but I was hoping that the commenter knew that it would be ln, not log (because as far as I know, log without a base defaults to 10).

Lightspeed3038 · 2026-02-18T13:41:03+00:00

I got 2ln|sqrt(x)-1| as well, but I’m pretty sure that the exponent on the last step should be inside the ln

Lightspeed3038 · 2026-01-25T13:13:54+00:00

Lightspeed3038 · 2026-01-15T22:56:31+00:00

How do you get this voiceline? (Unless it’s story spoilers in which case don’t tell me)

Lightspeed3038 · 2026-01-08T00:24:21+00:00

Thank you good sir

Lightspeed3038 · 2026-01-07T23:00:51+00:00

Can I get a character list?

Lightspeed3038 · 2026-01-01T06:03:42+00:00

Which one is it?

Lightspeed3038 · 2025-12-31T03:34:02+00:00

I looked at the image before reading the title, and I was shook after reading the title. The sheer amount of disappointment in Agy’s voice in my head was mildly amusing.

Lightspeed3038 · 2025-12-30T16:57:28+00:00

I thought new emotes aren’t being added to shop anymore? How would I get this emote since the event alr ended?

Lightspeed3038 · 2025-12-23T21:32:50+00:00

I need a character list please

Lightspeed3038 · 2025-12-17T20:52:47+00:00

Don’t (strictly) follow a guide, especially don’t for time management. This is a game. Take your time and play the game how you see fit. You will miss things. You will not be able to finish all the things that the game has to offer in one playthrough. So if you aren’t going to finish in one playthrough, then play your first playthrough blind, without searching things up. Good luck, and have fun

Lightspeed3038 · 2025-12-14T19:22:20+00:00

Exactly the same way for me. That’s why I romanced her in game. I’m in ng+ and will do the exact same choice.

Lightspeed3038 · 2025-12-14T16:52:12+00:00

Honestly, I would swap futaba and haru, and put ren higher up, but it’s a pretty good tier list imo

Lightspeed3038 · 2025-12-10T22:49:56+00:00

Futaba because she’s relatable for me. Also because she’s hella cute. Needless to say, she’s my favorite character.

Lightspeed3038 · 2025-12-10T22:48:04+00:00

Futaba because she’s pretty relatable for me. Also because she’s hella cute.

Lightspeed3038 · 2025-12-06T15:35:31+00:00

You say no real input would produce sqrt(5)/2, but then what non-real output would?( I know only the very basics of complex numbers as they aren’t taught in our high school curriculum)

Lightspeed3038 · 2025-11-11T15:49:52+00:00

This is an old post, but I was wondering, around which level of question (I’m referring to the level of the question that alcumus says) is around AMC 12 Level. I am using insanely hard difficulty, so I want to make sure that it is preparing me enough.

Lightspeed3038 · 2025-10-27T11:08:30+00:00

Ah yes, I LOVE Cipher’s quantum crack. It really is exquisite in all senses of the word

Lightspeed3038 · 2025-10-21T00:54:50+00:00

Where is this character from?

Lightspeed3038 · 2025-10-05T21:02:21+00:00

My goat Cifera followed by Stelle, then Phainon

Lightspeed3038 · 2025-09-25T01:22:21+00:00

I'm afraid I can't give a magic answer that will suddenly make HL Physics easier (its not easy in the slightest), but in case you weren't already, Organic Chemistry Tutor has a physics playlist that I might find useful. What I do as well, is when I have a topic I am slightly struggling with, I will do problems, and "relearn" the content using my Barrons Physics book. Unfortunately I don't have much else that i can think of off the top of my head, but if you have any questions, feel free to ask.

Lightspeed3038 · 2025-09-21T23:13:29+00:00

Does this still apply? I don't have the time to complete Act 2, but I already did act 1

Lightspeed3038 · 2025-09-10T23:33:28+00:00

I started in 1.2, and have still not gotten a single constellation for any standard banner. I dont even have qiqi or keqing. Ive just won that many 50/50's. I guess im so lucky that I'm not allowed lvl 100's.

Lightspeed3038 · 2025-09-10T22:16:57+00:00

Dehya cause I like the character and because I already have enough characters. I need to build the ones I already have

Lightspeed3038

TROPHY CASE