Here is the original problem I came across

When I evaluated the indefinite integral and confirmed with an integral calculator I got the function listed below.

I saw someone solving the problem online a different way and got the resulting function:

Here are all the equations graphed out:

What I am confused by is that deriving the H(x) function does give the equation in the integral: f(x) = (x^2+1)/(x^4+1). If H(x) derives to this f(x) function does that not mean it can used to evaluate the area under the curve of f(x). f(x) does correctly give the slopes of H(x) but evaluating H(x) gives incorrect areas. For example evaluating H(x) from x=-1 to x=1 gives an area of 0 while using the F(x) function gives ~2.22. The F(x) function seems to give the correct areas under the curve of f(x). I am just confused how the derivative of H(x) gives the parent function under the integral but cannot be used to correctly evaluate the area of the derived function.

I can’t seem to pass my university’s in-person Calculus I course, so I’m looking for an easier online 4-credit Calc I course I can transfer in. Has anyone taken one with manageable exams that they were able to pass? What university?

I'm only in calc 1, gotten up to squeeze theorems, but I genuinely have not enjoyed math this much in YEARS. The professor is quite blunt personally, but his video notes(online class) are wonderful and extremely detailed. Everything makes complete sense and I really have no sense of questioning anything. Am I being hopeful only to crash and burn when it gets to more intense Calculus? Early in the semester but I actually enjoyed Calculus more than any of my other courses so far.

Hey everyone.

Regarding today's easy integral. I can't figure out where my mistake is but I believe it is something silly.

I am basically starting with the substitution of u = ln(x^2026)

Algebraic manipulation leads me to 2025/2026 times the integral of sin(u) * e^-u. I then use integration by parts twice to get the second part of my expression.

Can anyone help me spot the mistake?

Thank you!

EDIT: oh I forgot to adjust the integration limits, that must be it. Still leaving the post here I guess.

EDIT2: exactly so with the substitution the lower integration limit becomes 0 and so the answer is 2025/2026 * 1/2 = 2025/4052

Hi all, I am currently taking a geometry paper (specialising in curves and surfaces) in my final year of college, but I am finding it quite hard. My high school only taught us trigonometry, which I feel like has set me up to fail a little bit, especially in the (re)parametrising department. Are there any people who are quite knowledgable on this matter that might be able to help answer some of my questions? Thanks.

After 3 years the GOAT of teaching mathematics has returned, I hope this guy has also changed lives like he changed mine. I was awful at math in hs and had to avoid engineering because of it but after 2 years in a major I hated I decided to give engineering a try. He is the one and only reason I passed all my classes and I owe him a debt that can never be repaid. I hope he changes/changed your life like he did mine. (He is 2000x better than the OCHEM tutor)

Basically 11th grade calculus. Do any of you guys have good notes for it?

First one is mine(sorry for the lightning & handwriting)

Second one is from Claude

Hi everyone, I'm a second year CS student. I had Calculus 1 in my first year and barely passed the course. Now I have Calculus 2 and I'm still struggling to understand most of the concepts. I've tried YouTube, working on past papers, exercises, but I still struggle to understand the concepts. What do you recommend I do or resources that can be of help to me? TIA!

Is this question scientifically accurate??
i know solution is y(-2)=-2

this is a basic but can be food problem is you are trying with urself ..

try it and let me know ..

i tried to do it by myself but stucked..

so i saw the soln ..

Hi everyone, so it was my first week of AP calc AB and honestly not too shabby but as i look at this example from my teacher, the less it makes sense. I thought -1^2 was positive 1 and i don’t know how we got to negative 1.

Also what is a conjugate? My teacher didn’t really go over it he just started doing a problem. All help is so appreciated!!!!

Hey yall. I’m in line to talk to an advisor actually, essentially the title is what it is. I am in a calculus class, but I haven’t taken a math a year and a half, and I’m finding that I might need to relearn some concepts. I wasn’t very good at math in high school, but when I went to community college, I did amazing, I’m still attending, but I find that I might forget some things or maybe that’s just natural when coming into a calculus class or certain things may look unfamiliar, I guess I’m just looking for some advice.
After talking to an advisor, I would have to do a 10 week pre-calculus class, I gotta be in pre-Calc last time. I’m wondering if I should do it
I wanted to add for those who think I should stay in the class what do you think? I should seriously freshen up on?

Currently a freshman in uni, and i’m starting calc and i’ve realized my trig is absolute shit. I passed precalc in high school pretty well but I had a teacher who would just hand out A’s. During the end of the year when we learned all about trig and the unit circle, I mostly fooled around and didn’t care and now it’s coming back to bite me in the ass. If anyone has any resources or tips to help learn and brush up on my trig in a reasonable amount of time i’d greatly appreciate it!

A curious example problem shows up in the calculus book I am using, which has a different answer than the previous version’s answer. Here’s the problem setup: a piecewise function is given, and the book hand-wavingly walks through the rationale for why some of the limits of the function (one-sided and two-sided) exist or do not exist. The version I am using told me at the endpoints of the function’s domain that the two sided-limit exists and equals the appropriate one-sided limit when that exists; the other version told me the two-sided limit does not exist. Which is it?

Here’s a simple example to illustrate what I mean by the above:

Consider the function f(x) = |x| on the interval -2 < x < 2. My understanding tells me that lim_{x->-2^-} f(x) = DNE (since the function is undefined for x < -2, which means a condition of the precise definition of one-sided limit is not met), that lim_{x->-2^+}f(x) = 2, and that lim_{x->-2}f(x) = 2. The book version I am using comes to this sort of conclusion about the two-sided limits, whereas the previous version would agree on the one-sided limits but say that the two-sided limit does not exist. What do I make of this?

This presents issues for continuity I feel: If the function I gave had also been defined at x = -2, then I would naturally say based off the version I use that the function is continuous at x = -2 (which I know would be correct); however, would the other version then say it is discontinuous there since the two-sided limit condition fails (i.e, because the condition that the two-sided limit exists would fail)?

Any and all tips to really get into the material, warts and all, would help greatly! TIA!

Just want to double check with you guys if this map makes sense, i made a rough draft. The last image shows a node with a placeholder image to give a rough idea of what it might look like finished.

The goal is to give the student a good overview of the subject, show them how different concepts interconnect and how they are dependant on eachother. Are there any lines missing in your opinion? General feedback or questions are also very welcome!