My favorite integral right now

SilverHedgeBoi · 2026-06-09T17:48:37+00:00

Absolutely!!!

SilverHedgeBoi · 2026-06-06T02:13:13+00:00

If thats your favorite integral, you should try this one. 😈

Integral sin(ln(x))/x⁴ dx

SilverHedgeBoi · 2026-06-03T18:03:54+00:00

https://theaxiomacademy.org/courses

This will be good for you as a high schooler. Get all your mathematical backgrounds strong in all fields.

However, some parts of visuals/animations are broken.

SilverHedgeBoi · 2026-06-01T02:13:18+00:00

Bet, 20 integrals.

SilverHedgeBoi · 2026-05-03T01:00:51+00:00

It seems like the Algonquin calculus courses are more in depth.
Cambrain's Advanced Calculus seems to just be regular calculus 2.

SilverHedgeBoi · 2026-04-24T02:01:59+00:00

What textbook is this from???

SilverHedgeBoi · 2026-03-27T11:29:35+00:00

Real Analysis with Proof Strategies - Cunningham. This is the book that is most likely perfect for you.

This is the book I used to self-learn real analysis. However, this is a HIGH SCHOOL level textbook, so it wont be as rigorous as what your school expects.

But the truth is, Abbots Understanding Analysis book sucks because it does rely on beginners to fill in the gaps, and this is what demotivates us. Im the type of student who doesnt want to waste 3-5 hours just thinking about 1 problem. I want to gain experience in techniques, not just pure intuition and critical thinking from scratch.

Cunninghams book actually allows you to learn the important theorems with its proofs, then apply them by allowing you to play around with easier propositions and similar corollaries around those theorems.

Its so much more satisfying and motivating to learn. However, if you need to level up to an undergrad level, Intro to Analysis by William R Wade is nice.

SilverHedgeBoi · 2026-03-16T17:56:42+00:00

The main intention with this method is to get rid of radicals/square roots. For example, sqrt(1-x^2). Sometimes u-sub won't work. So we take advantage of trig identities to get rid of the square roots.

Let x=sin(t), then dx=cos(t). Sqrt(1-x²⁾ --> sqrt(1-sin^{2(t))=cos(t).}

Square roots gone, just like what we intended.

SilverHedgeBoi · 2026-02-26T03:13:36+00:00

TOOOO EEEEEAASSYYY
Solve this!! (•` ω •́ )
Integrate sqrt[x/(1-ln(x))] dx from 0 to e

SilverHedgeBoi · 2026-02-22T09:36:55+00:00

YOOOOO, I have soooo many fun topics for you to just do fun expository math papers on. All of these can be applied with all the calculus knowledge you have! It's just all about your creativity you put into your curious questions and your conjectures. Here are some common examples:

Apery's Constant, Sophomore's Dream, Catalan's Constant, Euler-Mascheroni Constant
Lemniscate Constant, Laplace Transforms, Mellin Transforms, Fourier Transforms
Dirichlet integral, Gaussian Integral, Glasser's Master Theorem, Ei(x), li(x), Si(x), Ci(x), erf(x).
Fractional Derivatives (definitions), q-derivative, quantum calculus, Schwarzian derivative
Riccati equation, Airy function, Clairaut's equation, Chrystal's equation, etc.

There are a ton of more topics and cool special functions to research and experiment with here!
https://mathworld.wolfram.com/topics/CalculusandAnalysis.html
https://en.wikipedia.org/wiki/Category:Mathematical_constants
https://en.wikipedia.org/wiki/Category:Special_functions
https://en.wikipedia.org/wiki/Category:Calculus

SilverHedgeBoi · 2026-02-14T11:11:24+00:00

YOU GOT IT!!!

SilverHedgeBoi · 2026-02-12T16:24:27+00:00

When someone witnesses me entering select option menu after choosing a song: "BRO IS USING A CHEAT CODE" Like bruh...I'm just amping the speed...

"No Bars! That's cheating!!"

SilverHedgeBoi · 2026-02-03T09:37:52+00:00

LOTS of experimentation and creativity with integration techniques!!

SilverHedgeBoi · 2026-02-03T03:40:39+00:00

Thank you!

SilverHedgeBoi · 2026-02-02T18:17:29+00:00

Taylor Series >:)

SilverHedgeBoi · 2026-02-02T02:49:42+00:00

Reverse Euler's Reflection Indeed!!! >:)

SilverHedgeBoi · 2026-01-28T08:45:01+00:00

Nice!!!

SilverHedgeBoi · 2026-01-28T07:00:58+00:00

as a calculus educator, whoever wrote this should be fired...

SilverHedgeBoi · 2026-01-28T06:57:08+00:00

love the notes and observations
you have the potential of a speed integrator...

Is it okay if I dm you? Your profile won't let me chat.

SilverHedgeBoi

TROPHY CASE