An absolutely wonderful integral!

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[@saraandsammyb.9599]

The goat is back to goat like things!

[@edmundwoolliams1240]

9:09 RIP Digamma 😢 At least you were a part of the solution process
The result at the end was cool!

[@SabaSa6a]

Let's change the minus sign to plus sign to revive Digamma😇

[@mcalkis5771]

You literally uploaded this as I had finished watching the previous one and was about to fall asleep.

[@maths_505]

Right on time I guess 😂

[@maths_505]

How'd you like the last video btw?

[@mcalkis5771]

@@maths_505 Always happy to see you take on physics problems. Especially those with interesting differential equations.

[@agrimmittal]

the intro is getting better and better

[@kappascopezz5122]

I think you forgot the negative sign from the chain rule of differentiating α^-s
Edit: Okay this doesn't matter later on because this term cancels out between the sin and cos versions

[@bibekbasnet7374]

Sir someone solved Integration (x^2+5)/(x+2) dx with bit different approach though this is very easy with long division. Can you explain his approach?

[@userr_ln7]

Perfect 🦭

[@mcalkis5771]

Here's something I really try to see; What if you presented the solution to the differential equation describing the Earth's motion around the sun, and actually derive its orbit. It's such an interesting problem in physics that I haven't seen too many people actually show the solution to, and I think the non linear differential equations would really fit with the rest of your stuff.

[@SuperSilver316]

It’s definitely a cult

[@maxochoa925]

That was dope!

[@robertsandy3794]

Bravo, bravo

[@3manthing]

"Was this necessary? Hell nah, man."
Whenever I faced a difficult exam, after I pounded my head several times, the night before the exam, I looked at my roomate, equally flustered, and said: Was this [chasing a degree in math] really necessary? And then, we usually reached the outstanding conclusion, that it's just 1 more evening, and went back to work.🤓🤓
And then the story repeated itself, at each difficult exam.😅

[@maths_505]

😂😂😂

[@ericthegreat7805]

If you can write each square root as a linear combination of sqrt(5) and some factor can we write all square roots in terms of phi? Thus proving the irrationality of all square roots since phi is irrational?

[@renerpho]

I don't think so.

[@bnice24]

Could you solve this problem: integral of x/lnx

[@vascomanteigas9433]

Ei(2*log(x)), which is the exponential integral function.

[@Mr_Mundee]

do this next plz: int from -infty to infty of cos(t)/(t^2 + 1)^x dt

[@maths_505]

Some contour integration would work nicely over here.

[@Mr_Mundee]

@@maths_505 you need a generalized residue tho, its a bit tough

[@Mr_Mundee]

goes to a repeated derivaitve, higher order residue

[@joelchristophr3741]

bro im that joel (who was calling you master)
you still didnt answer my qn bro😭😭
int (0 to 1) [ (e^x) / (1+x) ] dx
please help me bro😭

[@maths_505]

That's cuz I couldn't solve it bro 😭😭 but in all seriousness I don't think that integral has a closed form. One application of integration by parts shows that.

[@sergiokorochinsky49]

[Ei(2)-Ei(1)]/e

[@joelchristophr3741]

@@maths_505 I don't know what is closed form even 😭😭 I should learn more 😭😭
You can solve it bro!💪
You're even solving much harder problems and this looks so simple

[@matteocilla9482]

i think you don’t have any ideas for the title of your vids😂

[@quite_unknown_1]

O_o

[@F-S.]

Cult.