The Answer Is A BEAUTIFUL Mathematical Constant...

Hope everyone enjoyed! Please comment with any questions or suggestions for new topics, and as always, subscribe to stay updated.
~ Thanks for watching!
Love to Roshan for the question.
I want to say a final thank you for all the support - 5k subscribers is insane and I'm so grateful to everyone!
#maths #mathematics #integrals #gamma #gammafunction #eulermascheroni #entrance #university #Oxford #Cambridge #JEE #problemsolving #taylor #maclaurin #gaussian #gauss #statistics #whoknew #fascinating #functions #euler #funproblems #proofs #functions #physics #sums #series #limits #whiteboard #math505 #blackpenredpen #integral #trig #trigonometry

[@whiteboarddude3566]

I appreciate you taking these integrals which sometimes seem random and then equating them to more famous mathematical creatures. It's also really great to follow along, work on the integral for a bit, then go back to the video to find you have taken the same step. Congratulations for 5000 subscribers. You've earned them : )

[@OscgrMaths]

Thanks so much! I'm really glad you enjoyed.

[@TheSourovAqib]

Ah the Euler Macaroni constant 🤌

[@np2oc-Hasanul]

Hi I have learnt so much from your videos
I wanted to put in a kind video request for cool trig identities if you arent too busy
e.g. I learnt from you the arctan(x) + arctan(x^-1) = pi/2 and this was a GAME CHANGER for me learning new techniques for oblique collisions in further mechanics!!!!
thanks so much : )

[@nirjharchaudhuri6484]

Great integral to wrap up the series! Congrats on 5k!!

[@OscgrMaths]

Thanks! Glad you enjoyed it.

[@ruaidhridoylelynch5522]

Love your videos, they are very helpful to me 🥰

[@OscgrMaths]

Thanks! I'm really glad you like them.

[@artemetra3262]

this is exactly how i did it, down to the variable names 😆 nice problem!

[@OscgrMaths]

Nice!! Great minds think alike 😁.

[@maxvangulik1988]

for a second there, i thought this was a product integral because dx is in the exponent in the thumbnail

[@debtanaysarkar9744]

Evaluate Sum{r=2 to ∞} (r(choose)2/(r+1)!)
I found it really cool

[@OscgrMaths]

Wow! That was a great question. Is it 1/2(e-2)?

[@debtanaysarkar9744]

@OscgrMaths Yesss

[@alphazero339]

Is there easier way than using eˣ taylor expansion and integrating x²eˣ to get the 1/(n+3) factor?

[@debtanaysarkar9744]

@alphazero339 Idk, maybe there is, I know 2 ways of solving it, both involving the Taylor series

[@peshepard412]

I wish you had a bigger board.

[@OscgrMaths]

Me too 😔

[@jcfgykjtdk]

Very clean

[@OscgrMaths]

@@jcfgykjtdk Thanks!

[@Swybryd-Nation]

Great job.
Btw, besides Feynman Techbique, How would you tackle Achmed’s Integral?

[@alphazero339]

Integrate

[@zlodevil426]

Bro got 5000 subs but not 5000 square millimeters on his board

[@OscgrMaths]

@zlodevil426 😓

[@hathouses]

So, how does taking the derivative of an integral in respect to a different variable work? Like, is there a nice way to work it out, in general? Since in this you used the digamma to evaluate it.

[@alphazero339]

For taking derivative with respect to x of integral which contains x (either as bound or inside the integrand) google "Leibniz integral rule"

[@OscgrMaths]

Differentiation under the integral sign is a tricky one. If the bounds are constants then you can just take the partial derivative of the integrand, but if not it's much harder. Take a look at Leibniz's rule for differentiation under the integral sign for more on that. Typically differentiating the integral and then evaluating it is what you do when using Feynman's trick so there's some great examples of it in videos that use that. Hope this helps and thanks for the comment!

[@maxvangulik1988]

t=tan(x)
I=int[-♾️,♾️](te^t•e^-e^t)dt
s=e^t
ds=e^t•dt
I=int[0,♾️](ln(s)e^-s)ds
I=Ř'(1)=-ř