A RIDICULOUSLY AWESOME LOG INTEGRAL: Integral of (ln(x))^2/(x^2+1) from zero to infinity

[@zunaidparker]

Another nice one! Would like to see you tackle these problems with new techniques e.g. setting up integration in 2 and 3 variables (xy/xyz) and using polar and spherical coordinate transformations. Would be a good change and showcase even more techniques.

[@holyshit922]

Series for 1/(1+x^2) is convergent when |x|

[@ThAlEdison]

Have you done this with starting with I(t)=Int_0^Inf((x^t)dx/(x^2+1)), differentiating twice and evaluating at 0?

[@MovieMosaicc]

Lol Sir , Your channel is growing faster then my hairs 😂😂😂😂

[@maths_505]

I pray that your hair growth accelerates 😂

[@JCPR-s6p]

Cette intégrale mérite d'être calculée avec le théorème des résidus

[@gamingwithteax9079]

Amazing video

[@maths_505]

Thanks bro

[@JCPR-s6p]

🗼This integral deserves to be calculated with the residue theorem

[@maths_505]

Already did that

[@usernameisamyth]

Awesome

[@nicogehren6566]

very nice solution, but in 3:10 min how did you know the sum isnt convergent?

[@maths_505]

The series is convergent when abs(x) is less than 1. exp(2t) is always bigger than 1 when x is positive (the interval of integration)

[@nicogehren6566]

@@maths_505 thanks.

[@robertsandy3794]

You wrote that the absolute value of x was less than 1. However, the bounds of integration were from 0 to infinity. What have I missed here?

[@maths_505]

e^(-x) is less than 1 on (0,infinity)

[@carlosdavid7430]

yo bro can you solve the integral going from 0 to infinity of (lnx)²arctan(x) ×1/(x^2+1)?
hope you enjoy this big boy!

[@maths_505]

Just use a x->1/x transformation and you'll see why this makes a short rather than a full video

[@carlosdavid7430]

@@richardheiville937 thats one way i solved it

[@ManishKumar-ic6hg]

Bro solve this problem if the denominator is( x^2 + x + 1)

[@uggupuggu]

rewrite it as
(x+1/2)^2+3/4 and then use trig sub

[@gamingwithteax9079]

Sir I am Ameer Sadiq your student

[@gamingwithteax9079]

Amazing video

[@maths_505]

Good game today bro

[@imafidonerisson5527]

Pls prove the summation

[@manstuckinabox3679]

LOG? I'M HERE BOY DW just wanted to say thank you for introducing me to these really cool techniques to solving integrals! I'm quite disappointed that usual calc 1-2 classes usually skim past these methods...

[@asriel522]

Actually the notation if ln²x is wrong,you're supposed to write (lnx)²

[@imafidonerisson5527]

It isn't wrong

[@maalikserebryakov]

nope cope