AN OVERPOWERED SUBSTITUTION FOR INTEGRALS: int(0,1) ln(1-x^2)/(1+x^2)

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Some interesting results derived using this cool log integral. Solution featuring one of the most overpowered substitutions in existence!
Proof of the integral formula :
• A breathtaking integra...
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Опубликовано:

13 окт 2024

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Комментарии : 24

@CM63_France 22 часа назад

Hi, "ok, cool" : 1:50 , 5:09 , 6:09 , 7:22 , 10:52 , 11:39 , 10:56 , "terribly sorry about that" : 6:37 , 8:58 , 10:46 , 11:56 .

@xanterrx9741 День назад

Great video , thanks Kamaal for your work hard work that you've puten into this and other videos .

@gambitito День назад

Integral bounds jumpscare 1:40

@MrWael1970 День назад

Thanks for your innovative integrals.

@SanAleksiusII День назад

Greetings from future fields medalist

@xinpingdonohoe3978 День назад

What are you going to do that will win you the Fields Medal?

@lokithe.godofmischief День назад

Ques i found, which seemed impossible Let f(x)=(x⁴)+(x³)+(x²) Let y depict the inverse of the function f(x) Then, evaluate the integral from (lower bound)2A to (upper bound)8A of (1/(y²+y⁴)) with the limit A tends to ♾️infinity The variable of integration is obviously dx, as y will be a function of x only

@lokithe.godofmischief 14 часов назад

@davidblauyoutube yeah it must be of that form, cause in the original question it said that the ans is lnα, find α. Do share the solution pls

@davidblauyoutube 21 час назад

What about convergence of the series? The sum of 1/k * ln 2 is the harmonic series...

@maths_505 20 часов назад

Well we can't split up the sum using linearity but it should work in the form I've presented where we have a difference of terms. An example of where something like this works is the series representation of the digamma function.

@holyshit922 День назад

u=(1-x)/(1+x) substitution twice Yes I would calculate it this way First way is too complicated First step can be ln(1-x^2) = ln(1-x) + ln(1+x) but it will not simplify integral a lot

@sundaresanabishek5127 День назад

Heyy Brooo fan from Sri Lanka ❤🎉

@MrElnath День назад

Why at 1.40 bounds becomes (0,1) instead remains (0, inf) ?

@Grecks75 День назад

Because bounds (0, inf) was only by mistake.

@MrElnath День назад

Right ! I watched the video again

@giuseppemalaguti435 День назад

Con semplici calcoli si arriva a I=-(1/2)INT(1+cosθ)dθ..θ=0..π/2...poi non ricordo come si risolve quell integrale..ho provato con β e Γ..ma non porta a niente..ho rifatto i calcoli..I=(-πln2/4)-2((1/2)(-πln2/2+G)=πln2/4-G