A tricky classical logarithmic integral
Integrate ln^2 x/(x^2 + 1)dx from 0 to 1 (Mis-1997) #calculus #definite_integrals #substitution #betafunction #cipher
Meditation Impromptu 02 by Kevin MacLeod is licensed under a Creative Commons Attribution 4.0 license. creativecommons.org/licenses/...
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Nice 🔥🔥🔥
Alternatively, note that 1/2 of the original integral = 1/1^3-1/3^3+1/5^3... = sum_(n=-inf)^inf{1/(4n+1)^3}. But cot(x)=sum_(n=-inf)^inf{1/(x-n*pi)}. Differentiate both sides two times to arrive at cos(x)/sin^3(x) = sum{1/(x-n*pi)^3}. Set x = pi/4, and clearly sum_(-inf)^inf{1/(4n+1)^3} = pi^3/32.
isn't there a video proving 2:18. I thought recent but can't find?
@cipherunity
28 күн бұрын
Done. I reloaded this video due to a small mistake and forgot to link the required video.
@0:20 You have to be more rigorous. You should have written t | (x-->0+) --> Infinity
@cipherunity
28 күн бұрын
I agree. I shall be careful in future.