what tricks unlock this integral??

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[unturnedd]

could have mentioned in the end that the result is equivalent to pi/sinh(pi)

[joydeepc]

You deserve more subs. Although I am below my age i am learning integrals.. one of the best videos on this topic

[jeffreywood]

9:20 For those wondering, use the substitution u = (1-t) for the second part of the integral, you swap the bounds of integration, but pick up a minus sign from the derivative, so the minus becomes positive and the bounds swap back to 0 to 1. Then just do the trivial substitution of u -> t, and you'll see the two parts of the integral are the same.

[karnetik]

i see a michael penn integral, i click

[ruilopes]

Deep Michael Penn lore on this video. Many recalls

[deebd]

Footnote: the final result can also be expressed as pi * csch(pi), where csch is the hyperbolic cosecant

[IoT_]

Not necessarily, but the answer could have been written as pi/sinh(pi)

[alipourzand]

At some point, I was affraid to see a complex result for the integral, but there was a happy end!

[bassboy]

Michael is basically Sean Evans who can do math.

[wolfmanjacksaid]

3:27 not a big fan of setting "u" equal to two different things

[billycheung]

Still curious why he can let u be different things of x and add them up to become an integral from 0 to inf 🤔🤔🤔

[angelosettanni]

i can' t understand the final result. can someone help me to understand?

[BrunoMoreiraTorres]

Funny things always seem to happen when you get an integral with bounds at 0, 1 or infinity and applies u=1/x 🤔

[ClaudioCabrera-dg]

How can I send you a similar problem so that you have a try in the channel?

[meurdesoifphilippe]

I love this world where there is no definition problem in 0

[celestialmath]

Isn't the answer 2π/(e^(-π)-e^(π))

[jardozouille]

So complicated ... wouldn't it be interesting to start by noting that ln(x/(2-x)) = 2 argth(x-1) ?

[قاسمشبرنگ]

In the last step, you forgot to divide by Gamma (1+i+1-i)=gamma(2)=1