Find this integral's closed form

We compute a closed form for this tangent/cotangent integral using u-substitution and two special functions.
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[@inigovera-fajardousategui3246]

I believe there is an easier way to start. If you shift from x to π/2-x keeping in mind that tan(π/2-x)=cotx and cot(π/2-x)=tanx, you get the same input with the bounds of integration going from π/4 to π/2 (once the negative sign from the differentiation flips the bounds). Then you can add both up to 2I going from 0 to π/2 and carry on with it. Anyway, nice video, as always

[@tgx3529]

Firs of all I used for n as natural numbers ( from the picture on TH-cam), there Is convergent only for n=0.
If I saw this solution, I tried to use something similar as you, only for integral u^n/(1+u^2) on (0; Infinity) - (Its the same Aš original integraI) I used the subsititution
1+u^2=k, then subsititution 1/k=r, then Is there the samé result..

[@sshkbf]

It would be pretty cool if solve me the following question which I found and I could not solve.
limit x approaches 0 of (x^x^^^x -x!)/(x!^x! -1)