I checked using Wolfram Mathematica that the integral is numerically equivalent to Pi/4 for any random real value of n. Can someone prove the integral?
Is there any similar looking beautiful integrals?
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There's a duplicate already on this site, so if someone could find it that would be nice, but make the substitution $x=\tan t$ followed by $t\mapsto\frac {\pi}2-t$. You should get the equation$$I=\int\limits_0^{\pi/2},\mathrm dt-I$$where $I$ is the integral under question – Frank W May 15 '24 at 06:18
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You may first try $x\mapsto \frac{1}{x} $. – Lai May 15 '24 at 06:21
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https://math.stackexchange.com/q/1465329/732917 had answered the question. – Lai May 15 '24 at 06:23