evaluating the integral of 1/(x^4+1) from 1 to inf

integral of 1/(x^4+1) by brutal-force partial fraction, https://youtu.be/GZFQNsy3p1U Derivative of tanh^-1(x) and coth^-1(x), https://youtu.be/GPvN5UWJlmE Integral of sqrt(tan(x)), https://youtu.be/6v0QqJ87gdM blackpenredpen