Integration of 1/(1+x^4)*dx

Question

what is the value of integration of 1 /(1+x^4)×dx

Answer 1

 \(\frac{1}{1 + x^4}\)

= \(\frac{\frac{1}{x^2}} {x^2 + \frac{1}{x^2}}\)

= \(\frac{1}{2} \times \frac{1 + \frac{1}{x^2} - (1 - \frac{1}{x^2})}{x^2 + \frac{1}{x^2}}\)

= \(\frac{1}{2} \times [\frac{1 + \frac{1}{x^2}}{x^2 + \frac{1}{x^2}} - \frac{1 - \frac{1}{x^2}}{x^2 + \frac{1}{x^2}}]\)

= \(\frac{1}{2} [\frac{1 + \frac{1}{x^2}}{x - \frac{1}{x^2} +2} - \frac{1 - \frac{1}{x^2}}{(x + \frac{1}{x})^2 - 2}]\)