Problem Compute the integral $$ I = \int_0^\infty \frac 1 {1+x^4} dx. $$ Answer This seems to be a popular problem illustrating various mathematical techniques. The standard approach is to use complex analysis and the Cauchy method of residues. The problem may be solved with more elementary techniques by using a series of clever substitutions. Both approaches rely on quite lengthy computations to obtain the answer $$ I = \pi \frac {\sqrt 2} 4. $$ Here, we would like to show that the answer may be obtained quite easily in the form of power series. Power series solution We write $$ I = \int_0^1 \frac 1 {1+x^4} dx + \int_1^\infty \frac 1 {1+x^4} dx = I_1 + I_2. $$