\int _0^\infty { {dx} \over {1 + x^4} } = {{1}\over 4} \int _0^\infty { {t^{-3/4}} \over {1 + t} }dt } = {{1}\over 4} B({{1}\over 4},1-{{1}\over 4} ) = {{1}\over 4} \Gamma ({{3}\over 4} ) \Gamma ({{1}\over 4} ) = {{\pi}\over{2 \sqrt {2}}}