令u=arctanx=∫(0到π/4)u/(secu)^4dtanu=∫ucos²udu=1/2∫ucos2u+udu=1/4∫udsin2u+u²/4=usin2u/4-1/4∫sin2udu+u²/4=π/16+π²/64+cos2u/8=π/16+π²/64-1/8
0.2255621096
