原式=∫(tanπ/4-tanx)/(1+tanπ/4tanx）dx
=∫tan(π/4-x)dx
=∫sin(π/4-x)/cos(π/4-x) dx
=-∫sin(π/4-x)/cos(π/4-x) d(π/4-x)
=∫dcos(π/4-x)/cos(π/4-x)
=ln|cos(π/4-x)| +C