>>140

t = tan(x/2) とおくと

∫ cos(x)/{1+cos(x)} dx = ∫{1 - 1/[1+cos(x)]} dx

　= ∫ {1 - 1/[2cos(x/2)^2]} dx

　= x - ∫ 1/[cos(x/2)]^2 d(x/2)

　= x - tan(x/2) +c

　= x - sin(x)/[1+cos(x)] + c,,