1/(1+sin x)求不定积分

1/(1+sin x)求不定积分

∫ dx/(1+sinx) = ∫ (1-sinx)/cos²x dx
= ∫ (sec²x - secx tanx) dx
= tanx - secx + C

∫dx/(1+sinx)
=∫dx/(1+cos(x-π/2))
=∫d(x-π/2)/[2cos(x/2-π/4)^2]
=tan(x/2-π/4)+C