1/(1+sin x)求不定积分

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1/(1+sinx)求不定积分1/(1+sinx)求不定积分1/(1+sinx)求不定积分∫dx/(1+sinx)=∫(1-sinx)/cos²xdx=∫(sec²x-secxta

1/(1+sin x)求不定积分
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