求积分∫dx/1+sinx

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求积分∫dx/1+sinx求积分∫dx/1+sinx求积分∫dx/1+sinx令tan(x/2)=t则sinx=2t/(1+t²)x=2arctant,dx=2dt/(1+t²)∫

求积分∫dx/1+sinx
求积分∫dx/1+sinx

求积分∫dx/1+sinx
令tan(x/2) = t
则sinx = 2t/(1+t²)
x = 2arctant,dx = 2dt/(1+t²)
∫dx/(1+sinx)
=∫2dt/(1+t)²
=-2/(1+t) + C
=-2/[1+tan(x/2)] + C

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