求积分∫dx/1+sinx

题目

求积分∫dx/1+sinx

答案

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