问题标题:
数学计算(有关不定积分)∫dx/(2*sinx/2*cosx/2)=∫d(x/2)/(tanx/2*cos^2x/2)=∫d(tanx/2)/tanx/2
问题描述:
数学计算(有关不定积分)
∫dx/(2*sinx/2*cosx/2)
=∫d(x/2)/(tanx/2*cos^2x/2)
=∫d(tanx/2)/tanx/2
更新时间:2024-04-27
胡玲玲回答:
∫dx/sinxsinx=2sin(x/2)cos(x/2)倍角公式
=∫dx/(2*sinx/2*cosx/2)dx/2=d(x/2)sin(x/2)cos(x/2)=tan(x/2)(cosx/2)^2
=∫d(x/2)/(tanx/2*cos^2x/2)dtan(x/2)=(sec(x/2))^2dx=dx/(cos(x/2))^2
=∫d(tanx/2)/tanx/2dln(tan(x/2)=dtan(x/2)/tan(x/2)
=ln(tan(x/2))+C
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