(1/2)∫根号（原式）dx^2=(1/2)∫根号（（1-x）/（1+x））dx
=(1/2)∫根号（（1-x^2）/（1+x）^2）dx
=(1/2)∫根号（1-x^2）/（1+x）dx
令x=sin（x）
=(1/2)∫cos（x）^2/（1+sin（x）dx
=(1/2)∫(1-sin(x)^2)/（1+sin（x））dx
=(1/2)∫1-sin(x)dx
=(1/2)[x+cox(x)](上限为π/2,下限为0)=π/4-1/2
【高数】问一道积分题（点击大图可放大）
(1/2)∫根号（原式）dx^2=(1/2)∫根号（（1-x）/（1+x））dx
=(1/2)∫根号（（1-x^2）/（1+x）^2）dx
=(1/2)∫根号（1-x^2）/（1+x）dx
令x=sin（x）
=(1/2)∫cos（x）^2/（1+sin（x）dx
=(1/2)∫(1-sin(x)^2)/（1+sin（x））dx
=(1/2)∫1-sin(x)dx
=(1/2)[x+cox(x)](上限为π/2,下限为0)=π/4-1/2