(（1-x^2）/(1+x^2))^0.5 再乘以x,求积分,急用

来源：学生作业学帮网编辑：学帮网时间：2024/05/14 18:46:19

∫√[(1-x^2)/(1+x^2)]xdx
=(1/2)∫√[(1-x^2)/(1+x^2)dx^2
x^2=cosu
=(1/2)∫√[(1-cosu)/(1+cosu)] dcosu
=(1/2)∫[sin(u/2)/cos(u/2)]*(-sinu)du
=∫(sinu/2)^2du
=(1/2)∫(1-cosu)du
=(1/2)u+(1/2)sinu+C
=(1/2)arccos(x^2)+(1/2)√(1-x^2)+C
或
=(-1/2)arcsin(x^2)+(1/2)√(1-x^2)+C

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