Question

(（1-x^2）/(1+x^2))^0.5 再乘以x,求积分,急用

Answer 1

∫√[(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