求不定积分：根号下[(1-x) / (1+x)] dx

题目

求不定积分：根号下[(1-x) / (1+x)] dx

答案

∫√[(1-x)/（1+x)]dx
=∫(1-x)/√(1-x^2)dx
=∫1/√(1-x^2)-∫x/√(1-x^2)dx
=arcsinx+1/2∫(1-x^2)^(-1/2)d(1-x^2)
=arcsinx+√(1-x^2)+c
c是常数