Question

被积函数1/(x×根号(x2

Answer 1

∫dx/[x√(x^2-1)]

=∫dx/[x*|x|*√(1-1/x^2)] 或x>0 =∫dx/[x^2√(1-1/x^2)]=-∫d(1/x)√(1-1/x^2)

=(|x|/x)∫dx/[x^2√(1-1/x^2)] =-arcsin(1/x)+C

=(-|x|/x)∫d(1/x)/√(1-1/|x|^2) x