∫1/x(x^2+1)^(1/2)dx=?请朋友们说下过程吧,
问题描述：
∫1/x(x^2+1)^(1/2)dx=?请朋友们说下过程吧,
答
∫ dx/[x√(x^2+1)]
let
x= tany
dx = (secy)^2dy
∫ (secy/tany) dy
=∫ cscy dy
=ln|cscy-coty| + C
=ln|√(x^2+1)/x - 1/x | + C