求解不定积分xdx/(x+根号x^2-1)_数学解答

求解不定积分xdx/(x+根号x^2-1)

人气：478 ℃　时间：2020-01-29 14:21:03

解答

∫x/(x+根号(x^2-1)dx=∫x(x-根号(x^2-1))dx
=∫(x^2-x根号(x^2-1))dx
=1/3x^3-1/2∫根号(x^2-1)d(x^2-1)
=1/3x^3-1/2*2/3*(x^2-1)^(3/2)+C（常数)
=1/3x^3-1/3(x^2-1)^(3/2)+C（常数)