求不定积分∫x/根号（1²+x²）dx_数学解答

求不定积分∫x/根号（1²+x²）dx

人气：338 ℃　时间：2020-04-10 03:46:14

解答

∫x/√(1²+x²)dx
=(1/2)∫[1/√(1²+x²)]dx^2
=(1/2)∫[1/√(1²+x²)]d(1+x^2)
=(1/2)ln(1+x^2)+Cx/√(1²+x²)dx=(1/2)∫[1/(1²+x²)]^(1/2)dx^2=(1/2)∫(1+x²)^(-1/2)d(1+x^2)=(1/2)√(1+x^2)+C