X⼀(X^2-2x-3)的不定积分怎么求?

2024-11-08 13:39:20
推荐回答(1个)
回答(1):

x = (1/2)(2x -2 ) +1

∫x/(x^2-2x-3) dx
=(1/2)∫(2x-2)/(x^2-2x-3) dx + ∫dx/(x^2-2x-3)
=(1/2)ln|x^2-2x-3| + (1/4)∫ [1/(x-3) -1/(x+1) ] dx
=(1/2)ln|x^2-2x-3| + (1/4)ln|(x-3)/(x+1)| + C