求不定积分∫1⼀x(x눀-1) dx

2025-03-10 16:45:21
推荐回答(1个)
回答1:

∫1/[x(x²-1)]dx
=½∫[1/(x-1) +1/(x+1) -2/x]dx
=½(ln|x-1|+ln|x+1|-2ln|x|) +C
=½ln|(x²-1)/x²| +C
=½ln|1-x⁻²| +C