dx/(x²-1)的不定积分?
问题描述：
dx/(x²-1)的不定积分?
ln(t-1)/(t+1)的绝对值+C,为什么?
答
∫1/(x方-1)dx
=∫1/(x-1)(x+1)dx
=1/2∫[1/(x-1)-1/(x+1)]dx
=1/2[ln|x-1|-ln|x+1|]+c
=1/2ln|(x-1)/(x+1)|+c