∫1/(t^2-1)dt
=∫1/(t-1)(t+1)dt
=1/2∫[1/(t-1)-1/(t+1)]dt
=1/2∫1/(t-1)d(t-1)-1/2∫1/(t+1)d(t+1)
=1/2ln|t-1|-1/2ln|t+1|+c