let
1/[(t^2-1)(t+1) ] ≡ A/(t-1) +B/(t+1) + C/(t+1)^2
=>
1≡孝袜 A(t+1)^2 +B(t-1)(t+1) + C(t-1)
t=1, =>A=1/4
t=-1, => C=1/2
coef. of t^2
A+B=0
B=-1/4
1/[(t^2-1)(t+1) ] ≡ (1/猛悔4)[1/(t-1)] -(1/4) [1/(t+1)] + (1/2)[1/(t+1)^2]
∫ dt/[(t^2-1)(t+1) ]
=∫ { (1/4)[1/(t-1)] -(1/4) [1/(t+1)] + (1/2)[1/(t+1)^2] } dt
=(1/枝慎正4)ln|t-1| -(1/4)ln|t+1| - (1/2)[1/(t+1)] + C
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