Evaluate:
Let
Putting t=ex
dt=ex dx
Now putting,
A(t+1)(t-3)+B(t-1)(t-3)+C(t-1)(t+1)=1
Now put t+1=0
Therefore, t=-1
A(0)+B(-1-1)(-1-3)+C(0)=1
B(-2)(-4)=1
Now put t-1=0
Therefore, t=1
A(1+1)(1-3)+B(0)+C(0)=1
Now put t-3=0
Therefore, t=3
A(0)+B(0)+C(3-1)(3+1)=1
Now From equation (1) we get,