Evaluate:

Let

Putting t=e^x

dt=e^x 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,