Question

If ∫e^t/(t + 1) dt for t ∈ [0,1] = a, prove that ∫(e^{– t}/(t – b – 1)) dt for t ∈ [b - 1,b] = – ae^{– b}.

Answer 1

Given 

Let t – b = –y 

dt = – dy

= – a^{e– b}